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Polymorphism in the Pharmaceutical Industry

Polymorphism in the Pharmaceutical Industry Solid Form and Drug Development

Edited by Rolf Hilﬁker Markus von Raumer

Editors Dr. Rolf Hilﬁker

Solvias AG Solid State Development Römerpark 2 4303 Kaiseraugst Switzerland

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Dr. Markus von Raumer

Idorsia Pharmaceuticals Ltd Preformulation & Preclinical Galenics Hegenheimermattweg 91 4123 Allschwil Switzerland

Library of Congress Card No.: applied for

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Bibliographic information published by the Deutsche Nationalbibliothek

Close up image of crystal (Getty ID 626957019, Daniel Grizelj)

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A catalogue record for this book is available from the British Library.

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliograﬁe; detailed bibliographic data are available on the Internet at . © 2019 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microﬁlm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not speciﬁcally marked as such, are not to be considered unprotected by law. Print ISBN: 978-3-527-34040-8 ePDF ISBN: 978-3-527-69783-0 ePub ISBN: 978-3-527-69785-4 oBook ISBN: 978-3-527-69784-7 Typesetting SPi Global, Chennai, India Printing and Binding

Printed on acid-free paper 10 9 8 7 6 5 4 3 2 1

v

Contents Preface to the Second Edition xv 1

Solid State and Polymorphism of the Drug Substance in the Context of Quality by Design and ICH Guidelines Q8–Q12 1 Markus von Raumer and Rolf Hilﬁker

1.1 1.2

Introduction 1 A Short Introduction to Polymorphism and Solid-State Development 1 A Short Introduction to Quality by Design (QbD) 3 The Solid State in the Context of Pharmaceutical Development 7 Typical Drug Discovery and Development 7 The Solid State at the Interface of Drug Substance and Drug Product 10 Biopharmaceutics and Bioavailability of Solids 11 Pharmaceutical Quality Assessment 14 Solid-State Development at Various Stages of the Pharmaceutical Development Process 15 The Solid State in the Discovery Phase 16 Salt and Co-crystal Screening and Selection 16 Polymorph Screening, Polymorph Landscape, and Polymorph Transformations 17 Crystallization and Downstream Processes 20 Formulation 21 Analytical Methods for Characterization and Physical Purity Determination 22 Conclusions 23 References 23

1.3 1.4 1.4.1 1.4.2 1.4.3 1.4.4 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.5.5 1.5.6 1.6

2

Alternative Solid Forms: Salts 31 P.H. Stahl, Bertrand Sutter, Arnaud Grandeury, and Michael Mutz

2.1 2.2

Introduction 31 Salt Formation and Polymorphism in Pharmaceutical Development 31 Target Properties of Active Substances for Drug Products Injectables 34

2.3 2.3.1

33

vi

Contents

2.3.2 2.3.3 2.3.3.1 2.3.3.2 2.4 2.4.1 2.4.2 2.4.3 2.4.4 2.5 2.5.1 2.5.2 2.5.3 2.6 2.6.1 2.6.2 2.6.3 2.7 2.7.1 2.7.2 2.7.3 2.7.4 2.8

Solid Dosage Forms 35 Dosage Forms for Other Routes of Application 36 Inhalation 36 Topical Products and Transdermal Route 36 The Basics of Salt Formation 37 Dissociation Constant 37 Ionization and pH 39 Solubility 40 Disproportionation 43 Approaches to Salt Preparation and Characterization 45 Initial Data 45 Selection of Salt Formers 45 Salt Preparation Procedures 46 Selection Strategies 49 Points to be Considered 49 Final Decision 51 Salt Form and Life Cycle Management of Drug Products 52 Case Reports 53 Overview of Salt Forms Selected 53 The Salt Selection Process 53 Case 1: NVP-BS001 53 Case 2: NVP-BS002 54 Discussion and Decision 56 References 56

3

Alternative Solid Forms: Co-crystals 61 Johan Wouters, Dario Braga, Fabrizia Grepioni, Luc Aerts, and Luc Quéré

3.1 3.2 3.2.1 3.2.2 3.2.3 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 3.3.6 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.5 3.6

Introduction 61 Types of Pharmaceutical Co-crystals 62 Salts vs Co-crystals 62 Ionic Co-crystals of API 63 Polymorphism and Co-crystals 65 Relevant Pharmaceutical Co-crystal Properties 65 Solubility 66 Dissolution Rate 67 Bioavailability 69 Melting Point 69 Stability 70 Challenges and Undesired Eﬀect of Co-crystallization 71 Analytical Tools to Characterize Co-crystals 73 Microscopy 74 X-Ray Diﬀraction 75 Thermal Analysis 77 Vibrational Spectroscopy 77 Solid-State NMR 78 Patent Literature Review 79 Current View on Regulatory Aspects of PCCs 83

Contents

3.6.1 3.6.2 3.7

Rules Governing Manufacturing (API GMP) 84 ICH Tripartite Guidelines on Speciﬁcations for New Drug Substances and New Drug Products 85 Conclusions 85 Acknowledgment 85 References 86

4

Thermodynamics of Polymorphs and Solvates 91 Gerard Coquerel

4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6 4.1.7 4.2 4.2.1 4.2.2 4.3 4.3.1 4.3.1.1 4.3.1.2 4.3.1.3

Basic Notions 91 Chemical Purity 92 Isotopic Purity 92 Structural Purity 92 Stability of the Component 93 Polymorphism, Desmotropy, Allotropism, and Chirality 93 Gibbs Phase Rule 93 Unary System or Unary Section Without Polymorphism 94 Unary System or Unary Section with Polymorphism 95 Access to Polymorphs 97 Mechanisms of Polymorphic Transition 98 Polymorphism in Binary Systems 98 No Mixed Crystals 98 Polymorphism of One Component Only 98 Three Enantiotropic Polymorphs 100 Two Enantiotropic Polymorphs and One Form with Monotropic Character 100 One Stable Polymorph and Two Forms with a Monotropic Character 100 Polymorphism of a Stoichiometric Compound 100 Polymorphism and Mixed Crystals 102 Polymorphism of One Component Only 102 Two Stable Polymorphic Forms for One Component with Full Miscibility in the Solid State (at a Certain Temperature) 105 Two Stable Polymorphic Forms for One Component with Limited Miscibility in the Solid State 108 One Stable Form and One Metastable Form (Monotropic Character) with Full Miscibility for the Metastable Form 109 One Stable Form and One Metastable Form (Monotropic Character) with Full Miscibility for the Metastable Form 111 Two Isostructural Monotropic Forms When Mixed Could Lead to an Enantiotropy 112 Limitations of the Concept of Polymorphism and Other Solid(s) to Solid(s) Transitions 112 Solvates 114 Diﬀerentiation Between Stoichiometric and Nonstoichiometric Solvates 116 Hygroscopicity, Deliquescence, and Eﬄorescence 117

4.3.1.4 4.3.1.5 4.3.2 4.3.2.1 4.3.2.2 4.3.2.3 4.3.2.4 4.3.2.5 4.3.2.6 4.3.2.7 4.3.3 4.3.3.1 4.3.3.2

vii

viii

Contents

4.4 4.4.1 4.5 4.6

Ternary Systems 119 Chiral Discrimination via the Formation of Solvates 121 Temperature of Desolvation – T g and New Polymorphs Only Accessible Through a Smooth Solvation – Desolvation Process Concluding Remarks 126 Acknowledgments 127 References 127 133

5

Toward Computational Polymorph Prediction Sarah L. Price and Louise S. Price

5.1

Could a Computer Predict Polymorphs for the Pharmaceutical Industry? 133 Predicting the Thermodynamically Most Stable Structure from the Chemical Diagram 134 Using Crystal Structure Prediction Studies as a Complement to Solid-form Screening 134 Methods of Calculating the Relative Energies of Crystals 136 Lattice Energy 136 Free Energy 139 Searching for Possible Crystal Structures 140 Comparing Crystal Structures 141 Calculation of Properties from Crystal Structures 142 Spectroscopic – PXRD, IR, ss-NMR 142 Other Properties: Solubilities, Morphologies, and Mechanical Properties 143 Crystal Energy Landscapes 145 Interpretation of Crystal Energy Landscapes 145 Example of Tazofelone 146 Potential Uses of Crystal Energy Landscapes in the Pharmaceutical Industry 148 Conﬁrming the Most Stable Structure is Known 148 Suggesting Experiments to Find New Polymorphs 148 Aiding Structural Characterization from Limited Experimental Data 149 Anticipating Disorder 149 Understanding Crystallization Behaviors 149 Outlook 150 References 151

5.1.1 5.1.2 5.2 5.2.1 5.2.2 5.3 5.4 5.5 5.5.1 5.5.2 5.6 5.6.1 5.6.2 5.7 5.7.1 5.7.2 5.7.3 5.7.4 5.7.5 5.8

6

Hygroscopicity and Hydrates in Pharmaceutical Solids 159 Susan M. Reutzel-Edens, Doris E. Braun, and Ann W. Newman

6.1 6.2 6.3 6.3.1 6.3.2 6.4

Introduction 159 Thermodynamics of Water–Solid Interactions 160 Hygroscopicity 161 Moisture Sorption Analysis 162 Hygroscopic Behaviors in Pharmaceutical Solids 166 Hydrates 168

123

Contents

6.4.1 6.4.2 6.4.3 6.5 6.6

Statistics of Hydrate Appearance 168 Hydrate Crystallization 170 Structures and Properties 174 Signiﬁcance and Strategies for Developing Hydrate-Forming Systems 180 Conclusions 184 References 184

7

The Amorphous State 189 Marc Descamps, Emeline Dudognon, and Jean-François Willart

7.1 7.2

Introduction 189 Amorphous/Crystalline Solids: Terminology and Brief Confrontation 190 Structural Aspects 190 The Concept(s) of Solid State: Rheological Aspect 191 Crystal Melting vs Glass Softening 192 Order and Disorder: Structural Identiﬁcation of Amorphous and Crystal States 193 How Disordered can a Crystal Be? 193 Crystallinity: Deﬁnition, Experimental Identiﬁcation 193 Small or Disordered “Perfect” Crystals 193 Structure of Glassy and Amorphous Compounds. How Ordered can They be? 194 Amorphous Stability, Crystallization Avoidance, and Glass Formation 198 Metastability, Driving Force for Crystallization 198 Kinetics of Crystallization via Nucleation and Growth 198 Conventional Glass Formation 201 Notes on the Assessment and Prediction of Amorphous Stability 202 Role of Molecular Mobility 202 Role of the Liquid/Crystal Interface Energy and Structural Similarity 202 Role of Polymorphism 203 Heterogeneous Nucleation 204 Conﬁnement and Size Eﬀect 204 To Summarize 205 The Glass Transition 205 Calorimetric Signature at T g 205 Calorimetric Glass Transition: Signiﬁcation 206 The C p Jump at T g : Fragile and Strong Glass Formers 207 Glass Transition and Entropy Crisis: The Kauzmann Paradox 207 Glassy Amorphous State: Instability and Energy Landscape 208 Molecular Mobility for T > T g 210 Mobility of Fragile and Strong Glass Formers 210 Link Between Mobility and Entropy 212 Cooperative Rearrangement Regions (CRR) 213

7.2.1 7.2.2 7.2.3 7.3 7.3.1 7.3.1.1 7.3.1.2 7.3.2 7.4 7.4.1 7.4.2 7.4.3 7.4.4 7.4.4.1 7.4.4.2 7.4.4.3 7.4.4.4 7.4.4.5 7.4.4.6 7.5 7.5.1 7.5.2 7.5.3 7.5.4 7.5.5 7.6 7.6.1 7.6.2 7.6.3

ix

x

Contents

7.6.4 7.7 7.7.1 7.7.2 7.7.2.1 7.7.3 7.7.4 7.8 7.8.1 7.8.2 7.8.3 7.8.4 7.9 7.10 7.11

Dynamic Heterogeneity: Non-exponentiality of the Relaxation 213 Molecular Mobility and Instability for T < T g 214 The Aging Phenomenon 214 Approximate Assessment of Stability 215 Fictive Temperature 216 Nonlinearity 217 Secondary Relaxations 218 Multicomponent Amorphous Systems: Solubility and Stability Issues 220 Solubility: Comparison of Crystalline and Amorphous States 220 T g of Amorphous Multicomponent System 223 Improved Dissolution Properties 224 Mixing and Stabilization 224 Methods of Amorphization 226 Inﬂuence of Processing on Properties 230 Concluding Remarks 231 References 232

8

Approaches to Solid-Form Screening 241 Rolf Hilﬁker, Fritz Blatter, Martin Szelagiewicz, and Markus von Raumer

8.1 8.1.1 8.2 8.3 8.3.1 8.3.2 8.3.3 8.3.4 8.4

Screening for Salts and Co-crystals 242 Example of a Co-crystal Screen 243 Polymorphs, Hydrates, and Solvates 245 Screening for Polymorphs, Hydrates, and Solvates 245 Crystallization Methods 248 Choice of Solvent 250 Types of Polymorph Screens 251 Characterization and Selection 253 Conclusion 255 References 256

9

Nucleation 261 Marco Mazzotti, Thomas Vetter, David R. Ochsenbein, Giovanni M. Maggioni, and Christian Lindenberg

9.1 9.2 9.2.1 9.2.2 9.3 9.3.1 9.3.2 9.4 9.4.1 9.4.2 9.5 9.6 9.6.1

Introduction 261 Homogeneous Nucleation 262 Classical Nucleation Theory 264 Two-Step Nucleation Theory 266 Heterogeneous and Secondary Nucleation 268 Heterogeneous Nucleation 268 Secondary Nucleation 268 Characterization of Nucleation 270 Deterministic Nucleation Rates 270 Stochastic Nucleation Rates 272 Order of Polymorph Appearance – Ostwald’s Rule of Stages 275 To Seed or Not to Seed? 277 Process Control 277

Contents

9.6.2 9.6.3

Polymorphism Control 279 Impurity Control 279 References 280

10

Crystallization Process Modeling 285 Marco Mazzotti, Thomas Vetter, and David R. Ochsenbein

10.1 10.1.1 10.1.2 10.1.2.1 10.1.2.2 10.1.2.3 10.2 10.2.1 10.2.2 10.2.3 10.2.4 10.3 10.4

Introduction 285 Population Balance Equations 286 Notes Regarding Population Balance Models 288 Energy Balances and Fluid Dynamics 288 Solution of Population Balance Equations 288 Applications 289 System Characterization and Optimization 289 Crystal Growth 290 Polymorph Transformation 291 Agglomeration 292 Optimization 295 Multidimensional Population Balance Modeling 297 Conclusion 300 References 301

11

Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective 305 Andrei A. Zlota

11.1 11.2 11.3

Introduction 305 API Critical Quality Attributes (CQAs) 306 Statistical Design of Experiments (DoE) for Crystallization Process Development 306 Example: DoE Methodology to Develop a Robust Crystallization Process, a Case of an API Developed as a Polymorphic Mixture 307 Process Analytical Technology (PAT) for Polymorph Control 314 Mixing and Scale-Up Investigations 316 Scale-Up Factors, Mass Transfer 316 Scale-Up Factors in Crystallization Processes 318 Mixing Impact on the Metastable Zone Width (MSZW) 324 Disappearing Polymorphs During Scale-Up 324 Polymorph Control Methods Based on Mixing 324 Heat Transfer 325 Conclusions and Outlook 326 References 326

11.3.1 11.4 11.5 11.5.1 11.5.2 11.5.3 11.5.4 11.5.5 11.5.6 11.6

12

Processing-Induced Phase Transformations and Their Implications on Pharmaceutical Product Quality 329 Seema Thakral, Ramprakash Govindarajan, and Raj Suryanarayanan

12.1 12.2

Introduction 329 Pharmaceutical Processes Causing Unintended Phase Transformations 333

xi

xii

Contents

12.2.1 12.2.2 12.2.2.1 12.2.2.2 12.2.3 12.2.4 12.3 12.3.1 12.3.2 12.3.3 12.3.4 12.4 12.4.1 12.4.1.1 12.4.1.2 12.4.1.3 12.4.2 12.4.3 12.4.3.1 12.4.3.2 12.4.4 12.4.5 12.4.5.1 12.4.5.2 12.4.5.3 12.4.5.4 12.5

Milling 333 Granulation and Drying – Hydration and Dehydration 336 Hydrate Formation 337 Dehydration 338 Compression 342 Freezing Aqueous Solutions 345 Pharmaceutical Processes Causing Intended Phase Transformations – Obtaining the Desired Physical Form 346 Spray-drying 346 Freeze-drying 347 Hot Melt Extrusion 349 Co-milling/Co-grinding 350 Phase Transformations During Pharmaceutical Processing – Implications 351 Creating Disorder – Amorphization 352 Altered Particulate and Bulk Properties 352 Implications on Chemical Stability 353 Solubility and Bioavailability Enhancement 356 Formation of Crystalline Mesophases 357 Restoring Order – Promoting In-process Recrystallization 358 In Frozen Solutions 358 Miscellaneous Processes 359 Amorphization and Crystallization During Freeze-drying 359 Changes in Chemical Composition 364 Hydrate Formation and Dehydration 364 “Co-amorphization” 365 Co-crystal Formation 366 Salt Formation and Disproportionation 366 Conclusion 368 References 369

13

Surface and Mechanical Properties of Molecular Crystals 381 M. Teresa Carvajal and Xiang Kou

13.1 13.2 13.2.1 13.2.2 13.2.3 13.2.4 13.2.5 13.3 13.4 13.5

Introduction 381 Surface Properties 382 Structure–Property–Response/Performance 385 Case Study #1 – Milling-Induced Agglomeration 386 Case Study #2 – Batch-to-batch Variability 390 Case Study #3 – Hydration–Dehydration 393 Case Study #4 – Surface Interactions and Bulk Properties 395 Remarks 399 Impact of Polymorphism on Powder Flow 401 Impact of Polymorphism on Mechanical Properties of Molecular Crystals 402 Impact of Polymorphism on Size Reduction by Milling 405 Impact of Polymorphism on Powder Compaction Properties 406 References 409

13.6 13.7

Contents

14

Analytical Tools to Characterize Solid Forms 415 Rolf Hilﬁker, Susan M. De Paul, and Timo Rager

14.1 14.1.1 14.1.2 14.1.3 14.2 14.2.1 14.2.2 14.2.3 14.3 14.3.1 14.3.2 14.4

Crystal Structure 415 X-ray Diﬀraction (XRD) 416 Vibrational Spectroscopy (Raman, mid-IR, NIR, and THz) 417 Solid-State NMR (ssNMR) Spectroscopy 424 Thermodynamic Properties 431 Diﬀerential Scanning Calorimetry (DSC) 431 Isothermal Microcalorimetry (IMC) 436 Solution Calorimetry (SolCal) 438 Composition Solvate/Hydrate Stoichiometry 439 Thermogravimetry (TGA, TG–FTIR, and TG–MS) 439 Dynamic Vapor Sorption (DVS) 440 Conclusion 443 References 443

15

Industry Case Studies 447 Ralph Diodone, Pirmin C. Hidber, Michael Kammerer, Roland Meier, Urs Schwitter, and Jürgen Thun

15.1 15.1.1 15.1.2 15.2 15.2.1 15.2.2 15.3 15.4

Introduction 447 Screening and Selection of Solid Forms 447 Control Strategy for the Solid Form 448 Case Study #1: Holistic Control Strategy for Solid Form 449 Solid-Form Control for Drug Substance 449 Solid-Form Control for Drug Product 450 Case Study #2: Solid-Form Control of API for Low-Dose Drug 451 Case Study #3: Development of Crystallization Process and Unexpected Inﬂuence of Impurity 453 Case Study #4: Hydrate/Anhydrate Dilemma 456 Case Study #5: Quality by Design by Selecting a Cocrystal 458 Case Study #6: Dealing with the Consecutive Appearance of New Polymorphs 460 Case Study #7: Amorphous API: Issues to be Considered in Drug Development 464 Case Study #8: Computational Prediction of Unknown Polymorphs and Experimental Conﬁrmation 466 References 467

15.5 15.6 15.7 15.8 15.9

16

Pharmaceutical Crystal Forms and Crystal-Form Patents: Novelty and Obviousness 469 Joel Bernstein and Jill MacAlpine

16.1 16.2 16.3 16.3.1 16.3.2 16.4

Introduction 469 Novelty and Obviousness 470 The Scientiﬁc Perspective 471 Novelty from a Scientiﬁc Perspective 471 Obviousness from a Scientiﬁc Perspective 472 The Role of Serendipity in Crystal Forms 475

xiii

xiv

Contents

16.5 16.6 16.7

History of Crystal-Form Patents 477 Typical Ex Post Facto Arguments on Obviousness 478 Conclusion 482 Acknowledgment 482 References 482 Index 485

xv

Preface to the Second Edition Since the ﬁrst edition of “Polymorphism in the pharmaceutical industry,” pharmaceutical research and development continued to progress and evolve. Exploration of new chemical spaces and the trend to select very low soluble compounds for pharmaceutical development has, on the one hand, boosted the application of alternative formulation approaches such as amorphous solid dispersions, and on the other hand, it has stimulated the search for alternative crystalline solids such as cocrystals. Thermodynamics and kinetics continue to rule the game and pose fascinating riddles and challenges to many scientists in the pharmaceutical industry and the academic world. What has also changed is the view of the regulators and the industry on how pharmaceutical development should be done. Eﬀorts to harmonize development and quality concepts resulted in new ICH guidelines Q8 to Q12 that introduce quality by design (QbD) to the pharmaceutical industry. One of the conclusions therein is that modern science should be better used throughout the product lifecycle. The ICH guideline Q11 general principle states that “The goal of manufacturing process development for the drug substance is to establish a commercial manufacturing process capable of consistently producing drug substance of the intended quality.” Furthermore, the drug substance quality is linked to the drug product: “The intended quality of the drug substance should be determined through consideration of its use in the drug product as well as from knowledge and understanding of its physical, chemical, biological, and microbiological properties and characteristics, which can inﬂuence the development of the drug product (e.g. the solubility of the drug substance can aﬀect the choice of dosage form). …”. All QbD considerations, be it for drug substance or drug product, will therefore necessarily be inﬂuenced by the solid form and solid state of the drug substance. The philosophy of the QbD framework with its knowledge- and science-based approach calls for a very good understanding of the system under investigation, which obviously includes the solid state of the drug substance. Such an understanding is not only limited to the internal order or disorder but also encompasses surface aspects of solids. Understanding is closely related to qualitative and/or quantitative description, which in turn requires very powerful and cutting-edge analytical technologies.

xvi

Preface to the Second Edition

QbD in the pharmaceutical industry is a dynamic concept and interpretation of guidelines will and do change over time. However, the basic idea behind the QbD framework and the underlying concept will remain unchanged. Several new chapters were introduced in this edition to provide a holistic view of very diﬀerent aspects of solid-form development in general and on polymorphism in particular. A general overview of the impact and importance of solid-form properties on drug development is given in Chapter 1. Next to salts, which are discussed in Chapter 2, a new Chapter 3 covering cocrystals describes the expansion of the possible solid-form space that can be considered for solid-form development. As moisture is ubiquitous in ambient conditions, the interaction of solids with water is explained in depth in Chapter 6. Understanding the thermodynamics of the system under investigation and visualization of stable phases in phase diagrams help to appreciate and highlight the possible complexity that such systems can show (see Chapter 4). The ﬁrst step of crystallization, and hence of polymorph formation, is nucleation, which is discussed in Chapter 9. Although one aspect is the identiﬁcation of the polymorph landscape of a given species (see Chapter 8), the large-scale making of the desired form, i.e. crystallization process development, remains one of the key challenges in pharmaceutical chemical development (Chapters 10 and 11). As mentioned above, noncrystalline, amorphous solids (Chapter 7) play an increasingly important role. When solid drug substance is ﬁnally formulated into a drug product, aspects related to surface and mechanical properties (Chapter 13) as well as possible processing-induced phase transformations (Chapter 12) become important. Chapter 5 demonstrates the power of polymorph prediction using sophisticated models while taking advantage of ever-increasing computing power. The various chapters on various analytical techniques in the ﬁrst edition are now summarized in Chapter 14. The diversity of problems and questions arising during solid-form development are presented by industry cases in Chapter 15. Finally, Chapter 16 presents and elucidates the aspects of novelty and obviousness when considering crystal patents. New chapters were introduced in the second edition, which means that some chapters of the ﬁrst edition had to be omitted. The ﬁrst edition, therefore, remains a useful tool that is complemented by this volume. What has remained the same is the excellent quality of the contributions for which we sincerely thank all authors. We are also grateful to Wiley-VCH for their support and encouragement. August 2018

Rolf Hilﬁker Markus von Raumer

1

1 Solid State and Polymorphism of the Drug Substance in the Context of Quality by Design and ICH Guidelines Q8–Q12 Markus von Raumer1 and Rolf Hilﬁker2 1 Idorsia Pharmaceuticals Ltd., Hegenheimermattweg 91, Allschwil, 4123, Switzerland 2

Solvias AG, Römerpark 2, Kaiseraugst, 4303, Switzerland

1.1 Introduction The way in which the pharmaceutical industry is approaching technical development has evolved very much in the recent years. Fresh concepts coming from other industries have been introduced with the desire to push for a more science and risk-based development approach throughout the product life cycle. Quality by design (QbD) in the pharmaceutical industry is an outcome of the eﬀorts to harmonize development quality concepts and understandings by regulatory agencies and resulted in the International Conference of Harmonization (ICH) guidelines Q8 [1], Q9 [2], Q10 [3], Q11 [4], and Q12 [5]. Although ﬁrst devised for pharmaceutical development (Q8), the QbD concepts and related tools were rapidly recognized as being very helpful for chemical development. A result of this process was the Q11 guideline that provides guidance for drug substance as deﬁned in the scope of the ICH guideline Q6A [6] (this guideline contains the well-known decision trees for polymorphism). The scope of this chapter is to give a short introduction to the solid-state development process in the pharmaceutical industry and to QbD. Questions on how QbD principles can be applied to solid-state development will be discussed, highlighting how the solid state is an important parameter to be considered in the pharmaceutical development process. For that purpose, some general insights into the relevance of the drug substance (DS) solid state throughout various ﬁelds of pharmaceutical development will be given.

1.2 A Short Introduction to Polymorphism and Solid-State Development Only a brief overview of solid-state development and polymorphism shall be given here. Subsequent chapters in this book will discuss the various aspects in more detail. Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development, First Edition. Edited by Rolf Hilﬁker and Markus von Raumer. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

2

1 Solid State and Polymorphism of the Drug Substance in the Context of QbD

Many organic and inorganic compounds can exist in diﬀerent solid forms [7–12]. They can be in the amorphous (Chapter 7), i.e. disordered [13], or in the crystalline, i.e. ordered, state. In accordance with McCrone’s deﬁnition [8], “The polymorphism of any element or compound is its ability to crystallize as more than one distinct crystal species,” we will call diﬀerent crystal arrangements of the same chemical composition polymorphs (Figure 1.1). Especially in the pharmaceutical context, the term “polymorph or polymorphism” is used more broadly by many authors and regulatory agencies. The amorphous state, as well as hydrates or solvates (both of which do not have the same chemical composition), are tacitly included by the term. Because diﬀerent inter- and intramolecular interactions such as van der Waals interactions and hydrogen bonds will be present in diﬀerent crystal structures, diﬀerent polymorphs will have diﬀerent free energies and therefore diﬀerent physical properties such as solubility, chemical stability, melting point, density, etc. (Chapter 4). Hence, the crystal form of a solid material in development is often considered a critical quality attribute (CQA, see next section). Of practical importance are also solvates [14], sometimes called pseudopolymorphs, where solvent molecules are incorporated in the crystal lattice in a stoichiometric or nonstoichiometric [12, 15] way. Hydrates (Chapter 6), where the solvent is water, are of particular interest because of the omnipresence of water. In addition to the crystalline, Polymorphs

Amorphous

Solvate/hydrate Stoichiometric

Non stoichiometric channel type

Salt

Active molecule Solvent/water molecule Acid

Co-crystal

Deprotonated acid Protonated active molecule Coformer (solid at r.t.)

Figure 1.1 Schematic depiction of various types of solid forms.

1.3 A Short Introduction to Quality by Design (QbD)

amorphous, and liquid states, condensed matter can exist in various mesophases. These mesophases are characterized by exhibiting partial order between that of a crystalline and an amorphous state [16, 17]. Several drug substances are known to form liquid crystalline phases, which can be either thermotropic, where the liquid crystal formation is induced by temperature, or lyotropic, where the transition is solvent induced [18–20]. Polymorphism is a very common phenomenon [11, 21–25] in connection with small-molecule drug substances. The literature values concerning the prevalence of true polymorphs range from 32% [26] to 51% [27–29] of small organic molecules (molecular weight 14

Very strong

14

4 and cocrystal complexes are observed exclusively for ΔpK a < −1 [26]. According to the FDA guidance on the regulatory classiﬁcation of pharmaceutical cocrystals [27], if an API and its salt or cocrystal former have a ΔpK a ≥ 1, there will be substantial proton transfer resulting in ionization and formation of a salt as opposed to a cocrystal. If the ΔpK a < 1, there will be less than substantial proton transfer and the complex should be classiﬁed as a cocrystal. A ΔpK a of more than 1 would predict that 73% of salt is formed. In general, it is accepted that when the pK a diﬀerence between a cocrystallizing acid and base is greater than 2 or 3, salt formation is expected with 90.5% and 96.7%, respectively, salt formation. Acid–base complexes with a ΔpK a of >4 have exclusively been reported as salts with 99% of salt is formed [26]. 2.4.2

Ionization and pH

After dissolving an acidic drug HA in water, the total mass concentration of A in solution, whether ionized (=[A− ]) or not (=[HA]), remains constant irrespective of the extent of the dissociation reaction and is the sum all of the species containing A: [AT ] = [HA] + [A− ]

(2.13)

In order to describe the extent of an ionization equilibrium, Eq. (2.13) is substituted into Eq. (2.2) for [HA] which yields Ka ⋅ ([AT ] − [A− ] ) = [H+ ] ⋅ [A− ]

(2.14)

39

40

2 Alternative Solid Forms: Salts

and the solution for [A– ] [A− ] =

Ka ⋅ [AT ] Ka + [H+ ]

(2.15)

Thus, the fraction of the ionized species is fA − =

Ka [A− ] = [AT ] [H+ ] + Ka

(2.16)

and, as per mass balance, the fraction of the unionized species is fHA = 1 − fA− =

[HA] [H+ ] = T [H+ ] + Ka [A ]

(2.17)

Transformed into an expression with convenient logarithmic terms, where [H+ ] is replaced by the deﬁnition of pH: pH = −(10 log[H+ ])

(2.18)

we have 1 (2.19) 1 + 10pKa −pH and for the undissociated acid 1 fHA = (2.20) 1 + 10pH−pKa For bases, the corresponding equations may be derived from Eqs. (2.6) and (2.7) in the same way. For the fractions of the protonated base, fBH+ , and of the unionized base species, f B , respectively, we get fA − =

1 (2.21) 1 + 10pH−pKa 1 fB = (2.22) 1 + 10pKa −pH These equations describe in a most condensed form the interrelationship between pK a and solution pH. They also illustrate the function of pK a as the key parameter providing the measure of strength of acids and bases. fBH+ =

2.4.3

Solubility

Most salt forms of an API are prepared in order to enhance the aqueous solubility of a drug substance. To assess the perspective, such an improvement, the interrelationship of pK a , solution pH, and intrinsic solubility S0 of simple weak electrolytes is reviewed, based on the theoretical solubility–pH proﬁles (Figures 2.2–2.4) of a base, an acid, and a zwitterionic compound. The solubility S of a basic API is the sum of the concentration of the ionized and unionized species. The acid counterion is assumed to be soluble not constituting a limiting factor S = [BH+ ] + [B]

(2.23)

2.4 The Basics of Salt Formation

1000

D

Solubility (g l–1)

100 10

C

1

B

0.1

A

0.01 0.001

pHmax 0

2

4

6

I pH

pKa

8

10

12

14

Figure 2.2 Theoretical solubility diagram of a basic substance, pK a = 9.0, and four of its salts characterized by diﬀerent solubility products. pHmax is indicated for salt B. 1000

H

Solubility (g l–1)

100

G

10

F

1

E

0.1 0.01 0.001

IpKa

0

2

4

I pH max

6

IpH

8

10

12

14

Figure 2.3 Theoretical solubility diagram of an acidic substance, pK a = 5.5, and four of its salts characterized by diﬀerent solubility products. pHmax is indicated for salt E.

At low pH (pH < pHmax ), where the solubility of the protonated base or salt is limiting, the solubility is described as (e.g. [25]): ) ( Ka S = [BH+ ]S + [B] = [BH+ ]S 1 + (2.24) = Ssalt (1 + 10pH−pKa ) [H3 O+ ] wherein subscript S indicates saturation. At high pH (pH > pHmax ), the solubility of the free base S0 is limiting and is described by the following equation (e.g. [25]): ( ) [H3 O+ ] + S = [BH ] + [B]S = [B]S 1 + (2.25) = S0 (1 + 10pKa −pH ) Ka The two solubility proﬁles describe the independent solubility each of the salt (low pH) and the free base (high pH). The pH at the intersection of the two

41

2 Alternative Solid Forms: Salts

100

10 Solubility (g l−1)

42

1

0.1

0.01 pKa,1

pKa,2

0.001 0

2

4

6

8

10

12

14

pH

Figure 2.4 Theoretical solubility diagram of an amphoteric substance, pK a,1 = 3.5, pK a,2 = 9.5.

solubility curves marks the pH of highest solubility, pHmax . At pHmax , both the solid phases of the salt and that of the free base exist and are in equilibrium. It can be expressed according to Bogardus and Blackwood [28] as ( ) S0 (2.26) pHmax = pKa + log Ssalt The diagrams show pH regions where solubility is independent of pH, and others below or above the pK a where the solubility increases exponentially with pH up to a cutoﬀ point. These are the regions where solubility improvement by salt formation can be expected. However, for each salt, the solubility levels oﬀ at a pH value beyond which no further increase of solubility is observed. This pH value is referred to as “pHmax .” In a drug salt suspension, the pHmax not only marks this change of pH–solubility relationship but also indicates a change in the nature of excess solid in equilibrium with the saturated solution. This statement becomes quite important for the preparation and isolation of solid salts: In the case of salt B of the basic compound in Figure 2.2, above pHmax (=7.2), the excess solid is formed by the free base, whereas below pHmax , the undissolved solid is the salt. pHmax is the only condition where both solid salt and solid free base can coexist in equilibrium with the solution. In Figures 2.2 and 2.3, the solubility branches for four diﬀerent salts, A–D for basic drugs and E–H for the acidic drugs, are entered. Each of them is characterized by the level of its maximum solubility plateau, associated with a speciﬁc pHmax . The region of the unionized drug substance remains uninﬂuenced by salt formation. The amphoteric substance (Figure 2.4) has a deep solubility plateau within the pH range between the pK a values. Beyond these, it can behave either as a base or as an acid, respectively; so salts can be formed with either acids or bases of appropriate strength, and diﬀerent salt solubility levels are achieved as described above for the monovalent basic or acidic substance. Theoretical equations for the above pH–solubility relationships can be found in Ref. [29].

2.4 The Basics of Salt Formation

During an experimental search of salts for high solubility, supersaturation phenomena can play an interfering role. A practical approach is to titrate aqueous suspensions of a sparingly soluble basic drug with one of a selected series of acids, e.g. hydrochloric, tartaric, fumaric, citric, or phosphoric acid. After incremental additions of acid, samples of the supernatant solution are analyzed for drug concentration. Increasing concentrations are found as the pH steps decrease. However, in a ﬁrst experiment, frequently much higher values may be found than can be reproduced in the later experiments. The reason for this phenomenon is that initially not even a trace of solid new salt present in the excess solid as the pH falls by the addition of acid below the theoretical pHmax ; hence, supersaturation is likely to occur, and more base would dissolve along the rising solubility line of the base. Depending on nucleation and the crystallization kinetics of the new salt, the system equilibrates sooner or later, and the concentration eventually arrives at the lower level typical for the solubility of the respective salt. However, although fast equilibration is common, the timescales can, in principle, vary widely, and at times, a desired solid salt may not crystallize within a reasonable period of time because of slow nucleation kinetics.

2.4.4

Disproportionation

The conversion of salt to the free form is a process known as disproportionation, which has been reported in the literature to occur during processing or on storage [25, 30–33]. Zannou et al. [31] described an example of disproportionation of a maleate salt of an API, where the pK a of the basic function of the API is 6.5 and the pK a of maleic acid is 1.9 and 6.6 [22]. The pK s can be calculated as −4.6, which predicts that salt formation proceeds to 99.4% completion, i.e. the equilibrium of Eq. (2.9) is shifted to the salt (BH+ )(A− ). Disproportionation can be understood by considering the above pH solubility proﬁles. Many publications have postulated the importance of pHmax for this disproportionation phenomenon, which depends on solubility S0 of the free drug substance and Ssalt of the salt as well as of the pK a of the drug substance. As outlined above, in the case of a basic compound A in Figure 2.2, above pHmax , the excess solid is made of the free base, whereas below pHmax , the undissolved solid phase in equilibrium is its salt. pHmax is the only condition where both solid salt and solid free base can coexist in equilibrium with the solution. For a weak basic drug forming a salt with an acidic counterion, the conversion from salt into free base can potentially occur when the pH exceeds pHmax inducing the free base crystallizing/precipitating out of the solution and will lead to disproportionation. The pHmax of a weak basic drug will occur at a pH below its pK a , and according to Eq. (2.26), the more higher the solubility of the salt, the lower is the pHmax and the more soluble salt will have smaller range of pH, where it is the favored form [33]. Salt formation often aims to improve solubility of a drug; however, with increasing solubility, the risk of disproportionation is also increasing. In solution, the disproportionation of a salt into the free form and the concept of pH and pHmax are well understood and described by the above ionic

43

44

2 Alternative Solid Forms: Salts

equilibria. This will also be driven by solubility products of diﬀerent species that may dominate the corresponding phase diagrams. However, the phenomenon of disproportionation in the solid state is less obvious to understand. In a general model, at low relative humidity below a critical value RH0 , the RH of deliquescence, water can adsorb on particle surfaces, but only at the critical RH0 , the solid will dissolve in the adsorbed water layer and form a saturated solution [34]. If the humidity is increased beyond RH0 , additional water will condense onto the aqueous layer and causes more solid to dissolve until all solid is dissolved, a phenomenon called deliquescence. For chemical reactions in solids, a model of saturated solution layers has successfully been applied to understand the chemical stability in the presence of moisture [34–40]. The model assumes, as mentioned above, the presence of a thin ﬁlm surface water layer around the drug particles below critical RH0 , in which the compound dissolves to saturation (microscopic “solvation” [25]). This model has been extended to understand the physical stability related to disproportionation reactions in solids [25, 32, 33, 41, 42]. The pH of the solution in the water layer surrounding the solid particles is referred to as the microenvironmental pH or solid surface pH [43]. Serajuddin and Jarowski [44, 45] established that the surface pH of a pharmaceutical solid corresponds to the pH of its saturated solution (or slurry) in water [25, 31, 39]. The concept of microenvironmental pH has successfully been used to explain many chemical reactions in the solid state [46–49] and also extended to describe the disproportionation of salts in the solid state [25, 30–33]. When the microenvironmental pH in a saturated water layer around the particle of a salt exceeds its pHmax and if the solubility of the free form is less soluble than the salt, precipitation or nucleation/crystallization of the free form can occur spontaneously. In bulk drug substance, the microenvironmental pH is only inﬂuenced by the acidity/basicity of the drug substance and the nature of the counterion. In the ﬁnal formulation, the microenvironmental pH is expected to be inﬂuenced by solubility of the salt and the excipients having acidic/basic functionalities [30–32] or residual acidity/basicity due to their manufacturing. It was found that the eﬀectiveness of the excipients depends on basicity, surface area, and physical state (crystalline or amorphous) [32]. Merritt et al. [25] developed a numerical model to understand disproportionation in the solid state and to predict the eﬀect of excipients on the disproportionation potential. The model uses the pH of a saturated solution of excipient(s) to describe the microenvironmental pH. Then, given salt, free base aqueous solubility, and pK a , the model allows to predict the stability of the salt and the compatibility with the excipients considered with respect to disproportionation [25]. In addition to selecting the optimal salt form, it is also important to understand how selection of diﬀerent excipients may also impact disproportionation and aﬀect physical and chemical stability under accelerated or long-term storage conditions, respectively.

2.5 Approaches to Salt Preparation and Characterization

2.5 Approaches to Salt Preparation and Characterization 2.5.1

Initial Data

Before successful experimental work in search of salts of a drug entity is initiated, two parameters need to be known. As outlined above, the pK a value(s) of the drug substance and the pH–solubility proﬁle must be determined experimentally. Alternatively, these can be predicted from any of the available estimation programs. Also, the aqueous solubility of the non-ionized form – free base or free acid, respectively – can be estimated at least by the order of magnitude by Yalkowsky’s general solubility equation [50, 51]. These data are useful to construct a “ﬁrst-guess” pH–solubility diagram. The ﬁrst step of a salt research also involves the collection of important information for proper design, which includes the mode of administration, any known or expected absorption problems, the intended dose range, as well as further physicochemical properties of the API, for example, the solubility in organic solvents and the chemical stability. 2.5.2

Selection of Salt Formers

Based on the pK a values, a series of salt formers can then be selected from those frequently used pharmaceutically [18, 22]. As outlined earlier, it is generally required that, in order to form a stable salt, the respective pK a values of an acid and base pair should diﬀer by at least 2–3 pK a units. Thus, the pK a of the acid is required to be at least 2–3 units lower than that of the base [22, 26, 52]. This corresponds to a situation in which the salt formation constant K s becomes 100 (ΔpK a = 2) and 1000 (ΔpK a = 3), and both compounds, brought together in water, are ionized to a degree of at least 90% and 96%, respectively. In recent times, it is observed that more and more basic drug candidates arrive at the development stage with low aqueous solubility and low pHmax . This limits the selection of potential salt formers to stronger acids such as hydrochloric, sulfuric, and sulfonic acids to form stable salts. Strong mineral acids such as HCl (pK a ≈ −6) and H2 SO4 (pK a = −3) can form solid salts with the weak base atazanavir having a pK a value as low as 4.25, pK s = −10.25 for HCl salt (K s = 1.8 × 1010 ) and pK s = −7.25 for sulfate salt (K s = 1.8 × 107 ), whereas attempts to isolate a salt with acetic acid (pK a = 4.76) or with benzoic acid (pK a = 4.19) would fail with such a weak base (pK s = 0.51/K s = 0.3 and pK s = −0.06/K s = 1.1). Instead, reducing the volume of a slurry or solution of the base in solution of the acids to dryness, in the case of acetic acid, would return just the base because the acid evaporates completely, or, in case of benzoic acid, a mixture of base and benzoic acid, respectively. An annotated compilation of salt formers including less frequently encountered ones and those used to solve special problems is available in [22]. Although we limit the description in this section to only salts and acidity constant in aqueous media, it should be noted that, in general, a search for salts is

45

46

2 Alternative Solid Forms: Salts

not only restricted to salts but may also extend toward cocrystals, in disregard of the above-mentioned pK a rules. As outlined in Section 2.2, signiﬁcant shifts in pK a can be observed depending on the nature of the media considered for the methodological design, broadening the number of opportunities. 2.5.3

Salt Preparation Procedures

The search of an appropriate salt form of a drug substance is usually performed in diﬀerent phases (Figure 2.5). In a ﬁrst phase, a large number of salt formers and conditions are investigated on small scale, typically followed by scale-up phases, where successful hits are prepared in larger amounts for more detailed investigations of their chemical attributes and properties [53, 54]. In the ﬁrst phase, a large number of counterions, typically 10–40, are investigated in 3–5 diﬀerent solvents or mixtures of solvents. Hence, crystallization experiments are typically performed at 20–200 mg scale. The investigations also include diﬀerent stoichiometric ratios between acid and base. Stoichiometry is especially important when the drug substance or the salt-forming agent has multiple reactive groups with diﬀerent pK a values. Nucleation and crystallization play a critical role in searching crystalline salt forms, and they are aﬀected by various factors such as solubility, supersaturation, rate at which supersaturation occurs, temperature, or reactivity of surfaces toward secondary nucleation and many others. However, at this stage, most of such factors are unknown. Preparing the salts at elevated temperature where all components are soluble, followed by cooling to crystallize the product, is recommended. In order to promote nucleation and further growth, various methods can be used as crystallization by slow evaporation of solvents, cooling crystallization, anti-solvent crystallization, slurry conversion, or combination of diﬀerent methods. If solids are obtained, they are usually isolated and only gently dried to ensure proper detection of potential solvated forms or hydrates. The solid materials are then usually tested for crystallinity by cross-polarized light microscopy and/or X-ray powder diﬀraction (XRPD), melting point, stoichiometry by NMR or ion chromatography, purity by high-performance liquid chromatography (HPLC), elemental analysis, residual solvents by loss on drying (thermogravimetric analysis, TGA), hygroscopicity, and solubility in aqueous media. The extent of characterization depends on the number of counterions, hits, and the amount of material available. With this respect, it follows the diﬀerent phases and scale of the experiments: a broad screening on small scale, 20–50 mg, to identify crystalline salt forms, followed by a ﬁrst scale up to 200 mg of the ﬁrst crystalline hits, for a more detailed characterization, which allow to narrow down the number of potential candidates to three to ﬁve salts. Salt preparation procedures are typically performed in parallel with processing crystallization experiments. In previous years, the traditional procedures have

Screening

Characterization

Feasibility

Search for crystalline hits with various salt counterions1 in different solvents - 10 – 50 counterions - different stoichiometric ratios - 3 – 5 solvents - 20 – 200 mg scale

Identification of successful hits as e.g. - Morphology by microscopy - Crystallinity by XRPD - Stoichiometry by NMR, IC, or elemental analysis - Residual solvents by TGA - Melting point by DSC - Hygroscopicity - Solubility

Scale up of suitable salt candidates - 3 – 5 candidates - > 2 g scale

Characterization of salt candidates - Stability - Stability in solution - Stability in bulk - Compatibility - Light stability - Physicochemical properties - Stoichiometry - Residual solvents and water - Solubility - Intrinsic dissolution rate - Hygroscopicity - Morphology - Polymorphism - Crystallization and slurry experiments - Effect of grinding and wet granulation

Scale up of 1–2 best candidates - 5 – 20 g scale

-

Feasibility of drug substance processing Feasibility of formulation Bioavailability

Final selection 1

In general the screening is not limited to salt counterions only, but may also extents towards co-crystal formers.

Figure 2.5 Diﬀerent phases of the search for an appropriate salt form.

48

2 Alternative Solid Forms: Salts

been replaced by partly or fully automated medium- or high-throughput screening (HTS) methods [53, 55–58]. Several pharmaceutical companies, scientiﬁc service providers, or instrument manufactures have developed processes and suitable platform to perform salt, cocrystal, and polymorphism screenings. Such platforms are typically based on standard 96-well plate formats. In parallel, analytical instruments, such as XRPD, Raman, melting point, and others, have also been developed to allow the analysis of small amounts of sample in an automated routine, including data collection and data processing. Sample amounts used for individual crystallization or salt forming reaction are often well below 10 mg or even below 1 mg per reaction well. In our experience, the use of fully automated high-throughput platforms have not been able to establish themselves for salt screening or have not replaced the more traditional or rational procedures. A typical HTS protocol includes distribution of concentrated solution of API into wells followed by addition of concentration solution of counterions. The fully charged HTS plates are then allowed to react at a certain temperature, followed by evaporation of solvents. Depending on solubility and in relation to the scale, often only small amounts of material were obtained per well, which allowed only a limited number of characterizations, mainly polarized light microscopy and XRPD or Raman analysis. However, because of the small amounts and probably phase purity, the results are not representative, and identiﬁcation of successful crystalline hits is diﬃcult. In any case, a scale-up of potentially crystalline hits is required in order to obtain material for further characterization. As the crystallization conditions under which the ﬁrst hits are obtained are oftentimes diﬃcult to reproduce, scale-up is not always straightforward and requires some additional development to reproduce a potential salt form. As the typical 96-well plate is a closed system, any manipulation during crystallization such as scraping the material sticked to the wall into the solution or inducing nucleation by scratching the walls of the reaction vessels are not possible. Although the conditions under which a proton transfer between an acid and a base can occur in solution are well understood as described above, the conditions under which a crystalline salt will precipitate out of the solution are widely unknown at that stage. Manual intervention and observation of the process ongoing in reaction vessels are often helpful for a successful crystallization and further optimization of processes. High-throughput platforms are complex and require dedicated personnel with background in diﬀerent disciplines from crystallization, analytics, automation to management, and evaluation of large datasets. This makes the application of such platforms less ﬂexible. The evaluation of results also necessitates the handling of a large number of results that may also be aﬀected by physical purity of the phases [59]. An approach with parallel small-scale experiments are often equally or even more successful. It oﬀers more ﬂexibility and simpler methods to search for suitable salt candidates, also avoiding potential caves (e.g. poor mixing because of poor wettability of components, manual intervention is not possible, clear solution is not reached, etc.). In a typical setup, one can also manipulate up to

2.6 Selection Strategies

96 experiments in parallel. The reaction vessels can be inspected visually and manually controlled, i.e. scraping material from the wall or addition of solvents is possible. In addition, information on the crystallization behavior can be gained, which is helpful for later scale-up experiments. In the next phase, the salt candidates that have been identiﬁed by a HTS or rational approach are prepared at a scale of at least 2 g and are investigated more extensively. The properties investigated are focused on chemical attributes (including purity, stoichiometry, residual solvent, water content, stability in solution and in bulk, compatibility with excipients, stability under light stress, etc.) and on physicochemical properties (including pH of solution, thermal properties, hygroscopicity, water sorption behavior, solubility in aqueous media and organic solvents, and intrinsic dissolution rates). As part of the salt selection, a ﬁrst investigation into the polymorphic behavior is performed. This includes equilibration slurry experiments in diﬀerent solvent systems, typically at 25 ∘ C and 50 ∘ C, crystallization experiments, eﬀect of grinding or wet granulation, and investigation of hydrate formation. A more extended investigation on polymorphism behavior is usually performed on the salt form ﬁnally selected for development. In addition to the characterization of the physicochemical properties of the salt candidates, it is also recommended to include drug substance processability and particle engineering aspects as a further part of the salt selection process. For this purpose, usually 5–20 g of the most promising one or two candidate(s) is prepared, and their processability is investigated in more detail. This includes investigation into typical process parameters, most appropriate class of solvent to perform crystallization, yield, removal of solvents and impurities, robustness of the crystallization process and ﬁltration, drying and milling behavior. In addition, more representative investigation on the crystalline form directed toward its bulk properties such as particle morphology, ﬂowability, cohesiveness, dustiness, and electrostatic behavior may be performed. Also, the possibility to modify these parameters may be investigated by appropriate engineering. Of course, the scope and extent of these feasibility studies will depend on the time and amount of drug substance available at that early stage of development. In the cases of very sparingly soluble, diﬃcult absorbable drug candidates, the investigations may even include in vivo studies (rat, dog) with experimental formulations in order to identify the most suitable salt form or solid-state form, respectively.

2.6 Selection Strategies 2.6.1

Points to be Considered

The ﬁnal decision on the salt and solid-state form of a drug substance is made based on the data collected from analytical and physical characterization of a certain number of salts prepared. The data are evaluated primarily against the requirements set by biopharmaceutical and therapeutical considerations for the

49

50

2 Alternative Solid Forms: Salts

use of the drug, as well as pharmaceutical and chemical–technological aspects in view of the development and manufacturing of dosage forms are considered as shown in Section 2.3, and the synthesis and isolation of the drug substance. The selection of the ﬁnal entity for further development must balance the therapeutical and biopharmaceutical aspects as well as the chemical–technological aspects. Thus, the form of a drug substance that is highly soluble and bioavailable, but lacks suﬃcient chemical or physical stability, may not be more suitable to be developed further than a chemically and physically very stable but very poorly soluble salt. It is not possible to present here a complete catalog of all the data to be provided for a complete assessment, and there are cases where just a minimum of information may lead to a reliable decision, but the most fundamental data can be found in the tables of the case reports presented in Section 2.7. Further categories of properties may have to be studied depending on the nature of the substance and on the therapeutic application of the future drug product. One of the key unknown is certainly the ﬁnal dose that may critically aﬀect the rating in terms of solubility needs. Some typical and also some less frequently encountered issues are summarized here in brief: • Solubility and dissolution rate. • Chemical stability, including potential interaction between drug entity and counterion, stability in the presence of pharmaceutical excipients (drug/excipient compatibility). • Disproportionation of the salt in solution, as drug substance or in the drug product (i.e. in close contact with excipients). • Stability of the morphic state in bulk form, in solid and suspension dosage forms. • Complex polymorphic “landscape.” • Hydrate formation and hydrate stability during storage and processing, chemical stability of hydrated vs anhydrous forms (inﬂuence of released hydrate water during storage), uptake of water of hydration by anhydrates in solid dosage forms with consequences for mechanical properties. • Molecular weight: large counterions may surmount the tolerable drug amount to be packed into a solid dose unit; in contrast, for extremely low-dose drugs, larger molecular weight can improve handling and content uniformity. • Safety of salt or cocrystal forming agent. By choosing suitable salt forms, • • • • • •

annoying polymorphism problems may be circumvented; high hygroscopicity resulting in deliquescence may be avoided; amorphous material may be turned into a crystalline salt; chemical stability problems may be circumvented; taste and smell problems may be minimized; the melting point may be raised for improving mechanical properties (e.g. for milling) up to the extent that liquid bases or acids are turned to solids;

2.6 Selection Strategies

• puriﬁcation of a drug substance can be achieved (as the last or penultimate synthesis step, potentially to also enhance optical purity by diastereomeric salt formation); • absorption rate may be controlled: retardation of gastrointestinal absorption by salts with low aqueous solubility/low dissolution rate; • transdermal absorption may be enhanced by lipophilic salt pairs; • irritation may be avoided (e.g. for inhalation or topical formulation); • two pharmacological principles can be combined (restricted to stoichiometrically ﬁxed ratios). 2.6.2

Final Decision

There was no question up to the late 1960s that it was the inventing chemist who synthesized a new chemical entity (NCE) that determined the salt form to be also used for in vivo studies, safety investigations, and for subsequent dosage form development. During the decades thereafter, the feedback from pharmaceutical development into medicinal chemistry caused a change in the awareness that certain substance properties may be unfavorable up to the point that further work with the drug candidate in the form provided could slow down or even be counterproductive to the process of developing dosage forms for clinical studies. Then, it could happen that technical problems or insuﬃcient bioavailability could cause a step back to the chemist. Later, a preformulation phase was introduced in early development for establishing the physicochemical database and technological properties of the candidate beforehand while biological and pharmacological work was still going on in discovery. Based on a ﬁrst assessment, the chemist was asked to prepare small amounts of a few salts. These were studied for the critical properties, and a ﬁnal recommendation for the salt form to proceed with was made. Figure 2.6 reﬂects the route from discovery to development in a concise scheme. The present paradigm in identifying the ﬁnal salt and solid-state form is shifted from investigating not only one candidate entity but also to study several interesting compounds in parallel including the search for suitable chemical and physical forms and to select the ﬁnal candidate as its ﬁnal salt and solid-state form from the resulting group of fully characterized pharmacologically similar entities. Thus, the decision point along the time line of the discovery development process of a drug product has shifted backward into the research phase (Figure 2.6). The ﬁnal decision calls representatives from biology, chemistry, chemical process development, pharmaceutical development, drug metabolism, safety, analytical development, regulatory aﬀairs, and patent aﬀairs to assess the data presented and to propose the candidate for development. Depending on the critical issues that will be discussed, some of these units have more weight in the decision while others play a more advisory role. An example may illustrate such a situation: An NCE has been characterized with the conclusion that an oral product would be equally feasible with the free base or with the lactate salt. Although the latter could also be used for manufacturing an injectable solution, such a solution can

51

2 Alternative Solid Forms: Salts Target finding

Lead optimization

Interesting compound 2 compound 1

Interesting compound 4 compound 3

Interesting compound 6 compound 5

Activity screening

Salt screening

X

Salt A Salt B Salt C

Salt A Salt B Salt C Salt D Salt E

Drug discovery

Lead finding

Salt A Salt A Salt B Salt B Salt C Salt D

Characterization

Final candidate and form selection Drug candidate

Development

52

Salt form and solvate / polymorph

Figure 2.6 Organizational sequence of activities in industrial research and development for identifying drug candidates and their suitable salt and solid-state forms.

also be prepared by dissolving the base together with the stoichiometric amount of lactic acid. So in this case, dosage form development had no preference. The ﬁnal decision here was taken by chemical process development with the argument that they had a preference for the salt formation as a further puriﬁcation step for the ﬁnal product. 2.6.3

Salt Form and Life Cycle Management of Drug Products

Salt issues reappear regularly during a drug’s life cycle. In most cases, a new drug is launched as a solid dosage form for oral use. Once established in therapy in its primary indication, other routes of administration are investigated; the ﬁeld of indications may also be widened. As a consequence, new products with the same drug substance are added to the product line. Such line extensions usually bring about the demand of other salt and solid-state forms that give to the drug a better match for the requirements of the additional products and ﬁelds of use. A typical example is the selection of a salt to improve the solubility of an acidic drug candidate for an immediate release form by using its sodium salt. Later, for the development of a slow-release form, a magnesium or zinc salt was selected,

2.7 Case Reports

which shows lower solubility and dissolution rate and was more suitable for this type of application.

2.7 Case Reports 2.7.1

Overview of Salt Forms Selected

About half of the APIs listed in the Orange Book published by the US FDA by the end of 2006 are salts [18, 19]. Among them, the most frequent salt selected was the hydrochloride followed by the sulfate, bromide, maleate, mesylate, tartrate, phosphate, and citrate. Although sulfonic acids such as methanesulfonic acids are known to form suitable salts, in particular, as they are strong acids, their use is nowadays limited as their corresponding sulfonic acid alkyl esters are known to exert genotoxic eﬀects. These esters may be formed during the synthesis of the drug substance, during the crystallization of the salt, or during storage, especially if the crystallization solvents are, or contain, alcohols, such as methanol, ethanol, or propanol [60–62]. The risk of presence of alcohols is not only limited to their use as solvents in synthesis, for recrystallization or washing, but should also be considered as potential impurity in non-alcohol solvents. 2.7.2

The Salt Selection Process

The selection of a physical form of an API – free form, salt, or cocrystal – is, in general, performed in 2–4 tiers depending on the physicochemical characteristics of the native form involved and the physical forms that were discovered. In the most clear-cut situation, the properties of the non-ionized form were so favorable that there is no need to look for a more suitable solid form. Nevertheless, it is a common practice to conduct a screening of potential candidates to explore potential physical forms for development in the early phase of development where information, if doses, formulation principle, etc., is limited. The following two case studies are presented as examples indicating the width of the ﬁeld of salt and solid-state selection for drug substances. Case 1 is a brief report on quite an uncomplicated substance and Case 2 illustrates a typical and most frequently encountered situation. 2.7.3

Case 1: NVP-BS001

For NVP-BS001, an oral solid dosage form with immediate release was foreseen with an upper single-unit strength of around 100 mg. The free base, melting point 220 ∘ C, crystallizes as plates, 90% of them measuring less than 30 μm in diameter. The aqueous solubility in buﬀered systems below pH 7 is very high, ranging from 20 mg ml−1 to more than 100 mg ml−1 , in contrast to the low solubility in plain water (0.2 mg ml−1 with a resulting pH of 8.2). The stability in aqueous solution is excellent with less than 1% degradation after three days at 100 ∘ C in 0.1 N

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54

2 Alternative Solid Forms: Salts

HCl and 0.1 N NaOH. Signiﬁcant degradation in solution is observed only by treatment with hydrogen peroxide. No detectable decomposition is found in the bulk powder after three days at 100 ∘ C. The crystalline form remains unchanged after equilibration experiments in a series of relevant solvents, for which a suspension of the solid in the respective solvent is subjected to vibration at a given temperature (usually room temperature), as well as after mechanical stress. The powder is not hygroscopic, its water uptake at 94% RH being only 0.24% by weight. Summarizing the essential characteristics, the free base of NVP-BS001 displays high aqueous solubility and excellent solid-state stability. With the demonstration of rapid dissolution of the powder, the project team decided that the manufacture of a salt would oﬀer no improvement of physical properties but would rather add to the complexity of chemical synthesis and product formulation. Clearly, such an ideal situation is an exception, representing the rare case where the unionized form of a ionizable drug displays excellent aqueous solubility over the whole physiological pH range. In addition, the solid-state properties of free base crystals were also outstanding. Usually, compromises on physicochemical properties need to be drawn as one single solid form rarely displays exclusively favorable properties, and the decision requires that the biopharmaceutical, processing, and storage-relevant parameters of the alternative forms are carefully weighed against each other. 2.7.4

Case 2: NVP-BS002

NVP-BS002 is a weak diprotic base (pK a1 = 11.5; pK a2 = 4). The route of administration intended was oral with an immediate release dosage form. The strength of a single dose unit was aimed at up to 150 mg. An investigation for crystallization with possible counterions without toxicity potential showed that the only suitable salt candidates were the hydrochloride and the maleate. Both salts were further characterized and their physicochemical properties were compared to those of the free base. The data are compiled in Table 2.2. Crystallinity: According to XRPD, the crystallinity was medium for all the three forms. Melting point: All melting points were found to be above 185 ∘ C, and no problems for milling were expected from this aspect. Morphology: The hydrochloride and the maleate salts were isolated as needle-shaped crystals, whereas the free base crystallized as column-shaped primary particles. Hygroscopicity: Exposure to 92% relative humidity caused weight gain, which was highest for the hydrochloride with 0.6% after one day and increased to 5.4% after three days. Although this water uptake is signiﬁcant, it is slow enough to allow powder processing without problems. Solubility: The aqueous solubility in water is best for the hydrochloride, but this salt has the lowest solubility in 0.1 N HCl as expected by a common ion eﬀect. Although the intrinsic dissolution rate of the three candidates is identical at a pH = 4, the maleate and hydrochloride salts dissolve faster than the free base in 0.1 N HCl.

2.7 Case Reports

Table 2.2 Physicochemical properties of NVP-BS002 solid forms. Parameter

Free base

Hydrochloride

Maleate

Salt:base mass ratio

1.000

1.094

1.299

Crystallinity (XRPD)

Medium

Medium

Medium

Melting point (DSC) (∘ C)

203

243

185

Morphology

Column

Needles

Needles

Initial

0.11

0.10

0.42

After one day at 80% RH

0.12

0.11

0.35

Loss on drying (%) by TGA

After one day at 92% RH

0.15

0.68

0.56

After three days at 92% RH

0.12

5.51

0.62

0.1 M HCl

0.22

0.17

0.29

Buﬀer pH 4.0

0

(4.14)

The high-temperature form provides full discrimination in the solid state, whereas the low-temperature form does not. It is important to emphasize that the above statements can be reversed. This means that when the temperature of a transition is elevated or decreased, there exists at least one solid solution between one polymorph of the solute and the impurity (the second component). A study on 1,3-dimethylurea (DMU hereafter) and water has shown that c. 0.002 mol fraction of water (hundreds of ppm in mass) is enough to decrease the temperature of transition from 58 to 25 ∘ C [41]. The full schematic binary system is shown in Figure 4.10. Because DMU has a hygroscopic character, the apparent temperature of transition between the Fdd2 high-temperature form and the P21 21 2 low-temperature form ﬂuctuates according to the moisture uptake of the sample. Hundreds of ppm of water is enough to lower the polymorphic transition by several dozens of degrees. Similar results have been reported for ammonium nitrate with water, where the genuine temperature of transition is at 55–56 ∘ C. Unfortunately, many text books show that the temperature is at 32 ∘ C. Actually, 300 ppm of water is enough to drop the temperature of transition down to the metatectic invariant at 32 ∘ C [42]. 4.3.2.2 Two Stable Polymorphic Forms for One Component with Full Miscibility in the Solid State (at a Certain Temperature)

NB: In the following diagrams, there is no composition unit. Therefore, the domains are just represented with a suﬃcient width in temperature and in composition for the sake of readability, but those domains can be very narrow in temperature (some degrees or less) and in composition (hundreds of ppm or even less). In Figure 4.11a,b, the low-temperature form of component A (⟨A2 ⟩) leads to a complete solid solution with component B (⟨B⟩), whereas there is a limited domain of miscibility in the solid state between ⟨A1 ⟩ and ⟨B⟩. The highest concentration of B in ⟨A1 ⟩ corresponds to the eutectic temperature (Figure 4.11a) and to the peritectic temperature (Figure 4.11b). The metastable equilibria represented with dashed lines correspond to the full miscibility between ⟨A1 ⟩ and ⟨B⟩. Figure 4.11c shows a complete miscibility in the solid state for the high-temperature variety A (⟨A1 ⟩) with ⟨B⟩. By contrast, there is a limited

105

4 Thermodynamics of Polymorphs and Solvates

100

100

60 55

ssl

50 ssl + ssll 45

ssl + Liq

40

Temperature

80

60

35 30 25

M

20 15

10

ssll + Liq

ssll

5 0

ssI + Liquid Temperature

106

ssll +

–30

40 %Molar water

20

sslI + Liquid

Liquid

P 0

Liquid + sslI + < DMU, 1H2O >

E

Liq +

–20 + E’1 –40

E’2 0

20

40 60 %Molar water

80

100

Figure 4.10 Binary system between 1,3-dimethyurea (DMU) and water (P = 1 atm). The inset shows the left part of the metatectic invariant close to the pure DMU.

domain of solid solution between ⟨A2 ⟩ and B. The three-phase domain is the horizontal line segment and is called a monotectoid invariant. At Tμ , ssα1 (X1) ↔ ssα2 (X2) + ssβ(X3) with a (small) negative heat transfer from the left to the right The miscibility gap in the solid state has at its top a critical point where the two solid solutions ssα1 and ssβ collapse into a single phase ss. If point C is far from the solidus curve, it is likely that the kinetics of the solid–solid demixing will be diﬀusion rate limited. On cooling, there is a progressive spontaneous segregation. This phenomenon increases toward the monotectoid invariant

4.3 Polymorphism in Binary Systems

T

T

Liquid Liquid 3

TFA1

3

1 TFA1

TFA2

4

2

Tτ

1

2

4

TFA2 Tτ

A

B

A

(a)

(b)

T

T TFB

TFB

Liquid

B

Liquid

1 TFA1 1 3 Tτ

2

4

1

TFA1 1

6 Tμ

2

2 2

5

3 1

A (c)

B

A

B

(d)

Figure 4.11 Presence of a complete solid solution for one polymorph. (a) Complete miscibility between ⟨A2 ⟩ and ⟨B⟩, for the A-rich part of the diagram, the equilibria are metastable (dashed 1 ssβ + liquid; lines). The stable phases in equilibrium in the diﬀerent domains are 2 ssα1 + ssβ; 3 ssα1 + liquid; 4 sss (complete solid solution by substitution, ssα2 and ssβ are identical). There is a eutectic invariant with solid solution between ⟨A1 ⟩ (ssα1) and B (ssβ). (b) Similar case as (a) but the addition of ⟨B⟩ to ⟨A1 ⟩ increases the melting point of ssα1; thus, there is the formation of a peritectic invariant. Metastable equilibria are represented in dashed lines and correspond to the full miscibility between ⟨A2 ⟩ and ⟨B⟩. The phases in equilibrium in 1 ssβ + liquid; 2 ssα1 + ssβ; 3 ssα1 + liquid; 4 sss (complete solid the diﬀerent domains are solution by substitution identical to ssα2 and ssβ). (c) Complete solid solution at high temperature, monotectoid invariant: The presence of component B depresses the temperature of transition down to the monotectoid invariant at T 𝜇 . The phases in equilibrium 1 sss + liquid; 2 ssα1; 3 ssα1 + ssα2; 4 ssα1 + ssβ; in the diﬀerent domains are 5 ssα2 + ssβ; 6 ssβ. The shaded area shows the stability domain of ssα2 vs temperature and composition. Point C is the critical point of miscibility in the solid state between ssα1 and ssβ. (d) Special case: The domain of stability of ⟨A2 ⟩ is just inserted in the stability domain of ⟨A1 ⟩. 1 sss + liquid; 2 sss; 3 ssα2 + ssβ. The shaded area shows the stability domain of ssα2 vs temperature and composition.

where ssα1 reversibly decomposes into ss2 + ssβ. Figure 4.11d is a special case: component A has two polymorphs, but their stability domains alternate: Form I (⟨A1 ⟩) is stable at low temperature and high temperature. ⟨A2 ⟩ is stable in an intermediate domain in temperature. The crescent domain is the limit of stability of ss2. In other words, component B favors the stability of ss1 by closing the loop.

107

108

4 Thermodynamics of Polymorphs and Solvates

4.3.2.3 Two Stable Polymorphic Forms for One Component with Limited Miscibility in the Solid State

In Figure 4.12a–c, the addition of B enlarges the stability domains of form I toward low temperature. In Figure 4.12a, there is a metatectic invariant in (b) and (c); the low temperature invariant is called eutectoid, but it would have been T

T

TFA1

TFA1

Liquid 2

Tτ

1

2

3 5

Tm

6 8 7

A

6

1

8

3

Tτ

5

4

B

Tε

7

A

(a)

B

(b)

T

TFB Liquid

3

1 Tτ

Liquid 1

Tp 4

5

2 8

TFA1 Tε

2

T

1

2

TFA1

Tp 4

8

3

1

5

7

Tπ

7

6

6

2 A

(c)

Liquid

B

A

B

(d)

Figure 4.12 : Two stable polymorphic forms for component A both with limited miscibility with B. (a) The temperature of transition decreases as the concentration of B increases. The phenomenon continues down to the metatectic invariant at T m . The phases in equilibrium in 1 ssα1 + liquid; 2 ssα1; 3 ssα1 + ssα2; 4 ssα2 shaded area; the diﬀerent domains are 5 ssα2 + liquid; 6 ssβ + liquid; 7 ssα2 + ssβ; 8 ssβ. (b) Similar to (a), the temperature of transition decreases as the concentration of B increases. The phenomenon continues down to the eutectoid invariant at T 𝜀 (note that this invariant should be more appropriately named 1 ssα1 + liquid; 2 ssα1; metatectoid). The phases in equilibrium in the diﬀerent domains are 3 ssα1 + ssα2; 4 ssα2 shaded area; 5 ssα1 + ssβ; 6 ssβ + liquid; 7 ssα2 + ssβ; 8 ssβ. (c) Similar to (b), the temperature of transition decreases as the concentration of B increases. The phenomenon continues down to the eutectoid invariant at T 𝜀 (note that this invariant should be more appropriately named metatectoid). The phases in equilibrium in the diﬀerent 1 ssβ + liquid; 2 ssα1 + liquid; 3 ssα1; 4 ssα1 + ssβ; 5 ssα1 + ssα2; 6 ssα2 domains are 7 ssα2 + ssβ; 8 ssβ. (d) Contrary to (b), the temperature of transition increases shaded area; as the concentration of B increases. The phenomenon continues up to the peritectoid invariant at T π (note that this invariant should have received a more appropriately name). The 1 ssβ + liquid; 2 ssα1 + liquid; 3 ssα1; phases in the equilibrium in the diﬀerent domains are 4 ssα1 + ssβ; 5 ssα1 + ssα2; 6 ssα2; 7 ssα2 + ssβ; 8 ssβ.

4.3 Polymorphism in Binary Systems

T TFA1

Liquid 2

1

3 T

TFB1

4

Te TFB2

5

T

6 A

B

Figure 4.13 Contrary to Figure 4.12d, the temperature of enantiotropic transition of A decreases as the concentration of B increases. The phenomenon continues as a stable equilibrium down to the eutectoid invariant at T 𝜀 (note that this invariant should be more appropriately named metatectoid). The phases in equilibrium in the diﬀerent domains are 1 ⟨B⟩ + liquid; 2 ssα1 + liquid; 3 ssα1; 4 ssα1 + ⟨B⟩; 5 ssα1 + ⟨A2 ⟩; 6 ⟨A2 ⟩ + ⟨B⟩. Note that 3 can be extended to the pure monotropic if metastable equilibria are considered, domain form of B (⟨B2 ⟩) (ssα1 present a continuum with ssβ2 – i.e. complete solid solution by means of substitution).

more logical to call it metatectoid. In Figure 4.12c, the stability domain of form I is extended toward high and low temperature. In Figure 4.12d, both forms lead to solid solution with B so that their domains of stability are enlarged toward high temperature. In Figure 4.13, the high-temperature form of A (⟨A1 ⟩) leads to a complete solid solution with a monotropic form of B (⟨B2 ⟩), but a limited domain in composition corresponds to a stable domain (the shaded area). By contrast, the low-temperature form of A (⟨A2 ⟩) does not show any sign of miscibility with B. In Figure 4.14, the low-temperature form makes a complete solution with a monotropic form of the other component. Even if there is a complete miscibility, only a part of the domain has a stable character (shaded domain). The diﬀerence between Figures 4.13 and 4.14 lies in the miscibility at high temperature. 4.3.2.4 One Stable Form and One Metastable Form (Monotropic Character) with Full Miscibility for the Metastable Form

Figure 4.15a shows two components having a complete miscibility in the solid state with a monotropic form of the other component. This is called crossed isodimorphism [43]. It means that the order of stability of the two polymorphs of component A is inverted in the case of B and vice versa. A cooling of a molten mixture of c. 40 mol% in B below the melting points of the monotropic forms can either give (i) a mixture of ssα1 + ssβ1 (equilibrium), (ii) ssα1 (metastable), (iii) ssβ1 (metastable), or (iv) an amorphous mixture (out of equilibrium upon quenching below the glass transition of the mixture). Figure 4.15b shows a complete solid solution by substitution between the two monotropic forms of components A and B. This is totally opposite to the stable forms of A (⟨A1 ⟩) and B (⟨B1 ⟩), both of which exhibit no sign of miscibility in

109

110

4 Thermodynamics of Polymorphs and Solvates

TFA1

T

2 Liquid

Tp

TFB1

3 T

4

1 Te

5 TFB2

6

A

B

Figure 4.14 Binary system under constant pressure. The temperature of transition between ⟨A2 ⟩ and ⟨A1 ⟩ low- and high-temperature forms, respectively, increases as the amount of B 1 ⟨B⟩ + increases in the crystal lattice. The stable phases in equilibrium in every domain are 2 ⟨A1 ⟩ + liquid; 3 ⟨A1 ⟩ + ssα2; 4 ssα2 + liquid; 5 ssα2 (shaded area); 6 ssα2+ ⟨B⟩. liquid; 3 can be extended to the pure Note that if metastable equilibria are considered, domain monotropic form of B (ssα2 presents a continuum with ssβ2 – i.e. complete solid solution by means of substitution). T e and T p stand for the temperature of the eutectic invariant and the peritectic invariant, respectively.

T TFA1

TFB1

2

1

3

TFA2

T

Liquid

TFB1

TFA1 TFA2

Liquid 1 2

Te

5

4

TFB2 3

A (a)

B

A

TFB2 B

(b)

Figure 4.15 (a) The stable polymorph of one component (⟨A1 ⟩) forms a complete solid solution with the monotropic form of the other (⟨B1 ⟩). This case is called crossed isodimorphism. There are two limited stable domains whose extensions in composition are metastable down to the melting points of the monotropic forms. The stable phases in 1 ssβ1 + liquid; 2 ssα1 + liquid; 3 ssα1; 4 ssα1 + ssβ1; equilibrium in every domain are 5 ssβ1. In (b), form ⟨A1 ⟩ does not show any miscibility in the solid state with the stable ⟨B1 ⟩. By contrast, the two metastable monotropic forms ⟨A2 ⟩ and ⟨B2 ⟩ are miscible in all proportions. Thus, there is a metastable complete solid solution by means of substitution: between ⟨A2 ⟩ and its solid solution ssα2 and ⟨B2 ⟩ and its solid solution ssβ2. The stable phases 1 ⟨B1 ⟩ + liquid; 2 ⟨A1 ⟩ + liquid; 3 ⟨A1 ⟩ + ⟨B1 ⟩ in equilibrium in every domain are

4.3 Polymorphism in Binary Systems

the solid state (simple eutectic without any detectable domain of partial solid solution). Puriﬁcation will be easy to manage by using the stable forms and uneasy with the metastable monotropic forms. Seeding could be recommended to access to the mixture of stable forms. 4.3.2.5 One Stable Form and One Metastable Form (Monotropic Character) with Full Miscibility for the Metastable Form

In this paragraph, the full miscibility is represented by a shaded area. This domain corresponds to a solid solution by means of substitution. In the four cases depicted in Figure 4.16a–d, the two components have two enantiotropic forms 1 (high temperature) 2 (low temperature). The T

T Liquid

Liquid

TFA1 1

TFA1

TFB1

TFB1

TFB2

4 2

2

TFB2

3 1 5

6

3

7

TFA2 4

8

TFA2

A

B

A

(a)

B

(b)

T TFA1

T

Liquid

Liquid TFA1

1

2

2

TFB1 3

4

TFA2

8 5

7 6

TFB2 TFA2

9

4

1 3

TFB1 TFB2

5

A (c)

A

B

B

(d)

1 ss1 + liquid; 2 ss1; Figure 4.16 (a) The phases in stable equilibrium in every domain are 3 ss1 + ss2; 4 ss2. This is a case of isodimorphism with a dual case of complete solid solutions: these solid solutions are obviously of substitution type (by opposition to insertion 1 ssβ1 + liquid; type). (b) The stable phases in stable equilibrium in every domain are 2 ssα1 + liquid; 3 ssβ1; 4 ssβ1 + ss2; 5 ss2 + liquid; 6 ssα1; 7 ssα1 + ss2; 8 ss2. 1 ss1 + liquid; 2 ss1; (c) The stable phases in stable equilibrium in every domain are 3 and 4 ss1 + ss2; 5 ss2. (d) The stable phases in stable equilibrium in every 1 ssβ1 + liquid; 2 ssα1 + liquid; 3 ssβ1; 4 ssβ1 + ss2; 5 and 8 ss2 + liquid: domain are 6 ssα1 + ss2; 7 ssα1; 9 ss2.

111

112

4 Thermodynamics of Polymorphs and Solvates

low-temperature forms are isostructural and can form a stable complete solid solution by substitution. In Figure 4.16a, the two forms are isostructural; they form two complete solid solutions: ss1 and ss2. In Figure 4.16b, at high temperature, the action of A in ⟨B⟩ is opposite to that of B in ⟨A⟩. Indeed, the presence of A in the high-temperature form of B (ssβ1) induces a depression in the polymorphic transition of the second form of B (ssβ2). By contrast, the presence of B in ssα1 raises the temperature of transition between the low-temperature form and the high-temperature form of ⟨A⟩. The invariant at high temperature is a metatectic. The one at low temperature is a binary eutectic. In Figure 4.16c, the two complete solid solutions do not behave in the same way. The high-temperature one (ss1) gives a single loop. The ss2 gives an intermediate maximum for a speciﬁc composition. This is another case of isodimorphism but a little bit less straightforward than in Figure 4.16a. In Figure 4.16d, the actions of the two components are also inverted as in (b), but in this case, the “low-temperature form” ss1 is strongly stabilized by the presence of the two components in the crystal lattice. Actually, this low-temperature form exhibits the highest thermal stability when the composition is close to 50–50 (note than there is no intermediate compound). 4.3.2.6 Two Isostructural Monotropic Forms When Mixed Could Lead to an Enantiotropy

The shaded parts in Figure 4.17a–c denote the stable domains in temperature and composition of the solid solutions between the two isostructural monotropic phases. It clearly shows that the intermediate mixed crystals are more stable than the mixture (homogeneous or not) of stable polymorphs (form 1) for certain compositions and at certain temperatures. In other words, the union of the “weakest varieties” could be more stable than the association – as a complete solid solution or partial solid solutions or even pure components – of the strongest forms [44]. Figure 4.17c shows a case similar to (b) except that the two stable pure components form partial solid solutions with the other component. In the case depicted in Figure 4.17b, the stable intermediate compound is actually a part of the complete solid solution between the two metastable forms. At low temperature, it reversibly decomposes into a mixture of ⟨A1 ⟩ and ⟨B1 ⟩ through a eutectoid invariant at T 𝜀 . In the case depicted in Figure 4.17c, the mixed crystals in the shaded domain are stable at low temperature. This should not be confused with an intermediate compound. The metastable equilibria clarify the context and serve to give the exact nature of this solid phase. It is also worth mentioning that symmetry-breaking experiments can occur when several polymorphs exist for a racemic mixture. Other necessary conditions have been detailed in a series of papers [45–51]. 4.3.2.7 Limitations of the Concept of Polymorphism and Other Solid(s) to Solid(s) Transitions

Every transition involving only solid phases are not related to polymorphism! Indeed, Figure 4.18a,b illustrates two situations that correspond to three solid phases at a time. In Figure 4.18a below, T π , the stoichiometric phase ⟨AB⟩ is

4.3 Polymorphism in Binary Systems

T

T

TFB1

4

Liquid

TFB1 1

Liquid

TFA1

TFA1

1

3

2

4

2

6

3

7 6

5 5

7

T 8

8

A

B

A

B

(b)

(a) T

Liquid

TFA1 3

2

4

8

1 TFB1

7 5

6

A

9

B

(c)

Figure 4.17 The shaded domain corresponds to the solid solution ss2 stemming from mixed crystals of the monotropic forms ⟨A2 ⟩ and ⟨B2 ⟩, which are isostructural. (a) The stable phases in 1 ssβ1 + liquid; 2 ssα1 + liquid; 3 ss2 + liquid; stable equilibrium in every domain are 4 liquid + ss2; 5 and 6 ss2 + ss1; 7 ss2; 8 ss1. ⟨A1 ⟩ and ⟨B1 ⟩ are also isostructural, but their solid solution ss1 has a Gibbs free energy higher than that of ss2 in the intermediate 7 . (b) The stable phases in stable equilibrium in every domain are 1 ⟨B1 ⟩ + liquid; domain 2 ⟨A1 ⟩ + liquid; 3 and 4 ss2 + liquid; 5 ⟨A1 ⟩ + ss2; 6 ⟨B1 ⟩ + ss2; 7 ss2; 8 ⟨A1 ⟩ + ⟨B1 ⟩. ⟨A1 ⟩ and ⟨B1 ⟩ do not make any solid solution. (c) The stable phases in stable equilibrium in 1 ssβ1 + liquid0; 2 ssα1 + liquid; 3 and 4 ss2 + liquid; 5 ssα1 + ss2; every domain are 6 ss2 + ssβ1; 7 ss2; 8 ssα1; 9 ssβ1.

stable. Conversely, above that temperature, this compound is not stable anymore when compared to the mixture of ⟨A⟩ and ⟨B⟩. At T π , there is a three-phase invariant: ⟨AB⟩ ↔ ⟨A⟩ + ⟨B⟩; ΔH > 0 from left to right

(4.15)

At this temperature, ΔG = 0 and consequently ΔS > 0. In Figure 4.18b, above T 𝜀 , the stoichiometric phase ⟨A2 B3 ⟩ is stable. Conversely, below that

113

114

4 Thermodynamics of Polymorphs and Solvates

T

TFB

Liquid TFA

T

Liquid

TFA

1

TFB

4 1

2

2

3 3

6

5 Tπ

4

5 〈AB〉

A (a)

Tε

7 B

A

〈A2B3〉

B

(b)

Figure 4.18 (a) Peritectoid invariant at T π . The stable phases in equilibrium in every domain 1 ⟨B1 ⟩ + liquid: 2 ⟨A1 ⟩ + liquid; 3 ⟨A⟩ + ⟨B⟩; 4 ⟨A⟩ + ⟨AB⟩: 5 ⟨AB⟩ + ⟨B⟩. (b) Eutectoid are 1 ⟨B1 ⟩ + liquid; invariant at T. The stable phases in equilibrium in every domain are 2 ⟨A1 ⟩ + liquid; 3 and 4 liquid + ⟨A2 B3 ⟩; 5 ⟨A⟩ + ⟨A2 B3 ⟩; 6 ⟨A2 B3 ⟩ + ⟨B⟩; 7 ⟨A⟩ + ⟨B⟩.

temperature, this compound is not stable anymore when compared to the mixture of ⟨A⟩ and ⟨B⟩. At T 𝜖 , there is a three-phase invariant: ⟨AB⟩ ↔ ⟨A⟩ + ⟨B⟩ ΔH < 0 from left to right

(4.16)

At this temperature, ΔG = 0 and consequently ΔS < 0. Other three-phase invariants such as binary monotectoid invariant and invariants in higher order systems (ternary, quaternary, etc.) exist, but details on these extra solid(s) to solid(s) transition are out of the scope of that chapter [52]. Deliberately, no G vs composition curves have been proposed as complementary view of the impact of polymorphism with several components. Polymorphism in the strict sense of the term involves only two phases whatever the order of the system is. The existence of order–disorder transition has also been proposed for racemic compositions of enantiomers [7]. 4.3.3

Solvates

The term “Solvate” encompasses the class of compounds where one or several molecules of solvent can be incorporated in the crystal lattice. A large collection of solvent molecules can exist in organic and metal organic components. These solvent molecules can be positionally and/or orientationally disordered. At that stage, it is necessary to clarify the terminology used for diﬀerent kinds of solvates: • Stoichiometric solvates are compounds having a ﬁxed ratio between the solvent molecule(s) and the solute, e.g. A-(H2 O)n . For instance, a monohydrate, sesquihydrate, dehydrate, etc., NB it does not mean that the solvent molecules occupy a single type of crystallographic site. For instance, a sesquihydrate can be crystallographically speaking and is represented by A-H2 O-0.5H2 O,

4.3 Polymorphism in Binary Systems

•

•

• •

• •

•

i.e. one water molecule occupies a site with twice the multiplicity as that of the other. Nonstoichiometric solvates are crystalline compounds having a variable ratio between the solvent molecules and the solute. For example, the phase can be written: A-(H2 O)X with limit 1 < x < limit 2 at a given temperature T 1 . In other words, this nonstoichiometric compound exists for diﬀerent amounts of water molecules inside the crystal lattice. At T 1 , this hydrate exists within a lower limit (L1 ) and an upper limit (L2 ). Below or above those limits, the system will consist of at least two phases. Inside the monophasic domain, many physical properties vary as a function of the water content (x). The experimental diﬀerentiation between stoichiometric and nonstoichiometric will be examined later. Hydrates: The solvent molecules are H2 O. It is important to note that this subclass of solvates is by far the most common for inorganic compounds, but is often observed for organic molecule as well. In the case of inorganic crystals, the formation of hydrates can lead to a complete solidiﬁcation of the system. This property is used for cements, concrete, plaster, etc. Molecules as poorly hydrophilic as methane, ethane, and many others, as well as several monoatomic gases such as xenon, can produce hydrates. These compounds have been named clathrates. By varying temperature and pressure, it may therefore be assumed that just about every compound can form at least one hydrate. When organic molecules get larger, the probability to ﬁnd a hydrate under ambient conditions increases as well. Typically, proteins contain more than one-third of their mass as water. Heterosolvates: Subclass of solvates that contain at least two diﬀerent solvent molecules, every solvent molecule having its particular crystallographic site. Mixed solvates: Subclass of solvates that contain at least two diﬀerent solvent molecules, but the two solvent molecules are in competition on the same crystallographic site, e.g. rulid-H2 O(X) -acetonitrile(1−X) with X 𝜖 [0; 1] [53]. The two solvent molecules can substitute one another across the full range of compositions. Of course, the composition of the medium is, most of the time, not reﬂected by the composition of the solid, which can show a preference for one solvent molecule. Isomorphous desolvates: Solid phases whose structures remain almost identical with or without the solvent molecules inside their crystal lattices. Eﬄorescent solvates: Solid phases that spontaneously release their solvent molecules “S” under speciﬁc environmental conditions, namely of temperature and partial pressure of S. Hygroscopic solids: Solid phases that absorb moisture above a certain temperature and humidity. The ultimate evolution will be a complete dissolution or transformation into a hydrate.

In the author’s experience, the conditional probability to detect additional solvates when one has already been obtained is greater than the probability to ﬁnd the ﬁrst solvate. In other words, when one solvate has been discovered, there is a good chance to ﬁnd others [54, 55].

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4 Thermodynamics of Polymorphs and Solvates

4.3.3.1 Diﬀerentiation Between Stoichiometric and Nonstoichiometric Solvates

This is an important problem in pharmaceutical industry where dosage is a crucial issue and where persistent physicochemical properties of the solid are mandatory. Basically, if a hydrate is nonstoichiometric, the exact dosage of the drug substance could pose a problem as it depends on the amount of water molecules at the time the drug substance is mixed with excipients. The ﬂuctuations in temperature lead to concomitant releases and reuptakes of the water molecules. These cycles can deteriorate some physical attributes of the powder or the tablets. Figure 4.19 shows on the left a stepped pathway with hysteresis. It corresponds to a stoichiometric hydrate. In the large majority of cases, there are nucleation and crystal growth of the hydrate and conversely a destructive (and possibly) reconstructive mechanism during dehydration. By contrast, the illustration on the right with the sigmoid shape pathway corresponds to a nonstoichiometric hydrate. Thermodynamically and also mechanistically, reversible release and uptake of water molecules occur, and almost no hysteresis exists between sorption and desorption. Of course, these behaviors take into account attainment of equilibrium that supposes a slow evolution in RH vs time and a crystal size distribution that helps the solid–vapor exchanges (i.e. small particles). Figure 4.20 is another way to illustrate the concept of nonstoichiometric hydrates. The monophasic domain is not restricted to a vertical line, but on the right-hand side, this monohydrate can sustain some vacancies of water molecules. By contrast, on the left-hand side of that domain, the boundary is indeed vertical as soon as every crystallographic site is occupied. One cannot possibly insert more than a single water molecule per molecule of solute because no other crystallographic site is available. The vast majority of the solvates, regardless of whether they are stoichiometric or not, do not give a congruent fusion but rather a noncongruent fusion [56], also called peritectic transition. The exceptions come from hydrates with a low melting point. For instance, hydrazine leads to a dihydrate with a congruent fusion at −54 ∘ C. Mass Mass

m0

RH 0

95%

m0 0

RH 95%

Figure 4.19 Ideal cases that show the moisture uptake and release vs relative humidity at a constant temperature. (a) Stoichiometric compound, (b) nonstoichiometric compound. RH stands for relative humidity.

4.3 Polymorphism in Binary Systems

Figure 4.20 Binary system showing a nonstoichiometric hydrate. Full lines correspond to stable equilibria. Dashed lines correspond to metastable equilibria: metastable solubility of the anhydrous M in water below T p and the metastable eutectic between M and water. The stable phases in equilibrium 1 ⟨M⟩ + saturated in every domain are 2 ⟨M⟩ + M-(H2 O)1−x ; solution; 3 M-(H2 O) + saturated solution; 4 M-(H2 O)1−x 0 ≤ x ≤ 𝜀 with 𝜀 = f (T); 5 ⟨ice⟩ + M-(H2 O); 6 ⟨ice⟩ + saturated solution.

T

Undersaturated solution

TFM

1 Tp 2

3

Te

Te′

6 4

5

M-H2O

H2O

M

It is possible to dehydrate in an aqueous solution! The temperature of the 1 in suspension has to be adjusted above the peritectic temperature (domain Figure 4.20). The ﬁltration and the subsequent drying also have to be performed above T p to make sure that no rehydration could take place. 4.3.3.2

Hygroscopicity, Deliquescence, and Eﬄorescence

Figure 4.21a illustrates the behavior of a relatively hygroscopic material; indeed, above 60% RH at temperature T 1 , the product tends to absorb the environmental moisture leading to a complete dissolution. Below 60% RH, the pure crystals ⟨M⟩ are in equilibrium with the gas phase. Starting from pure ⟨M⟩ at that temperature T 1 , if the powder is exposed to 75% RH. The evolution of the system is depicted by arrows from point I to point F on the blue horizontal line segment. This pathway means that the powder will ﬁrst be sticky, and then clearly the solid will dissolve completely in the liquid phase: a saturated solution at point S. u.s.s.+ (H2O)v

PH2O

u.s.s. 〈M〉 + saturated solution I

S

u.s.s. + (H2O)v

PH O 2

Saturated gas u.s.s. + (H2O)v

F

〈M〉

〈M-3H2O〉 + saturated solution

+

〈M-3H2O〉 E

60%

80% S

〈M〉 + (H2O)vap H2O

60%

15% H2O

M

Figure 21a at T1 (a)

F

〈M-3H2O〉 + (H2O)vap

〈M〉 + (H2O)vap

M

u.s.s.

Figure 21b at T1 (b)

Figure 4.21 (a) Evolution of a solute (up to deliquescence) exposed in an atmosphere above 60% RH where ⟨M⟩ is not stable. (b) Possible evolution of the same solute when a hydrate can crystallize (u.s.s. = undersaturated solution).

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Ultimately, this solution will become undersaturated and in equilibrium with the vapor phase. Point F represents the ﬁnal evolution, but as detailed below, it is a metastable equilibrium. It is implicitly assumed here that the vapor phase is an inﬁnite reservoir of moisture. Thus, starting from a dry solid, the excessive environmental RH (>60%) will lead to a complete dissolution of the solute (illustration of a deliquescent phase). Nevertheless, the system could subsequently ﬁnd a novel way to return to a solid phase in equilibrium with the gas phase. Figure 4.21b shows this secondary evolution. A trihydrate has appeared by spontaneous nucleation (or by seeding). The ﬁnal evolution of the system represented by point E is now in the ⟨M-3H2 O⟩ + (H2 O)vap domain. Therefore, without modiﬁcation of the environmental conditions, the system will release the excess of adsorbed water to quantitatively yield the trihydrate in stable equilibrium with the gas phase (point E). The two steps depicted above are not always so well separated. Indeed, the point representative of the system can make a U turn before reaching point E. The trihydrate can reversibly be decomposed by putting that phase at T 1 and a relative humidity below 15%. Under these conditions, the trihydrate is called eﬄorescent. Figure 4.22 shows the combined presence of polymorphs: ⟨M1 ⟩ and ⟨M2 ⟩ and the solvate (⟨M-An⟩ (stoichiometric compound)). The two enantiotropic forms of M are in equilibrium at T τ . Above that temperature ⟨M1 ⟩ is more stable than ⟨M2 ⟩, below that temperature ⟨M2 ⟩ is stable. There are three stable invariants. At T p , the peritectic invariant of the solvate, i.e. the noncongruent melting of the solvate, ⟨M-An⟩ is in equilibrium with a doubly saturated solution and ⟨M1 ⟩. At T τ , there is a two-phase invariant corresponding to the polymorphic transition ⟨M1 ⟩ ⟨−⟩ ⟨M2⟩. At T e , the solution is doubly saturated in ⟨M-An,⟩ and in ⟨A⟩. There are also three horizontal dashed lines symbolizing metastable equilibria. At T τ , this is the extension of the stable two-phase invariants. When the system shows this metastable equilibrium, it implies that the solvate did not crystallize, and all the curves and invariants in which the solvate is involved should not be considered. The two other metastable invariants are eutectic invariants, which involve at T e ′ a doubly saturated liquid and ⟨M2 ⟩ + ⟨A⟩, and at T e ′′ a doubly Figure 4.22 Isobaric binary system between a solute M and a solvent A. If the system is in stable equilibrium, domains 1–6 contain the 1 ⟨M1 ⟩ + saturated following phases: 2 ⟨M1 ⟩ + ⟨M-An⟩; solution; 3 ⟨M2 ⟩ + ⟨M-An⟩; 4 ⟨M-An⟩ + ⟨A⟩; 5 ⟨M-An⟩ + saturated solution; 6 ⟨A⟩ + saturated solution.

TF1 Under-saturated solution

1

Tp

2 Tτ 3

5 6

Te′

Te

Te″ 4

M

〈M-An〉

A

4.4 Ternary Systems

Figure 4.23 Isobaric binary system between a solute M and a solvent A. If the system is in 1 – 6 represent stable equilibrium domains, 1 ⟨M1 ⟩ + saturated the following phases: 2 ⟨M2 ⟩ + saturated solution; solution; 3 ⟨M2 ⟩ + ⟨M-An⟩; 4 ⟨M-An⟩ + saturated 5 ⟨M-An⟩ + ⟨A⟩; 6 ⟨A⟩ + saturated solution; solution.

TF1 TF2

Under-saturated solution 1

Tτ 2

Tp

4

3

Te Te″

6 T e′

5 M

〈M-An〉

A

saturated liquid and ⟨M1 ⟩ + ⟨A⟩. It is worth noting that an in situ desolvation by thermal treatment above T p will deliver ⟨M1 ⟩. Figure 4.23 also shows the combined presence of polymorphism of ⟨M⟩ and the formation of the solvate, ⟨M-An⟩ (stoichiometric compound). The two enantiotropic forms of M are in equilibrium at T τ above the peritectic invariant of the solvate. There are two stable three-phase invariants: at T p , the peritectic invariant of the solvate, i.e. the noncongruent melting of the solvate ⟨M-An⟩, is in equilibrium with a doubly saturated solution and ⟨M2 ⟩. At T e , a eutectic invariant, the solution is doubly saturated in ⟨M-An⟩ and in ⟨A⟩. There are also two horizontal dashed lines symbolizing two metastable eutectic invariants, which involve, at T e ′ , a doubly saturated liquid ⟨M2 ⟩ + ⟨A⟩ and, at T e ′′ , a doubly saturated liquid and ⟨M1 ⟩ + ⟨A⟩. An in situ desolvation by heating above T p and below T τ will lead to ⟨M2 ⟩.

4.4 Ternary Systems Note that U.S.S. stands for unsaturated solution, i.e. homogeneous solution in equilibrium. Figure 4.24a–d depicts diﬀerent probable cases between a solute M, water, and an organic solvent. In these four-phase diagrams, the solute is much less soluble in water than in the organic solvent. In Figure 4.24a, the stoichiometric DMSO solvate has only a limited stability domain where it is the only stable solid phase in equilibrium with a saturated solution. Point I is the common point of the two solubility curves, i.e. that of the DMSO solvate and that of the solute. The triangle M-I-M_DMSO is a triphasic domain where the two solid phases can coexist with the doubly saturated solution I. Starting from a concentrated suspension of ⟨M_DMSO⟩ in DMSO solution, it is possible to desolvate M_DMSO at the temperature of this isotherm by addition of a suﬃcient quantity of water so that the overall composition of the 3 . Owing to the high boiling point of DMSO, this prosystem enters in domain cess has a substantial beneﬁt in comparison to thermal treatment, associated or not, with a drop in pressure.

119

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4 Thermodynamics of Polymorphs and Solvates

DMSO

MeOH

u.s.s. I

1

u.s.s. I

I″ 1

I′

2

M_DMSO

M-MeOH 3

2

3 4

M

M

H2O

(a)

H2O

M-H2O

(b) DMF

Acetonitrile

u.s.s.

u.s.s. 1

I 1 K M-DMF 7 M (c)

4 6

2 H 5

M-2H2O

Solvate

J 3

2

3 M

H 2O

M-H2O

(4)

H2O

(d)

Figure 4.24 (a–d) Isothermal and isobaric ternary phase diagrams, M (solute), water, and organic solvent. (a) There is a DMSO monosolvate, (b) there are a methanol solvate and a monohydrate, (c) there are a DMF solvate, a hydrate, and a heterosolvate H, and (d) there are a monohydrate and an acetonitrile solvate that form a mixed solvate. In every domain, the 1 ⟨M_DMSO⟩ + saturated solution; 2 ⟨M⟩ + ⟨M_DMSO⟩ doubly stable phases are (a) 3 ⟨M⟩ + saturated solution. (b) 1 ⟨M-MeOH⟩ + saturated solution; saturated solution I; 2 ⟨M-MeOH⟩ + ⟨M-(H2 O)⟩ + doubly saturated solution I; 3 ⟨M-(H2 O)⟩ + saturated solution; 4 ⟨M⟩ + ⟨M-(H2 O)⟩ + ⟨M-MeOH⟩. (c) 1 ⟨M-DMF⟩ + saturated solution; 2 ⟨H⟩ + saturated 3 ⟨M-2H2 O⟩ + saturated solution; 4 ⟨M-DMF⟩ + doubly saturated solution I + ⟨H⟩; solution; 5 ⟨M-2H2 O⟩ + doubly saturated solution J + ⟨H⟩; 6 ⟨M-2H2 O⟩ + ⟨M-DMF⟩ + ⟨H⟩; 7 ⟨M-2H2 O⟩ + ⟨M-DMF⟩ + ⟨M⟩. (d) 1 undersaturated solution; 2 ⟨M_Acetonitrile(1−X) H2 OX ⟩ + saturated solution; 3 ⟨M⟩ + ⟨M_Acetonitrile(1−X) H2 OX ⟩ .

In Figure 4.24b, there are a monomethanol solvate and a monohydrate. The pure solute ⟨M⟩ cannot be in stable equilibrium with any solution whatever the ratio between methanol and water. Nevertheless, there is a metastable equilibrium, which involves ⟨M⟩ and a metastable saturated solution (dashed line). This line ends at point I′ where the metastable branch of the methanolate solubility ends as well. Therefore, if the kinetics of crystallization of the hydrate is slow and by contrast the corresponding kinetics of ⟨M⟩ is fast, it is possible to obtain the pure transient metastable ⟨M⟩ phase by addition of water to a concentrated methanolic suspension. If ﬁltration and drying are performed fast enough,

4.4 Ternary Systems

⟨M⟩ could be obtained without heating with a good yield. An alternate process is to seed and to slurry the suspension in order to obtain the monohydrate. There is also another metastable point I′′ (close to the binary side M-MeOH), which corresponds to the doubly saturated solution at the intersection of the metastable solubility of M and the extrapolation of the hydrate solubility curve. There is another metastable three-phase domain delineated by I′′ , M, and M-H2 O. Figure 4.24c is a similar case as (b), except that the two solvates have a limited domain of stability due to the existence of heterosolvate H. The three solid phases that can exist in a stable equilibrium with a saturated solution are the DMF monosolvate, the dihydrate, and the heterosolvate H. Point I is a doubly saturated solution in DMF monosolvate and heterosolvate H. Point J corresponds to the doubly saturated solution in dihydrate and heterosolvate H. ⟨M⟩ can only be in a metastable equilibrium with its saturated solution. The metastable solubility curve of ⟨M⟩ is represented by a dotted line. Point K corresponds to the metastable invariant point when the heterosolvate H does not appear. It represents a doubly saturated solution in DMF monosolvate and dihydrate. Several other metastable invariants, i.e. doubly saturated solutions, are not represented for the sake of clarity (for instance, involving M and M-DMF, M and M-2H2 O, H and M). Figure 4.24d represents the case of a mixed solvate ⟨M_Acetonitrile(1−X) _H2 OX ⟩ with 0 ≤ X ≤ 1. Thus, there is a complete solid solution between two pure solvates [57]. The isothermal phase diagram contains three domains, i.e. one monophasic area, the undersaturated solution (USS), and a biphasic area shaded by the tie-lines. These line segments connect the composition of the saturated liquid phase and that of the solid phase. In perfect agreement with the Gibbs phase rule, these two compositions are not independent because in this biphasic domain, the number of degrees of freedom is 1 (v′′ = 3 − 2 = 1). It is often seen in phase diagrams that those tie-lines converge to a point (or a restricted area) inside or outside (i.e. virtual compositions) the diagram. In case this point is the M apex, it would mean that the behavior of that solid solution is almost ideal without any discrimination between the liquid phase and the solid phase. The third domain in a shape of a triangle is composed of two phases: ⟨M⟩ and ⟨M_Acetonitrile(1−X) _H2 OX ⟩ with 0 ≤ X ≤ 1 [53]. 4.4.1

Chiral Discrimination via the Formation of Solvates

A screen for conglomerates (i.e. the racemic mixture is a mechanical mixture of homochiral crystals) is an important search for the preparative access to a pure chiral substance. It can also be used for the resolution of the racemic mixture via the application of the preferential crystallization [58] or even for the deracemization via Viedma ripening [59], temperature cycling [60], and ultrasound [61] if the interconversion between the two enantiomers can be easily ensured in the same medium as that used for the selective crystallization. Let us suppose that we have a chiral amine that we wish to resolve on the industrial scale. One possibility among others will be to test diﬀerent non-chiral acidic components so that the two enantiomers will not lead to the crystallization of a

121

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4 Thermodynamics of Polymorphs and Solvates

H2O

1

Solid solution + S, 1H2O

7

2

Solid solution + R, 1H2O

3

Solid solution J + S, 1H2O + R, 1H2O

4

S, 1H2O + R, 1H2O + liquid I

5

S, 1H2O + saturated solution

6

R, 1H2O + saturated solution

7

Unsaturated solution

6

5 I 4

R, H2O

S, H2O 1

3 J

S

2 R

T

Liquid

Figure 4.25 Schematic ternary isotherm and binary system (increasing temperature downward) of a couple of enantiomers that form a complete solid solution in the binary system and a conglomerate of hydrates (below a peritectic temperature).

heterochiral compound (racemic compound). There is a large variety of organic acids that can be used to ﬁnd a conglomerate-forming system. Nevertheless, it is advisable to test several organic solvents for every salt because it increases the possibility to identify the spontaneous chiral discrimination in the solid state. The presence of three partners of crystallization (the amine, the acid, and the solvent) has shown to be eﬀective in several screens of conglomerates [62–66]. Figure 4.25 gives a simpliﬁed representation of the (binary and ternary) heterogeneous systems between (+) and (−) trans-1,2-diaminocyclohexanium citrate monohydrate with water. There is barely any chiral discrimination in the binary system without water. The complete solid solution induces only a very poor segregation in the biphasic solid–liquid loops. By contrast, the ternary isotherm shows a full chiral discrimination as soon as a suﬃcient amount has been introduced in the system. The (+) and (−) monohydrates salts make a stable conglomerate without detectable solid solution, i.e. a spontaneous resolution at its best. (+) and (−) Triethanolammonium modaﬁnate (TMM) [64] with water results in two situations represented in Figure 4.26. The isotherm above T p corresponds to a racemic compound-forming system. The isotherm represented at T < T p corresponds to a conglomerate-forming system. Thus, at T < T p , it is possible to resolve the racemic mixture by application of the so-called preferential crystallization [58]. Figure 4.27 depicts the resolution of a chiral molecule by formation of diastereomeric salts. Salt p is less soluble than salt n. Below the peritectic transition at T p a hydrate of the less soluble salt is even less soluble than the salt p. This beneﬁcial case will render the resolution more eﬃcient by operating below the ternary peritectic transition.

4.5 Temperature of Desolvation – Tg and New Polymorphs Only Accessible

A = H2O

u.s.s. 1

Isotherm < Tp 2

3

Isotherm > Tp II III

I IV S

V RS

R

1 ⟨TMM(S)⟩ + saturated Figure 4.26 The stable phases in every domain are at T < T P : 2 ⟨TMM(R)⟩ + saturated solution; 3 ⟨TMM(S)⟩ + ⟨TMM(R)⟩ + doubly saturated solution; racemic solution. The stable phases in every domain are at T > T P ar – I: ⟨TM(S)⟩ + saturated solution; II: ⟨rac-TM⟩ + saturated solution; III: ⟨TM(R)⟩ + saturated solution; IV: ⟨TM(S)⟩ + ⟨rac-TM⟩ + doubly saturated solution; V: ⟨TM(R)⟩ + ⟨rac-TM⟩ + doubly saturated solution.

Figure 4.28 depicts a rare case that can have dramatic consequences. Three times in the author’s career, the following phenomenon has happened. A resolution was functioning reasonably well up to one day, when the slurry was kept under stirring during a whole week end (these events happened at the pilot scale and even at the industrial scale after years of success). On the following Monday, ﬁltration gave an intermediate compound whose asymmetric unit contained the molecular species of salt n and salt p plus a solvent molecule A. After the apparition of that phase, the site was contaminated, and no resolution was anymore possible in that solvent. Therefore, a major modiﬁcation of the process was necessary [67].

4.5 Temperature of Desolvation – Tg and New Polymorphs Only Accessible Through a Smooth Solvation – Desolvation Process The two main topics of this section are connected when desolvation and re-solvation are considered. The so-called “Rouen-96” model [68], mainly applicable to organic compounds, has been proposed to classify the various pathways between the mother (solvate) phase and the daughter phase (supposed to be non-solvated but could apply to a sub-solvate as well). The most important concept of that model is the limit of transmission of the structural information. A crystal (here initially a solvate) contains a certain quantity of structural information (i.e. the location of the atoms in the unit cell). The whole amount or a part of this structural information can be transmitted to the daughter phase.

123

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4 Thermodynamics of Polymorphs and Solvates

A

Te

9

ε T

2

4

1

10 8

π

T

(salt p) -A Tp

3 Te′ Salt n

Salt p 7

6

5

T

Figure 4.27 Polythermic projection of the ternary system between two diastereomeric salts and an achiral solvent. The three binary systems are put ﬂat on the plane of projection. Salt n and salt p give a eutectic without partial solid solution. Salt n–solvent A binary system shows a simple eutectic. Salt p–solvent A binary system includes a stable eutectic at T e , a metastable eutectic at T e′ and peritectic transition at T p . From the binary eutectic between the two diastereomers, a stable monovariant valley goes down to point π, a ternary peritectic transition of ﬁrst kind. Two monovariant valleys merge to give a single monovariant valley for T < T π , the solvate of salt p, ⟨(salt p)-A⟩ could coexist with salt n in equilibrium. At point 𝜀, the ternary eutectic, three monovariant valleys gather. Below T 𝜀 , there are three solids in equilibrium: ⟨Salt n⟩, ⟨Salt p-solvate⟩, and ⟨A⟩. If ⟨salt p-solvate⟩ does not crystallize, the system could rely on the metastable equilibrium shown with dotted lines. Three monovariant valleys gather at point 𝜀′ . In that case, the resolution will be less productive than that involving the hydrate. If the system is in stable equilibrium, domains 1–10 contain the following phases: 1 ⟨salt p⟩ + saturated solution; 2 ⟨(salt p)-A⟩ + saturated solution; 3 ⟨(salt p)-A⟩ + ⟨salt p⟩; 4 ⟨(salt p)-A⟩ + ⟨A⟩; 5 ⟨salt p⟩ + liquid; 6 ⟨salt n⟩ + liquid; 7 ⟨salt n⟩ + ⟨salt p⟩; 8 ⟨salt 9 ⟨A⟩ + saturated solution; 10 n⟩ + saturated solution; ⟨salt n⟩ + ⟨A⟩ .

It is important to distinguish two classes among the thermodynamic reversibility in the solvation–desolvation process. A solvation–desolvation equilibrium could proceed by destruction and reconstruction in both directions [69, 70]. It can also proceed through a cooperative process that preserves at least a part of the structural information [68]. In this second case, the extreme situation is a topotactic reaction in which the crystal structures of the solvate and the non-solvated are almost identical (except, of course, the presence of the solvent molecules) [71–73]. For complex situations, structural similarities can be

4.5 Temperature of Desolvation – Tg and New Polymorphs Only Accessible

A 7

T

1

8 6

T

2

Salt n

Salt p 5

4

3

T

Figure 4.28 If the system is in stable equilibrium, domains 1–8 contain the following phases: 1 ⟨salt p⟩ + saturated solution; 2 ⟨salt p⟩ + ⟨A⟩; 3 ⟨salt p⟩ + liquid; 4 ⟨salt n⟩ + liquid; 5 ⟨salt n⟩ + ⟨salt p⟩; 6 ⟨salt n⟩ + saturated solution; 7 ⟨A⟩ + saturated solution; 8 ⟨salt n⟩ + ⟨A⟩.

observed from a solvate to a sub-solvate, and on further desolvation, the process could be fully destructive–reconstructive (or not, for the latter) [74]. Figure 4.29 illustrates a common case of a solute A that gives a stable stoichiometric hydrate up to the binary peritectic invariant at T p . The black dashed lines represent the metastable solubility of the anhydrous phase ⟨A⟩. The dashed lines down to T F (AII ) represent the solidus (in blue) and liquidus of a putative nonstoichiometric hydrate A-H2 O(1−X) , respectively. For X = 0, there is a new polymorph whose melting point T F (AII ) can be much below the temperature of fusion of the stable anhydrous phase T F (AI ). In case the dehydration is performed smoothly at a temperature below T F (AII ) and T g (the glass transition of the anhydrous phase) on suﬃciently small particles to avoid an excessive resident time of the solvent molecule inside the solid, it is possible to obtain a new polymorph AII , which has a structural similarity with the former hydrate. This process has been described in the case of rimonabant [75], but it is certainly applicable to many other molecular solvates. It shows that varying temperature, pressure, and the crystallization process is not suﬃcient to obtain exhaustively all the polymorphs of a given component. It is necessary to

125

126

4 Thermodynamics of Polymorphs and Solvates

T

TFAI u.s.s.

1 Tp 2

3

4

H2O

Figure 4.29 If the system is in stable equilibrium, domains 1–5 contain the 1 ⟨A1 ⟩ + saturated following phases: 2 ⟨A-H2 O⟩ + saturated solution; solution; 3 ⟨ice⟩ + saturated solution; 4 ⟨ice⟩ + ⟨A-H2 O⟩; 5 ⟨A1 ⟩ + ⟨A-H2 O⟩.

5

A-H2O

TFAII

A

explore systems of higher order with preferably volatile solvent molecules, which can build solvates whose structural information could be partially preserved during well-managed desolvations. In the case of rimonabant, the excursion into the ternary system (water and acetone) leads to the crystallization of a monohydrate. By a smooth dehydratation at RT (by lowering the water vapor pressure by exposure to P2 O5 ; note that RT is far below the glass transition temperature: T g = 77 ∘ C), one can produce an anhydrous phase whose melting point (≈100 ∘ C) is about 75 ∘ C below the melting point of the stable polymorph.

4.6 Concluding Remarks Phase diagrams are very useful tools for diﬀerent scientiﬁc ﬁelds. In the present context, it is clear that polymorphs and solvates (as well as co-crystals, host–guest associations, clathrates, etc., see Ref. [76] for a classiﬁcation) can be prepared in a logical way by using pertinent data included in phase diagrams. A careful examination of phase diagrams is also convenient for an easy to access to the relative stability of solid phases (polymorphs, solvates, etc.) under the inﬂuence of temperature, pressure, or additional components. The construction of these phase diagrams is certainly the most diﬃcult part of the job. Stable and metastable states are sometimes diﬃcult to diﬀerentiate. Kinetics of recrystallizations (i.e. achieving equilibrium) could be slow and chemical decompositions can add hurdles to the correct establishment of the lines of equilibrium. It must also be emphasized that the construction of phase diagrams needs data coming from diﬀerent techniques, which have to be submitted to both critical analysis (unbiased data) and rigorous interpretation. It is worth mentioning that a single reproducible experimental fact could be enough to reconsider the interpretation of the whole phase diagram. This is not the weakness of phase diagrams but actually their strength: all the experimental points must be put into a consistent set of stable and metastable lines, respecting the basic rules of thermodynamics of equilibrium. Sometimes, well-designed experiments have thus to be carefully performed to decide about diﬀerent possible interpretations.

References

Despite these diﬃculties, including the selection of the best possible analytical methods and the time spent for the subtle interpretations (and maybe for the reinterpretations) of many experimental data, phase diagrams put in a concise way a lot of consistent information very useful for other researchers. This accumulation of robust knowledge should be encouraged.

Acknowledgments Dr. Marie-Noelle Petit is deeply thanked for the illustrations.

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5 Toward Computational Polymorph Prediction Sarah L. Price and Louise S. Price University College London, Department of Chemistry, 20 Gordon Street, London WC1H 0AJ, UK

5.1 Could a Computer Predict Polymorphs for the Pharmaceutical Industry? A computer program that could reliably predict the polymorphs of a given molecule would have to encapsulate a quantitative theory for the causes of polymorphism. These are mainly kinetic: we obtain polymorphs when a metastable structure nucleates and grows more readily than the most stable form. Only polymorphs that have suﬃcient kinetic stability not to readily transform to a more stable form are of practical relevance to solid-form selection. There is considerable academic research and discussion on how we can establish and measure these kinetic factors, which depend on the details of the crystallization conditions. The condition variables range from those that may be easily controlled, such as temperature, to the hard to detect, such as the presence of speciﬁc impurities. Thus, the impossibility of including all kinetic factors in a polymorph prediction code is analogous to the problems of devising a polymorph screen that can cover all the conditions that could generate new polymorphs (Chapter 8). What is feasible is a computer program to predict the most stable structure for a given molecule, which also generates the alternative crystal structures that are suﬃciently close in energy to be thermodynamically plausible as polymorphs. In this sense, crystal structure prediction (CSP) methods can produce the crystal energy landscape of thermodynamically plausible structures that, depending on kinetic factors, may be observable polymorphs. This chapter outlines the principles behind the recent applications of CSP methods to the processes relevant to pharmaceutical development. The methodology behind CSP algorithms, as applied to small molecules, has been described [1, 2] and is under active development for larger, more ﬂexible molecules that are more typical of the smaller molecules of interest to the pharmaceutical industry. The theories that link crystal structure to properties, processing parameters, and formulation control in the materials science tetrahedron [3] mean that computational methods of estimating relevant properties from experimental crystal structures can be applied to the computer-generated structures. Hence, this chapter emphasizes the emerging principles of computational studies of pharmaceutical polymorphs. Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development, First Edition. Edited by Rolf Hilﬁker and Markus von Raumer. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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It emphasizes the similarities and diﬀerences between computational studies on small molecules, such as aspirin and paracetamol, and those that may be useful as complements to the polymorph screening and experimental characterization of the pharmaceuticals in industrial development. 5.1.1 Predicting the Thermodynamically Most Stable Structure from the Chemical Diagram It is a fundamental scientiﬁc question as to whether it is possible to predict the crystal structure of a molecule from its chemical diagram. Most CSP methods rely on the assumption that the crystal structure would be the most thermodynamically stable of all possible structures. It was quickly realized that such a CSP program could be used to design molecules to pack in a way that gave desirable solid-state properties, such as cage molecules that crystallize to give highly porous organic materials [4], energetic molecules that pack densely, or molecules with a high non-linear optical coeﬃcient that pack to preserve this property. The Cambridge Crystallographic Data Centre (CCDC) has been testing progress in our ability to predict crystal structures from the chemical diagram since 1999 [5], by inviting the developers of the CSP codes to submit their predictions of unpublished crystal structures. The molecules whose crystal structures were the targets in the sixth Blind Test [6], which had a submission date of August 2015, are shown in Figure 5.1. Almost all target crystal structures were in at least one of the lists of 100 structures submitted by the 21 participating groups [6]. It will be noted that the sixth test contained one molecule that was pharmaceutical and another large ﬂexible molecule whose functional groups are more typical of organic electronic materials, and both were subjected to an industrial polymorph screen. This, and the change in the number of structures submitted, explicitly recognizes the role of polymorphism in crystallization, though various blind test targets have been shown to be polymorphic after the challenge had been issued [5, 7, 8]. The blind tests have been more relevant to the pharmaceutical industry since the ﬁfth blind test in 2010 [9], which was the ﬁrst to have a molecule of the size and ﬂexibility of model pharmaceuticals. This challenge inspired algorithmic developments that allowed a few groups to predict this structure [9]. The rapid evolution of the computer algorithms for CSP means that the reader should consult the paper describing the latest blind test, currently [6], to see the current range of methods that can be used. 5.1.2 Using Crystal Structure Prediction Studies as a Complement to Solid-form Screening The application of CSP methods to the pharmaceutical industry is rather diﬀerent from that of the molecular design, as the active pharmaceutical ingredient (API) has already been synthesized and the requirement is to ﬁnd its solid forms (Chapters 1 and 8). It has been recognized from the early days of high-throughput crystallization [10] that CSP studies could play a key role in avoiding latent polymorphism, particularly the late appearance of more thermodynamically stable structures. The potential for CSP also helping structurally characterize

N N

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H

H

H

H

N+

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S

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O

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CI

CI–

H O

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H

XXII 12/21 rank 1

O

H

XXIV salt hydrate 1/8 rank 2

CI

XXVI largest so far 3/12 rank 1

H O

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CH3 CH2

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CI CI

XXIII 5 polymorphs: A,B,D 4,8,3/14 rank 23,1,2

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O

XXV co-crystal 5/14 rank 1

C [Z'=2] and E [Z'=2, disordered], 1,0/3 rank 6,Figure 5.1 The molecules whose crystal structures have been used in the Cambridge Crystallographic Data Centre’s sixth blind test of crystal structure prediction [6]. The results x/y show that x of the y groups who tackled this system had the correct structure in their two lists of 100 structures, and the rank is that of the best submission (e.g. rank 1 shows that at least one entry had the correct structure as the most stable).

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polymorphs has pervaded the development of various techniques of determining crystal structures that beneﬁt from having a plausible starting model. It has been recognized for almost two decades that combining the theoretical predictions with the most extensive experimental polymorph screening and characterization is essential to advance our understanding of the nature and extent of polymorphism of organic molecules [10, 11]. For the pharmaceutical industry, this joint approach provides support for the Quality by Design agenda for pharmaceutical manufacturing (Chapter 1) [12]. The calculations involved in a CSP study provide some of the ﬁrst-principles-based modeling that is anticipated as necessary from an engineering view of pharmaceutical development [12]; the design of pharmaceutical products and processes is based on the properties of the solid form of the API involved and needs to work around any competing forms. CSP calculations have a long way to go before they could be used to quantitatively assess the risk of new solid forms, which is a combination of the probability of their occurrence and the severity of the harm that would be caused [12]. This chapter outlines the current state of calculations on pharmaceutical crystals.

5.2 Methods of Calculating the Relative Energies of Crystals Calculations are performed on perfect, ordered, inﬁnite crystals, with the modeling of disorder and defects in organic materials being in its infancy and accounting for the eﬀects of temperature being only a little further advanced (Section 5.2.2). A scientiﬁc breakthrough in 2014 was the calculation of the lattice energy of benzene within 1 kJ mol−1 accuracy [13], which required the use of the low-temperature crystal structure and careful analysis of the experimental heat of sublimation and heat capacity data to derive the experimental value for comparison. As the energy diﬀerences between polymorphs is often around 1 kJ mol−1 [14], the computer modeling of the thermodynamics of the organic solid state relies on cancellation of errors. 5.2.1

Lattice Energy

The lattice energy is the simplest crystal energy to calculate, being the energy required to break up the hypothetical, static crystal (eﬀectively 0 K ignoring even the zero-point energy motion) into its components, either the inﬁnitely separated molecules in their lowest energy conformation or all nuclei and electrons inﬁnitely separated. The conceptually and computationally easiest deﬁnition of the lattice energy, Elatt , Elatt = Uinter + ΔEintra naturally separates the intermolecular interaction energy between the molecules in the crystal, U inter , and the change in the energy of the individual molecule as it changes conformation between the gas phase and crystal, ΔEintra , to

5.2 Methods of Calculating the Relative Energies of Crystals

improve the intermolecular interactions. Many CSP methods are based on making this division, as the conformational energy diﬀerence ΔEintra can be taken as zero for rigid molecules and is usually quite small [15]. Exceptions can occur when the conformational change drastically improves the intermolecular interactions, for example, when the isolated molecule has an intramolecular hydrogen bond that becomes a strong intermolecular hydrogen bond in the crystal [16]. The main contributions to the intermolecular interaction energy are the exchange-repulsion, dispersion, and electrostatic and induction energies, as deﬁned by the theory of intermolecular forces [17]. The exchange-repulsion is the exponential repulsive force from the overlap of the molecular charge distributions, which is critical in determining the separations within the crystals. The dispersion force is the universal attractive force, which contributes to the lattice energy of all crystals, even argon, and is of quantum mechanical origin, linked to the correlation of electron density ﬂuctuations. Hence, dispersion forces are particularly challenging to estimate by current electronic structure theories [18, 19]. As the dispersion energy is always attractive, errors in modeling the dispersion tend to cancel between structures with the same density. The electrostatic energy dominates hydrogen bonding and the interactions between more polar functional groups. In crystals where the electrostatic ﬁelds are strong, such as in salts or molecules capable of hydrogen bonding, the ﬁeld induces a change in the molecular charge distribution from that of the isolated molecule. The additional stabilization is termed the induction or polarization energy. Pharmaceutical molecules that have a variety of ﬂexibly linked polar and non-polar functional groups provide a great challenge in balancing the diﬀerent contributions, often qualitatively referred to as the conformational energy (ΔEintra ), and the hydrogen bonding, π–π, halogen, van der Waals, and other types of interactions that make up the intermolecular energy (U inter ). The molecule can make small or large conformational changes to improve the hydrogen-bonding geometries or pack more densely and so increase the dispersion contribution. Hence, the accuracy of relative lattice energies is very dependent on the molecule and the diﬀerences in the crystal structures involved. Conventional transferable force ﬁelds in most molecular modeling packages have their uses, but none have proved adequate in the blind tests of CSP. This can be attributed to the limited functional form using the same atomic charges to model both intermolecular and intramolecular interactions [20]. Various methods based on using the molecular charge density to evaluate lattice energies are being developed and have shown their promise for the lattice energies of smaller organic molecules [21]. Molecule-speciﬁc force ﬁelds derived from a substantial body of ab initio calculations on the molecule, its dimers and sometimes larger clusters, are also proving worthwhile [22–24] with the advantage that the functional form may be suitable for other forms of molecular simulation such as molecular dynamics. The approach that has proved most widely applicable in CSP studies to date is to use ab initio calculations on the isolated molecule to provide ΔEintra and the molecular charge distribution in a given conformation. This ab initio charge distribution is then analyzed to give a distributed multipole (DMA) representation [25–27] that is used to model the electrostatic contribution to the intermolecular lattice energy U inter . The use

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of a charge, dipole, quadrupole, etc., on every atom to represent its charge distribution means that the electrostatic eﬀects of lone pairs and π electron density are included. This is important in getting a realistic description of the orientation dependence of hydrogen bonding and π–π interactions. Thus, the use of DMAs makes a signiﬁcant improvement in the relative lattice energies of structures, compared with the best atomic charge representation of the same charge density, particularly for hydrogen-bonded systems [28]. This anisotropic atom–atom electrostatic model has often provided an adequate model for the electrostatic contribution to U inter in CSP studies when the other contributions to intermolecular lattice energy are represented by an atom–atom exp-6 functional form, i.e. ∑

lattice

Uinter =

∑

A𝜄𝜅 exp(−B𝜄𝜅 Rik ) − C𝜄𝜅 R−6 + Uikelec (DMA(M, N)) ik

M,N i∈M,k∈N

where atom i of type 𝜄 in molecule M is separated by Rik from atom k of type 𝜅 in molecule N. The sets of exp-6 parameters that are most commonly used to represent the repulsion–dispersion contributions are the FIT parameters [29], or the WILL01 parameters [30, 31]. These have been ﬁtted to reproduce organic crystal structures and some heats of sublimation, when the exp-6 model is used in conjunction with an explicit electrostatic model derived for the speciﬁc molecule. Thus, the exp-6 parameters absorb, to some extent, the errors in the approximations being made, such as neglect of induction and thermal eﬀects. The WILL01 parameter set uses hydrogen interaction sites that are displaced slightly toward the bonded atoms, representing the displacement of the charge density that leads to the systematic underestimation of bond lengths to hydrogen in X-ray crystal structures. A crude, but often eﬀective, way of estimating the eﬀect of the polarization in molecular crystals (when this may be greater than the diﬀerential eﬀect absorbed in the parameterization of the exp-6 potential) is to calculate the molecular wave function in a polarizable continuum with a dielectric constant 𝜀 = 3, a value typical of molecular crystals [32]. This aﬀects both ΔEintra and the DMAs in a manner that is independent of the speciﬁc crystal structure. The separation of the lattice energy calculation into molecular electronic structure calculations (for ΔEintra and the DMA) and optimization of the lattice energy with an anisotropic atom–atom potential holding the molecule rigid, as done in DMACRYS [29], means that many molecular electronic structure calculations are needed for ﬂexible molecules. The approximation that the molecular charge density is independent of conformation can be poor. Hence, to optimize the lattice energy as a function of both the crystal structure variables and the molecular torsion angles requires cycling through both molecular electronic and crystal calculations and is made more eﬃcient by using a database of the ab initio calculations, as in the algorithm CrystalOptimizer [33, 34] . The alternative approach is to use periodic electronic structure methods directly on the crystal structures. Here, the main problem is that the electronic structure methods that are eﬃcient enough to be applied generally do not model the dispersion interaction. Hence, the leading method has a dispersion correction added to a speciﬁc density functional (usually the Perdew–Burke-Ernzerhof

5.2 Methods of Calculating the Relative Energies of Crystals

(PBE)) functional that has been parameterized by ﬁtting to organic crystal structures [35]. The sixth blind test showed [6] that the relative energies evaluated by this method could be improved by a more theoretically based dispersion correction [36]. Periodic dispersion-corrected density functional theory (DFT-D) calculations, usually with the PBE functional and a variety of dispersion corrections, have shown their value in helping correct experimental crystal structures [37], particularly the X-ray placement of hydrogen atoms. Polymorphic lattice energy diﬀerences are usually less than 5 kJ mol−1 , though some conformational polymorphs can go up to 10 kJ mol−1 [14]. This is a major challenge to all current methods of calculation, as shown for small molecules [21] or even getting the ranking correct for pharmaceuticals. Thus, to evaluate a CSP study, or compare calculations on known polymorphs, it is wise to estimate how sensitive the relative crystal energies are to the method used. The periodic and molecular electronic structure calculations are extremely demanding of computer resources, requiring research clusters. Hence, most CSP methods are based on a hierarchy of increasingly accurate methods, re-ranking only the most promising structures. The successful submissions in the sixth blind test were using hundreds of thousands of CPU hours. Hence, although the availability of high-performance computing resources is becoming more widespread in the pharmaceutical industry, there is always going to be the issue of the aﬀordability of the most theoretically desirable method and the likely errors in the calculations for the speciﬁc purpose. 5.2.2

Free Energy

The lattice energy does not include any temperature eﬀects, and so can only predict the relative stability of diﬀerent crystal structures at low temperatures. The Helmholtz free energy can be estimated from the second derivatives of the lattice energy, using this harmonic approximation for the lattice modes and elastic constants. A recent survey of the energy diﬀerences between 508 known pairs of polymorphs, using rigid body estimates of the lattice vibrations, found that only 9% changed in energy order between 0 K and room temperature [38]. The usually small diﬀerence in entropic contributions explains why lattice energy can be used in CSP studies, at least as a ﬁrst approximation. Periodic electronic structure calculations do not make the distinction between molecular and lattice modes, and so may be more accurate for pharmaceuticals, though very much more expensive [21]. It has been shown that the metastability of aspirin form II is due to the coupling between collective electronic ﬂuctuations and quantized lattice vibrations by such calculations [39]. These calculations are assuming that the temperature-induced molecular motions are very small, so that the harmonic approximation is valid, and so can only suggest that there is a phase transformation when there is a change in the sign of the relative free energy. Molecular dynamics simulations of the molecular motions can show transformations: the diﬀerence between benzene [40] and 5-ﬂuorouracil [41] in the proportion of lattice energy minima that are free energy minima reﬂects the ease of molecular motion within the benzene crystal and transformations between its observed polymorphs. However, estimating free energies from

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molecular dynamics simulations is diﬃcult because of the compromise between suﬃcient statistical sampling and using a suﬃciently accurate model for the lattice energy. Thus, the calculation of energy diﬀerences between known polymorphs, let alone all those generated by CSP studies, is currently challenging for computational experts. A few studies have reported attempts to evaluate qualitative relative stabilities of drug molecules [42, 43], and it is clear that much more reliable thermodynamic data (Chapter 4) is needed to calibrate computational methods [14].

5.3 Searching for Possible Crystal Structures A CSP study is only as good as the search space covered. It will always generate crystal structures with the input molecular connectivity and stoichiometry, and the user speciﬁes the range of space groups and the number of independent molecules in the asymmetric unit cell (Z′ ). This latter variable is important: it is far more expensive to cover the search space when there are the additional variables deﬁning the relative position (and conformation) of two or more independent molecules in the asymmetric unit cell. Hence, studying the possibility of hydrate formation is restricted to stoichiometric hydrates and needs multiple, computationally expensive searches [44]. For a single-component search, a Z′ = 2 search should duplicate the structures found in a Z′ = 1 search, but may generate others, which may be closely related to a Z′ = 1 structure, or could be intrinsically diﬀerent, for example, when the two molecules are involved in diﬀerent hydrogen bonds or adopt very diﬀerent conformations. As crystallographic techniques have matured, an increasing number of crystal structures with Z′ > 1 have been determined [14]. Unfortunately, the incidence of Z′ > 1 structures for known polymorphic systems is about 20%, almost double that for all crystal structures [14] within the Cambridge Structural Database. A further choice is how much molecular ﬂexibility needs to be considered in the ﬁrst stages of the search to ensure that all conformational polymorphs could be generated [15]. This is a major reason why CSP for pharmaceuticals is so much more demanding than for molecules with less ﬂexibility. Molecules composed of aromatic groups ﬂexibly linked have a tendency to crystallize in an extended conformation [45] as this often allows a denser packing (stabilized by the dispersion forces), whereas the most stable isolated molecule conformations will have better intramolecular interactions but may have awkward shapes that cannot pack densely. The many possible compromises between the molecular conformation and its possible crystal packings should be explored in the CSP search. Once packed into a crystal, further structural optimization can only reﬁne the conformation, not cross large energy barriers: this is similar to the experimental diﬃculty in solid-state transformations between conformational polymorphs. Hence, there can be larger energy diﬀerences between conformational polymorphs than for polymorphs whose molecular conformations have a common nearest conformational energy minimum [14, 15]. Hence, an extensive

5.4 Comparing Crystal Structures

CSP study shows which conformations can generate stable crystal structures and so contributes to the investigation of the extent to which conformational polymorphism is determined by the conformational behavior in solution, late desolvation, and the mechanisms of nucleation, crystallization, and growth. For some applications, it is appropriate to limit the search space in the CSP study. For example, if only enantiopure crystals are of interest, then the number of space groups that need to be included is drastically reduced from around 60 to 5, if you are willing to risk not covering some unusual space groups. However, it is vital that the output of the CSP search is interpreted in terms of the input limitations: false conclusions that all polymorphs are known have been made on the basis of very limited searches. For a given set of search variables, there are a variety of ways of generating potential crystal structures, based on many different optimization methods [6]. The methods that have been most frequently applied successfully to pharmaceutical molecules are the commercial program GRACE [46] and the academic development program CrystalPredictor [33, 34]. These programs have internal checks on the extent to which the search is complete, within the chosen range of space groups, Z′ , etc. Millions of structures are generated for pharmaceutical-type molecules and subjected to minimization by either a molecule-speciﬁc force ﬁeld (derived from DFT-D calculations) or an isotropic atom–atom force ﬁeld with atomic charges and an estimate of ΔEintra derived from molecular ab initio calculations. The resulting search may still be assessed as incomplete.

5.4 Comparing Crystal Structures The huge computational costs of generating reasonable coverage of the likely crystallographic structures of pharmaceuticals, combined with the costs of the ﬁnal accurate energy evaluations, mean that duplicate structures have to be eliminated as eﬃciently as possible. This quickly merges into the issue of how diﬀerent do crystal structures have to be to be considered as distinct polymorphs [47] rather than a sample-dependent variation. A comparison of the simulated powder X-ray diﬀraction pattern and the ability to overlay a cluster of at least 15 molecules from the structure, both within reasonable tolerances, will eliminate almost all duplicate structures. Other approaches for comparing the unique computer-generated crystal structures with all the experimentally known forms, including solvates, salts, and cocrystals and the structures of related molecules, are needed to beneﬁt from molecular-level insight into the crystallization tendencies of the molecules. The program Mercury [48] provides many useful crystal structure comparison tools, such as the ability to determine the hydrogen bond graph sets [49] or determine how many molecules, n, of the coordination clusters within two structures can be overlaid (and quantiﬁed by the root-mean-square diﬀerence, rmsdn ). This procedure can be used to make relationship trees for families of structures [50]. Another complementary pairwise comparison tool, XPAC [51], allows identiﬁcation of common supramolecular constructs of common points

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within diﬀerent molecules. Both these methods help determine whether there are common stacks or layers of the molecules (or molecular fragments) as a recurring theme within a molecule’s real and computer-generated solid-form landscapes. Diﬀerent crystal structures can be visualized, and the polymorphic diﬀerences made more obvious by calculating Hirschfeld surfaces [52] and associated properties [53]. Analysis of the diﬀerent contributions to the lattice energy from the various pairs of molecules within the crystal structure, using PIXEL [54, 55], can also reveal how polymorphs diﬀer in the molecule–molecule contacts that contribute to overall similar energies. CCDC tools can also provide a structural informatics “health check” on crystal structures [56].

5.5 Calculation of Properties from Crystal Structures 5.5.1

Spectroscopic – PXRD, IR, ss-NMR

A major use of CSP studies is to help determine crystal structures from experimental data that is insuﬃcient to determine the structure, or add conﬁdence when there are multiple possible solutions. The calculation of the powder diﬀraction pattern from a crystal structure is trivial, depending only on the wavelength of the radiation. However, the powder pattern is very sensitive to the cell parameters and hence to the anisotropic thermal expansion of organic crystals, as can be seen by comparing powder patterns at diﬀerent temperatures. Crystal structures predicted by lattice energy minimization neglect thermal expansion, and so the cell dimensions are in error by typically a few percentage and depend on the extent to which the method used has been parameterized against experimental structures partially absorbing thermal expansion. Methods are being developed to facilitate the automatic use of CSP structures to help solve structures from powder [57]. There are many examples in the literature of CSP being used to determine structures from powder diﬀraction data, ranging from cases where the powder pattern cannot be indexed [58] through to suggesting a set of possible structures that are consistent with the indexing [59, 60], to providing the correct proton positions [61]. Transmission electron microscopy and electron diﬀraction have also been used to detect and characterize new polymorphs and propose their structures by comparison with CSP-generated structures [62]. In the case of theophylline, this detected a novel polymorph at a level of polymorphic impurity that was undetectable by powder X-ray diﬀraction [63]. The calculation of the solid-state NMR spectrum (Chapter 14) from the crystal structure is considerably more challenging, being a function of the electronic structure, though this can now be done using either plane-wave density functional [64] or fragment-based molecular orbital calculations [65]. Applications include determining a crystal structure of AZD8329, an 11β-HSD1 inhibitor investigated for use in the treatment of type 2 diabetes. The structure of Form 4, one of the two forms considered to have superior properties for development, was proposed [66] by comparing the experimental proton solid-state NMR spectrum with those calculated from CSP-generated structures. This structure

5.5 Calculation of Properties from Crystal Structures

was in excellent agreement with that independently determined from powder X-ray diﬀraction, with the advantage of NMR spectroscopy having located the carboxylic acid proton position. Solid-state NMR calculations have also been used to unravel the atomic-level dynamic hydration [67] of a HT2A agonist being studied for the treatment of sleep disorders. The use of calculated solid-state NMR to complement experiment in unraveling the behavior of pharmaceutical materials is likely to grow as the calculations become more routine. The low-frequency vibrations of solids, as measured by infrared, Raman, or terahertz spectroscopy (Chapter 14), can also be estimated within the harmonic approximation, with the caveat that second derivatives are more sensitive to method and computationally demanding than the lattice energies and corresponding forces used in structure optimization. The frequencies are used in statistical mechanical formulae to estimate free energies, heat capacities, etc. (Section 5.2.2), so these quantities are less demanding of accuracy than producing spectra that can be used for polymorph identiﬁcation. Nonetheless, considerable progress has been made in interpreting terahertz spectra for carbamazepine polymorphs [68] and in investigating novel polymorphs [69]. Hence, there is increasing scope for using CSP to generate a set of thermodynamically plausible structures and their spectra to help characterize the structures of polymorphs where suitable crystals for single crystal diﬀraction cannot be grown. The size of the necessary CSP search can be reduced using experimental data, for example, ss-NMR may be used to conﬁrm Z′ , or indexing the powder pattern reduces the possible space groups. Spectral similarities to other forms can suggest that the search be conducted with a limited range of conformations or dimer structures, such as the use of π–π stacked dimer structures in CSP to ﬁnd structures for the anhydrous forms of the antibiotic levoﬂoxacin [70]. An advantage of using a CSP search can be to show that there is more than one structure that is compatible with the experimental data. 5.5.2 Other Properties: Solubilities, Morphologies, and Mechanical Properties In an ideal world, the computational prediction of the properties of all potential polymorphs would reduce the experimental eﬀort and time required to design the pharmaceutical product and processing. It might even allow the decision to target an elusive, hard-to-nucleate predicted polymorph because of its desirable properties. However, although methods are being developed for calculating all practically relevant properties of organic materials, real progress in theory and code development requires critical validation of the accuracy and reliability of the calculations over a range of types of molecules and variability of polymorphic structures. Schemes have been proposed to use the crystal structure to predict solubilities [71], and indeed, lattice energy diﬀerences can provide a ﬁrst approximation to the solubility diﬀerences needed to design chiral resolution by crystallization [72]. However, as solubility is an exponential function of the free energy, such estimates are very dependent on the accuracy of the lattice energy diﬀerences and other assumptions such as the equality of the heat capacities and

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that solutions are ideal. Good semiqualitative predictions of extreme similarities or diﬀerences in solubilities can be derived from the lattice energies of the crystal structures, or, in principle, of the CSP generated most stable structure in racemic or enantiopure space groups [73]. However, whereas the most stable racemic structure in a CSP study of naproxen was suitable for helping solve the structure from powder data, the lattice energy diﬀerence with the enantiopure form was a few kilojoules per mole greater than the energy diﬀerence derived from the heats of fusion or solubility measurements [74]. The surface structure of an organic crystal can be estimated as a cut from the perfect crystal structure, and a morphology estimated using the Bravais–Friedel–Donnay–Harker model [75] relating the growth rate to the separation of the lattice planes. The nature of the intermolecular forces can be taken into account by calculating either the surface energy or the attachment energy [76, 77] for the possible crystal faces and used to predict either the equilibrium morphology or the growth morphology. The growth morphology, being based on the energy of interaction between slices of the crystal structure, is appropriate for crystals grown by sublimation by a birth and spread model below the roughening temperature. Such qualitative morphology estimates, of whether the intermolecular arrangement of the molecules favors a fairly isotropic equant morphology or very anisotropic growth resulting in plate or needle like crystals, can be useful. Further models for morphology prediction are being developed based on more realistic models of crystal growth [78]. However, the eﬀect of solvent and impurities in accelerating or inhibiting various faces means that it is still a major research area to be able to predict morphologies using the kinetics of crystal growth and dissolution, as well as the bulk perfect crystal structure. The gross polymorphic diﬀerences in the elastic tensor and derived mechanical properties can also be estimated by calculations based on idealized perfect crystals. These calculations can be based on the harmonic approximation, like the lattice frequencies (Section 5.5.1), and so are subjected to the same caveats as the corresponding free energy estimates (Section 5.2.2). The calculations will determine whether the crystal structure has a very weak shear plane or whether it is elastically more isotropic. Thus, such models distinguish the key mechanical property diﬀerences between the polymorphs of paracetamol [79], where the layer structure of form II is more susceptible to shear and hence can be tableted without binders, unlike form I [80]. However, such estimates are only quantitatively comparable with elastic tensors measured from large, perfect single crystals [81], and take no account of the major eﬀect of crystal defects on the mechanical properties of individual crystals, let alone the inter-crystallite arrangement and interactions that can dominate the mechanical properties of polycrystalline samples. A practical reason for generating the elastic matrix as part of a lattice energy minimization is to conﬁrm that the structure is mechanically stable, i.e. a true local minimum. Structures that have no residual forces when minimized within a certain space group can be mechanically unstable, and in this case, minimizing in the appropriate lower symmetry space group can generate a lower energy structure with more independent molecules in the unit cell. Hence, a Z′ = 1 search can generate some closely related Z′ = 2 structures. Some CSP-generated

5.6 Crystal Energy Landscapes

structures may be so mechanically weak that they appear implausible, though this was wrongly used to explain why aspirin was not known in the form that was later established as form II [82]. Similarly, extreme morphologies showing faces with a poor growth rate may be useful in assessing CSP-generated structures [83], though many polymorphs that are diﬃcult to characterize because of problems in growing single crystals have an extremely thin plate or ﬁne-needle morphology.

5.6 Crystal Energy Landscapes A CSP search algorithm generates the crystal energy landscape, the set of structures that are suﬃciently close in energy to the most stable to be thermodynamically plausible as polymorphs. As it is the energy barrier and kinetics of transformation to more stable structures, rather than the thermodynamic energy diﬀerence, that determines whether a metastable polymorph is practically important, we cannot conﬁdently place an upper energy limit on the crystal energy landscape. Similarly, an estimate is needed for the allowance that has to be made for the errors in the calculation of relative thermodynamic stability, which is also rather molecule dependent. However, if we assume an extensive search with a good accuracy in the relative crystal energies, and view the crystal energy landscape as those structures that have a thermodynamically favorable packing within the experimentally estimated range of likely polymorphism, we can use crystal structure analysis tools (Section 5.4) to interpret the crystal energy landscape. 5.6.1

Interpretation of Crystal Energy Landscapes

There are the cases of monomorphic crystal energy landscapes where one structure is so much more thermodynamically stable than any other that it has to be the only single component structure that will be observed. Such landscapes have been observed, for example, for isocaﬀeine [84] and strychnine [85]. This is the type of energy landscape that would be desired for easy preparation of a functional organic material. Such an energy landscape requires a uniquely favorable packing deﬁning all three dimensions of the crystal. A molecule could have a particularly favorable packing motif in fewer dimensions, for example, a strongly hydrogen-bonded layer structure. However, there could be more than one way of stacking these layers to give structures that are competitive in energy. In this case, the crystal energy landscape does not indicate whether the diﬀerent structures are possible polymorphs, or whether the structures would not remain distinct during nucleation and growth resulting in the same structure. The alternative structures could be present as stacking faults, or polymorphic domains, as in the case of aspirin [86]. The existence of related structures that are very close in energy can mean that conﬁgurational entropy would give a thermodynamic preference for static disorder, as in the low-temperature form II of caﬀeine [84]. At high temperatures, molecular motion can dynamically average over a range of lattice energy minima, rationalizing the high temperature, dynamically disordered phases of caﬀeine and cyclopentane [87].

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The most interesting case is when the crystal energy landscape generates alternative structures that have a very diﬀerent structure from the known forms, but are calculated to be more stable, or very competitive in energy, to the observed polymorphs. These could be conformational polymorphs, containing strong hydrogen-bonding motifs or other packing diﬀerences such that there would be a very high barrier to a solid-state transformation to the known structures. Here, the question is which of these structures correspond to as yet undiscovered polymorphs. Thus, unless the crystal energy landscape is clearly monomorphic, the interpretation requires careful comparison of the computer-generated crystal structures and the evidence available from experimental screening work. The process is illustrated for one example, in detail, followed by a brief survey of the type of information that has been extracted from recently published case studies exploring the complementarity of CSP studies with industrial-type polymorph screening [88]. 5.6.2

Example of Tazofelone

One test of the value of CSP was to revisit the solid-form diversity of tazofelone, which had been under development and screened about 17 years earlier [89]. The result of the CSP search on tazofelone [90], Figure 5.2a, shows that certain conformations cannot pack to form a low-energy structure, and indeed, there are only two conformational regions and a limited number of hydrogen-bonding motifs in this Z′ = 1 crystal energy landscape (Figure 5.2c). The crystal energy landscape for enantiopure tazofelone (Figure 5.2b) shows that it can only pack well in one type of conformation within the Z′ = 1 limitation of the search. The known structure is Z′ = 2, with broadly the same types of conformations and AB:R22(6) hydrogen-bonding chains, though this structure is signiﬁcantly more stable because the two diﬀerent conformations allow the hydrogen-bonding chains to pack better. The similarity in packing and the energy diﬀerences give considerable conﬁdence that there are unlikely to be any long-lived metastable enantiopure polymorphs. The hydrogen bonding does not correspond to the most favorable amide:amide motif predicted by the hydrogen-bonding propensity tool [91], and so from just this structure and the health check, there would have been considerable concern that there was another more stable enantiopure polymorph. The value of CSP, particularly if the solid-form screening only covers the one enantiomer, is also illustrated by a melatonin agonist, where the CSP generated a polymorph that had only been crystallized for the inactive hand and not for the active form [92]. It was speculated that this unusual occurrence of the two hands of a molecule having diﬀerent polymorphs was related to diﬀerent chiral impurities triggering the ﬁrst nucleation. The importance of seeding in nucleation is also shown by tazofelone: the enantiopure crystal can initiate the crystallization of a solid solution of the two hands of the molecule from a racemic liquid [93]. This could be seen from the racemic crystal energy landscape (Figure 5.2c) having two structures that are isomorphous (virtually the same cell and closely related packing with same motif ) with the known enantiopure Z′ = 2 structure. This is possible only because a change in the conformation of the molecule can mimic the change in

–125.0

Enantiopure structures

Total lattice energy (kJ mol–1)

Total lattice energy (kJ mol–1)

Summary CSP search in all space groups

O N

–127.5

S

–130.0 t-Bu

–132.5

t-Bu O H

–135.0

Cutoff for crystal energy landscape –137.5

–125.0 –127.5 –130.0 –132.5 –135.0

Cutoff for crystal energy landscape

–140.0

–142.5 61

–142.5 62

(a)

63

64

65

66

67

68

69

70

71

Packing coefficient (%)

Enantiopure structure

–137.5

–140.0

61

(b)

62

63

64

65

66

67

68

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Packing coefficient (%)

Crystal energy landscape

Total lattice energy (kJmol–1)

Cutoff for crystal energy landscape

Solid solution : A Enantiopure structure

–137.5

F:R22(8);C11(10)

AB:R22(6)

Racemic form III Racemic form I Solid solution : B

–140.0

AB:R22(8)

Racemic form II

AB:R44(12)

–142.5 61

(c)

62

63

64

65

66

67

Packing coefficient (%)

68

69

70

71

AB:no H-bonds

Figure 5.2 A crystal structure prediction study of tazofelone: (a) Summary of the output, each symbol represents a mechanically stable crystal structure, with the color referring to the type of conformation and the symbol to the hydrogen-bonding graph set. The large open symbols denote the experimentally observed structures, with those in yellow being the Z ′ = 2 structures that could not be generated by the Z ′ = 1 search. (b) The enantiopure structures and (c) an enlargement of the crystal energy landscape, the structures considered as thermodynamically plausible structures that could be formed from a racemic solution or melt. The key only shows the structural motifs (conformation and hydrogen bonding) that give rise to low-energy structures. The diagram for F:R22(8);C11(10) is actually an overlay of the layer in the three racemic polymorphs. Source: Price et al. 2014 [90]. Adapted with permission of Elsevier.

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chirality within the crystal packing. The knowledge that crystallization of nearly enantiopure tazofelone would absorb rather than reject the other enantiomer is important for process design, though the costs of generating the racemic crystal energy landscape is much larger than just considering the chiral space groups. Racemic tazofelone can adopt crystal structures with the most favorable hydrogen-bonding motif (F:R22(8);C11(10); Figure 5.2), and indeed, the most stable structure generated is the most stable form. However, the racemic crystal energy landscape generates a few other structures in which the same hydrogen-bonded sheets are stacked in diﬀerent ways, with very little diﬀerence in energy. When the CSP study was performed, a second Z′ = 2 polymorph, based on the same sheet as the most stable form, was known. Revisiting the experimental screening of tazofelone, to calibrate the CSP study, quickly found form III, another polymorph based on the same sheet stacked in a diﬀerent way, and also found diﬃculty in obtaining sharp melting points for even single crystals. This led to unusual scrutiny of the diﬀraction data, which showed smearing consistent with disorder in the stacking [90]. Hence, having multiple structures based on diﬀerent stackings of the same sheet on the racemic crystal energy landscape showed that tazofelone was unlikely to crystallize without a signiﬁcant number of stacking faults or polymorphic domains.

5.7 Potential Uses of Crystal Energy Landscapes in the Pharmaceutical Industry 5.7.1

Conﬁrming the Most Stable Structure is Known

Since the ritonavir crisis, a major incentive for developing CSP methods is to eliminate the risk of a more stable form being found. Recently, there have been cases where CSP has shown that a more stable form exists, and careful experimental work inspired by the CSP has found the kinetically unfavored but thermodynamically most stable form. One example is aminoquinaldine monohydrate [94], and similar work on the less stable anhydrate also found a novel polymorph. In the case of creatine, one limited CSP study had concluded that it was monomorphic, but a more extensive search predicted two other polymorphs that were close in energy with one being the most stable [95], both of which were subsequently found. In these cases, the concurrent, complementary computational and experimental work led to ﬁnding all the lowest energy structures on the crystal energy landscape. 5.7.2

Suggesting Experiments to Find New Polymorphs

The analysis of the CSP-generated crystal structures may suggest an experiment to ﬁnd the unobserved forms. For example, if the unobserved form is denser, but energetically competitive with the known forms, then it is worth trying crystallization under pressure. This has been successful in producing a new polymorph of dalcetrapib [96], which proved to have disordered hydrocarbon tails and be only slightly less stable than the known form.

5.7 Potential Uses of Crystal Energy Landscapes in the Pharmaceutical Industry

A more speciﬁc means of targeting a predicted polymorph is to look for isomorphous structures to be used as a heterogeneous template. Thus, the catemeric form V of carbamazepine was ﬁrst produced by sublimation onto an isomorphous crystal of dihydrocarbamazepine form II [97]. An elusive predicted cocrystal of caﬀeine with benzoic acid could only be produced by seeding with a ﬂuorinated benzoic acid, an experiment that was replicated in four geographically diverse laboratories [98]. 5.7.3 Aiding Structural Characterization from Limited Experimental Data The ability to calculate the spectra from the CSP-generated structures (Section 5.5.1) means that the crystal energy landscape can be used to characterize polymorphs where single crystals cannot be grown, for example, the racemic structure of naproxen [74], or suggesting a structure for form III of olanzapine, which has not yet been produced except in mixtures with form II [59]. 5.7.4

Anticipating Disorder

The occurrence of closely related structures on the crystal energy landscape such as giving rise to very similar simulated powder patterns raises the possibility of a tendency to disorder, as has already been illustrated for tazofelone (Section 5.6.2) and caﬀeine (Section 5.6.1). A pharmaceutical example is form III of 3-(4-dibenzo[b,f ][1,4]oxepin-11-yl-piperazin-1-yl)-2,2-dimethylpropanoic acid, where there were three CSP-generated structures that gave a plausible match to the PXRD data, two of which could be combined in a disorder model, where varying degrees of disorder also gave a good match [60]. This structural insight into form III, which could only be produced by desolvation of a solvate, meant that the variable properties of diﬀerent samples could be attributed to expected variations in degrees of disorder with desolvation process rather than indicating a phase mixture. 5.7.5

Understanding Crystallization Behaviors

Some pharmaceuticals are proliﬁc solvate formers, such as axitinib [99] and olanzapine [59]. This can be linked with an inability of the molecule to pack well with itself, i.e. having a crystal energy landscape with a low packing index [60]. Indeed, many inclusion compounds have the framework generated in a CSP study at high energy and low density, and the structures of porous organic cage molecules can be predicted ignoring the eﬀects of the solvent [100]. For olanzapine, the layers seen in the sets of isomorphous solvates are generated in the CSP, but at high energy because they stack badly without the inclusion of solvent [59]. Often CSP generates the favored packing motifs of a molecule that are seen in its other solid phases. As molecules become larger, and more ﬂexible, the mechanism of crystallization may play an increasing role in determining which structures on the crystal energy landscape are seen. Polymorphs that are formed by desolvating

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solvates could be quite metastable because of the limited scope for the molecule to rearrange within the solid state. However, this argument extends to labile solvates (i.e. crystals that readily lose the solvent on removal from the mother liquor) or crystallization in a two-step nucleation process, where the prenucleating cluster has conformations or molecular association (e.g. hydrogen bonded dimers) of the API already formed. Some structures on the crystal energy landscape may be thermodynamically favorable but seem statistically unlikely to form, for example, enantiopure hydrogen-bonded sheets from a racemic solution as seen for a mandelic acid [101]. This illustrates that the crystallization of racemic structures may be favored by kinetics via statistical process in nucleation and growth [102] rather than thermodynamics. Hence, the crystal energy landscape for pharmaceuticals can often raise the question as to why more polymorphs have not yet been found [103]. Some structures on a lattice energy landscape are certainly artifacts of the neglect of temperature eﬀects, or inaccuracies in the relative energies. Others require careful consideration as to whether the structure is not observed because the right experiment has not yet been done, or because it could not be done. For example, GSK269984B crystallizes readily by itself in a dense structure with an intramolecular hydrogen bond and low-energy conformation. There are thermodynamically plausible conformational polymorphs stabilized by intermolecular hydrogen bonds [104]. Are these not observed because they will always be kinetically unfavorable relative to the fast crystallization into the most stable form? If we take the example of the computationally generated crystal structures of tazofelone without hydrogen bonds or with the sterically crowded hydroxyl–hydroxyl hydrogen bond holding together the dimers (Figure 5.2 contrast AB:R22(8) with FC:R22(8);C11(10)), is it reasonable to assume that these will not form in kinetic competition with the structures with better hydrogen bonding? Thus, the main use of CSP as a complement to experimental solid-form screening is to determine what types of structures are thermodynamically competitive with the known forms. This may suggest that more experimentation is warranted to rationalize the complex crystallization behavior seen for many pharmaceuticals.

5.8 Outlook With the rapid increase in computer power, and the development of more sophisticated algorithms for increased accuracy, our ability to model the structures, energies, and properties of organic crystals is rapidly increasing. There is still a long way to go before free energies, and static or dynamically disordered crystals can be modeled routinely even for small molecules, and the conformational ﬂexibility of most pharmaceutical molecules makes calculating their crystal energy landscapes challenging. However, as shown by the blind tests, considerable progress is being made in performing extensive enough searches, at a worthwhile level of accuracy in the relative energies, that realistic

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6 Hygroscopicity and Hydrates in Pharmaceutical Solids Susan M. Reutzel-Edens1 , Doris E. Braun2 , and Ann W. Newman3 1 Eli Lilly and Company, Small Molecule Design and Development, Lilly Corporate Center, Indianapolis, IN

46285, USA University of Innsbruck, Institute of Pharmacy, Department of Pharmaceutical Technology, Innrain 52c, 6020 Innsbruck, Austria 3 Seventh Street Development Group, PO Box 251, Kure Beach, NC 28449, USA 2

6.1 Introduction Water, an ever-present component of the environment, can have profound and oftentimes adverse eﬀects on drug product manufacturing and performance. Introduced through the active ingredient, excipients, or the atmosphere, it can induce phase transitions, dissolve soluble components, and increase interactions between the drug and excipients [1]. Moisture sorption can aﬀect powder properties important for pharmaceutical processing, such as bulk density, ﬂow, blending, and compaction [2–5]. For some solid oral dosage forms, sorbed water can compromise disintegration, dissolution, and chemical stability [6–10]. Because of its wide-ranging impact on physical and chemical properties, water must be accounted for at all stages of drug substance and product manufacturing, as well as throughout the shelf life of the drug product. Not surprisingly, hygroscopicity, a measure of the water vapor taken up by a solid with the potential to aﬀect surface and bulk properties [11], is one of the most important criteria for informing the selection of the solid-state form of the drug in a solid oral dosage form. The moisture sorption properties of excipients, such as direct compression carriers, disintegrants, and binding agents, are similarly evaluated to ensure that in combination with the drug, the product performs and is stable throughout processing and on storage. When a compound co-crystallizes with water, a new crystalline phase, termed a hydrate, is formed. Hydrates are a subset of a larger class of crystalline solids, termed solvates, which are characterized by the inclusion of the solvent of crystallization in the crystal structure of the compound. Uniquely, hydrates may be obtained either directly through crystallization from solution or indirectly through water vapor uptake in the solid state. Compounds may form multiple hydrates having the same stoichiometry (hydrate polymorphs) or diﬀerent and possibly nonstoichiometric, amounts of water. Importantly, as distinct thermodynamic phases, hydrates can have very diﬀerent properties, such that assurance Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development, First Edition. Edited by Rolf Hilﬁker and Markus von Raumer. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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of product performance can only be achieved through absolute control over hydrate appearance (or disappearance). Thermal, spectroscopic, and diﬀraction techniques that are now commonly used to characterize hygroscopicity and hydration state have been the subject of a number of monographs [12–15]. The objectives of this chapter are to review the basic concepts of water–solid interactions, to highlight the use of gravimetric vapor sorption (GVS) analysis for characterizing hygroscopic behaviors in pharmaceutical solids, and to illustrate through selected case studies the link between observed hydration/dehydration behaviors and molecular-level solid-state structure. Key issues and strategies for evaluating water uptake in hydrate-forming systems and managing the risks that arise from water–solid interactions are also discussed.

6.2 Thermodynamics of Water–Solid Interactions On a molecular level, water has the ability to interact with solid substances in many ways, including (i) physisorption or binding to the surface, (ii) physical entrapment to form liquid inclusions, (iii) absorption in localized disordered regions, (iv) chemical addition [16], and (v) hydrate formation. This is shown schematically in Figure 6.1. Water molecules may attach to exposed functional groups on solid surfaces via van der Waals, ion–dipole, or hydrogen-bonding interactions, or they may simply ﬁll void spaces in the bulk of the solid.

Physisorption

Absorption

Liquid inclusions

Chemical addition

Hydrate

Figure 6.1 Water–solid interactions.

6.3 Hygroscopicity

A statistical analysis of the Cambridge Structural Database (CSD) has shown that while water prefers to maximize its hydrogen-bonding interactions within hydrate crystal structures, severe steric interactions often preclude two H-bond donors and two acceptors from forming an idealized four-coordinate, i.e. tetrahedral, geometry [17]. Indeed, three-coordinate water molecules are most common, with ∼50% of the structures having water used twice as a donor and once as an acceptor [18]. Although its own hydrogen-bonding environment is not always optimal, water, by virtue of its small size, can help to satisfy donor and acceptor groups of molecules that do not pack well with themselves in the solid state. The H-bond lengths and angles in crystalline hydrates have, in fact, been described as “quasi-normal,” reﬂecting the strain-absorbing ability of water [19]. Water in pharmaceutical solids can be in the form of individual molecules, clusters, monolayers, and multimolecular layers. Its accumulation through physisorption, absorption in disordered regions of otherwise crystalline particles, or capillary condensation (in porous solids) will eventually lead to condensed water that may dissolve water-soluble components, and in extreme cases, to deliquescence [20, 21]. Thermodynamically, the water vapor sorption–desorption properties of a solid depend on the water activity of the surrounding medium. Water activity (aw ) relates to the fugacity or escaping tendency of water in a sample, and at constant temperature and pressure, it is given by p/p0 , the water vapor pressure in a material (p) relative to that of pure water (p0 ). In solution, aw = 𝛾 w ⋅ Xw , where 𝛾 w is the activity coeﬃcient of water, and X w is the mole fraction of water present in the aqueous phase. Conveniently, when equilibrium is reached, the water activity of a solution expressed as a fraction is essentially equal to the relative humidity expressed as a percent [20, 22]. Thus, a relative humidity of 10% would correspond to a water activity of 0.1 in solution, and 100% RH would correlate to a water activity of 1. This relationship allows phase behaviors established in the presence of water vapor to be transferred to diﬀerent aqueous solutions and vice versa. Importantly, rather than the total amount of water that is present, it is the diﬀerence in water activity between components or a component and the environmental humidity that provides the thermodynamic driving force for moisture ingress/egress.

6.3 Hygroscopicity Hygroscopicity is a term commonly used to describe the interaction of a material with water. It has also been described as a property of substances to absorb moisture from the air [23]. In the absence of a universally accepted deﬁnition [24–27], we use the term to represent any situation where a particular amount of water vapor, at a given RH and temperature, is taken up by a solid by means of noncovalent interactions. Various parameters are used to evaluate hygroscopicity, including the critical RH [24, 25], hygroscopicity potential [28], hygroscopicity coeﬃcient [29], and heat of adsorption [30]. Two of the more widely used classiﬁcation systems for hygroscopicity are found in the European Pharmacopoeia [31] and the Handbook of Pharmaceutical Excipients [32]. The European Pharmacopoeia classiﬁes the hygroscopic behavior

161

162

6 Hygroscopicity and Hydrates in Pharmaceutical Solids

Table 6.1 Hygroscopicity classiﬁcation. European pharmacopeia

Handbook of pharmaceutical excipients (Callahan and coworkers)

Classiﬁcation

Criteriaa)

Criteria

Nonhygroscopic

—

Class I: Essentially no moisture increase 90% RH in 1 week (wk)

Slightly hygroscopic

Mass increase, x, where 0.2 ≤ x < 2% (w/w)

Class II: Essentially no moisture increase 80% RH in 1 wk

Moderately hygroscopic [27]/ hygroscopic[32]

Mass increase, x, where 2 ≤ x < 15% (w/w)

Class III: Moisture content does not increase >5% (w/w) 80% RH in 1 wk

Very hygroscopic

Mass increase, x, where x ≥ 15% (w/w)

Class IV: Moisture content will increase as low as 40–50% RH; greater than 20% (w/w) increase in moisture content at >90% RH in 1 wk

Deliquescent

Suﬃcient water is absorbed to form a liquid

—

a) Percent water uptake at 25 ± 1 ∘ C and 80 ± 2 %RH. Allow to stand for 24 h.

of pharmaceuticals (drugs and excipients) in four distinct groups (Table 6.1). A slightly diﬀerent classiﬁcation system proposed by Callahan and coworkers [27] is applied in the Handbook of Pharmaceutical Excipients (Table 6.1). These classiﬁcations have in common that they are solely based on determining the increase in mass over a speciﬁed time. However, as discussed throughout this chapter, any classiﬁcation system will be of limited value unless the measurements are tied to studies that evaluate the mechanisms by which the water is taken up and the impact of water sorption on the properties of the solid [11]. 6.3.1

Moisture Sorption Analysis

Water uptake in pharmaceutical solids is typically measured gravimetrically by subjecting the solid sample to various RH conditions at constant temperature for a given period of time. The weight change of the solid is measured as a function of the relative humidity and then translated into a water vapor sorption isotherm. The (de)sorption isotherms generated by GVS analysis are most commonly used to characterize the overall hygroscopicity of a solid material [33], but may also be used to extract detailed information regarding water–solid interactions [34] and possible form changes [35] (Section 6.3.2). A thorough evaluation of hygroscopicity must consider both the equilibrium moisture content of a material as a function of RH and the rate at which equilibrium is attained. A time course plot of moisture sorption data to highlight the kinetics of water vapor uptake is shown for microcrystalline cellulose in Figure 6.2a.

6.3 Hygroscopicity

80

10 8

60

6

40

4 20

2 0 0

500

1000

% Weight change (rel. to dry substance)

(a)

1500

2000

0 2500

Time (min)

1.2

Short equilibration

1.0

Medium equilibration

0.8

Long equilibration

0.32

0.21

0.6 0.11

0.4

Mol ratio (water)

% Weight change (rel. to lowest weight)

12

% Relative humidity

100

14

0.2 0 0 (b)

10

20

30

40

50

60

70

80

0 90 100

% Relative humidity

Figure 6.2 (a) Sorption kinetics of microcrystalline cellulose, showing the extent and rate of water uptake upon incrementally increasing the RH. (b) Water vapor sorption (closed symbols) and desorption (open symbols) isotherms of a nonstoichiometric hydrate collected using diﬀerent equilibration criteria at 25 ∘ C.

A number of experimental procedures must be considered in measuring water vapor sorption/desorption isotherms to ensure that the results properly reﬂect the properties of the solid in a reproducible and time-eﬃcient manner. For one, it is important to fully characterize the sample before the water uptake experiment to provide a comparison for any changes in form that may occur during sample pretreatment or the analysis itself. Characterization would minimally include X-ray powder diﬀraction (XRPD) and water/solvent content, but could be expanded to include other forms of analysis that show diﬀerences in the material, such as spectroscopic techniques. When collecting isotherm data on automated (dynamic vapor sorption) instruments, equilibrium criteria, including the maximum weight change within a certain period of time and the maximum equilibration time, need to be selected. The criteria chosen will determine the length of the runs and the quality of the data. For quick runs to get an overview of water sorption, conditions

163

164

6 Hygroscopicity and Hydrates in Pharmaceutical Solids

such as 2 orders of magnitude without appreciably changing the crystallinity (Figure 6.9b). Careful examination of the form B crystal structure revealed an extended hydrogen bond network of water molecules running parallel to the crystallographic a-axis (Figure 6.9c), which coincides with the longest axis of the columnar-shaped crystals. Because high-energy micronization cleaves slip planes that are approximately perpendicular to the long axis, the water network becomes signiﬁcantly exposed upon jet-milling, allowing for easier egress. Owing to the analytical challenges associated with characterizing drug products [79], the solid-state stability and moisture sorption–desorption pathways exhibited by a drug substance are generally established for highly crystalline samples in isolation of the excipients. Even then, it is important to recognize that some properties are not inherent to the crystalline form but instead are produced by uncontrolled crystallization or mechanical stresses, such as milling and granulation, which introduce defects and imperfections. In fact, it has been suggested that the eﬀects of water–solid interactions on the properties of crystalline drugs are directly linked to the extent to which the solid contains localized regions of disorder and higher molecular mobility [80]. Water will tend to concentrate in these regions, where it can plasticize the solid suﬃciently to induce physical and/or chemical processes (Chapter 7).

179

6 Hygroscopicity and Hydrates in Pharmaceutical Solids

Change In mass (%)

5

Cycle 1 sorp Cycle 1 desorp Cycle 2 sorp Cycle 2 desorp

4

Micronized

3 2 Non micronized

1 0 0

20

40

–1

60

100

80

Sample RH (%)

(a) 20 000 Intensity (Counts)

180

15 000 10 000

Non micronized Micronized

5000

Single crystal prediction

0 5

(b)

10

15

20 25 2Theta (°)

30

35

(c)

Figure 6.9 (a) GVS isotherms of nonmicronized and micronized GSK ApoA-1 upregulator form B. (b) XRPD patterns of nonmicronized and micronized form B overlaid with the simulated pattern from the crystal structure and (c) view of the form B crystal structure (YARREQ), showing water pockets (1.2 Å probe radius). Source: Adapted from Ref. [78] with permission.

6.5 Signiﬁcance and Strategies for Developing Hydrate-Forming Systems The assessment of water uptake is necessary early in the development of a compound to determine hydrate formation, the type of hydrate formed, the critical RH for deliquescence [81], and the possible presence of minor amounts of

Is the material crystalline or amorphous?

Crystalline

Does the material sorb 0.5 and a few micrometers) is composed of very narrow peaks (Bragg peaks). These peaks are positioned at discrete diﬀraction angles (2𝜃) and are of diﬀerent intensities. The position of the peaks is determined by the parameters of the unit cell (Bragg’s law). The intensity of the peaks is directly related to the nature and disposition of the repeating molecular motif. 7.3.1.2

Small or Disordered “Perfect” Crystals

Size eﬀect: If crystallites that compose the powder are of nanometer size ( Tg

6

ε″

5

4

3 1.2

315 K 363 K

ε″

0.9

0.6

0.3

200 K 250 K 3 2 1 log (τ) 0 –1 –2 –3 –4 β –5 –6 –7 –8 –9 –10 –11 5

0.0 1e–3 1e–2 1e–1 1e+0 1e+1 1e+2 1e+3 1e+4 1e+5

(a)

Frequency (Hz)

300 K

350 K

430 K

Tm

Tg

α

4

3

2

1000/T (K)

(b)

Figure 7.13 (a) Real and imaginary part of the dielectric susceptibility of amorphous indomethacin at diﬀerent temperatures between 315 and 363 K. Solid lines are a ﬁt with an Havriliak–Negami function. Source: Carpentier et al. 2006 [59]. Adapted with permission of ACS Publications. (b) Relaxation maps of amorphous indomethacin (Arrhenius diagram: log (𝜏) as a function of 1000/T (K)), which allow us to locate the temperature evolutions of the relaxation times of all identiﬁed processes.

where the activation energy E, which opposes the motion, is more or less constant. E corresponds approximately to the energy required to break an intermolecular bond. 𝜏 𝛼 (T) would become inﬁnite for T = 0 K. • For fragile liquids (especially molecular liquids with weak dispersive bonds), the evolution of the relaxation time at the approach of T g is even faster (super-Arrhenius behavior). It is then necessary to imagine that the activation energy depends on the temperature E = E(T) and increases very strongly during cooling. It is multiplied by a factor 5–6 between T m and T g . This shows that the observed dynamic process does not involve individual molecular motions. It involves a high degree of molecular cooperation that develops as the temperature decreases. Figure 7.14 shows, on an Arrhenius diagram where the temperature is rescaled with respect to T g (Angell plot), the viscosity evolution of several undercooled liquids ranging from strong to fragile [52, 53]. It is found that the most fragile compounds are those for which the curvature is the strongest. The slope measured at T g is then the largest. The value of this slope deﬁnes the kinetic fragility index m [46, 52, 53, 61]: m = d(log10 𝜏𝛼 )∕d(Tg ∕T) (taken at T = Tg )

(7.8)

The “strongest” liquids have an index m ≈ 16. The most fragile have indices of the order of m = 200. Indomethacin has a fragility index of the order of m = 79–83 [59], a value that is typical of relatively “small-molecule” compounds: for nifedipine (m = 83) and for salol (m = 73). For sorbitol, which is a little more fragile, m = 93, whereas for glycerol, which is of intermediate fragility, m = 53.

211

7 The Amorphous State

1011

Zr46.75Ti8.25Cu7.5Ni10Be27.5 Zr41.2Ti13.8Cu12.8Ni10Be22.5

Strong

Mg65Cu25Y10

107

SiO2 Na2O 2SiO2

In do .

glycerol –

K+Ca2+NO3

103

0-Terphenyl

(OTP)

OT

P

Viscosity (Pa s)

212

10–1

Fragile OTP

10–5 0.4

0.6

0.8

1.0

Tg /T

Figure 7.14 T g -scaled Arrhenius representation, proposed by Angell [52, 53], of viscosity for a wide variety of glass formers from strong to fragile, includes plot for indomethacin estimated from the data shown in Figure 7.13. Source: Busch 2000 [60]. Adapted with permission of Springer.

For polymers, the fragility index is generally quite high: for polystyrene, m = 139 and for poly(vinyl chloride), m = 191. The link between kinetic and thermodynamic fragility was brieﬂy discussed in Section 7.5.3. Vogel–Fulcher–Tammann equation (VFT). The temperature dependence of the relaxation times (or viscosity) is fairly well described by the VFT equation: 𝜏𝛼′ = 𝜏0′ exp(E′ ∕[T − T0 ])

(7.9)

′

where 𝜏0′ (𝜏0′ < 10−14 s), E , and T 0 (0 < T 0 < T g ) are adjustable parameters. For fragile liquids, the VFT equation predicts a virtual divergence at a temperature T 0 > 0 rather than 0 K (for very strong liquids). T 0 is then typically located a few tens of degrees below T g . The Williams–Landel–Ferry equation (WLF) is often used to describe the evolution of relaxation times and viscosity. It is mathematically equivalent to the VFT equation [62]. 7.6.2

Link Between Mobility and Entropy

There is an apparent link between the evolution of mobility and thermodynamic characteristics: Strong liquids have an Arrhenius dynamic behavior and have also a small value of ΔC p at T g .

7.6 Molecular Mobility for T > Tg

Fragile liquids have a super-Arrhenius dynamic behavior and generally have a high ΔC p at T g . For fragile compounds, the Kauzmann temperature T K is usually close to the VFT temperature T 0 . This suggests that the conﬁgurational rearrangements (responsible for the evolution of the entropy) would be blocked at T K if the liquid could be cooled to this temperature while remaining at equilibrium. Adam and Gibbs (AG) [63] have built a theory based on this relationship. It assumes the existence of a phase transition to a noncrystalline state, which has zero conﬁgurational entropy and inﬁnite relaxation time at T K . This connection is expressed by the Adam Gibbs (AG) equation [53, 63–65]: 𝜂 ∝ 𝜏 ∝ A exp C∕T Sc (T)

(7.10)

At the cost of some approximations, this relation can be written as follows: 𝜂 ∝ 𝜏 ∝ A exp [E′ ∕(T − TK )]

(7.11)

This relationship has the same form that Eq. (7.9). It allows to interpret the VFT equation in terms of evolution of the entropy and therefore of correlations between molecules. NB we must be careful that, below T g , the critical slowdown is only virtual because the structure of the amorphous compound is practically frozen at T g . Therefore, we cannot use as an argument (which is sometimes done) that, for T < T K , a glassy compound would necessarily be stable because there would be no possible molecular mobility. Relaxational molecular mobility can persist in practice below T K , even if extremely slow. 7.6.3

Cooperative Rearrangement Regions (CRR)

AG hypothesized the development within the liquid of regions (CRR) where the molecules would rearrange cooperatively and whose size would increase when the temperature decreases [66]. In this description, the decrease in conﬁgurational entropy is related to the decrease in the number of CRRs as their size increases. At T K , the size of the CRR becomes inﬁnite, which corresponds to the ideal glass. The size of CRR is a few nanometers at T g [67]. The non-Arrhenian slowdown observed is associated with the increase in the size of the CRRs, which have increasing diﬃculty in reorganizing. This image is useful, but the nature of the CRRs, their interactions, the heterogeneity of their dimensions, etc., are very poorly understood [50]. Figure 7.15 schematically shows the evolution of the sizes of the CRRs in parallel with the non-Arrhenian evolution of the relaxation time and of the viscosity. 7.6.4

Dynamic Heterogeneity: Non-exponentiality of the Relaxation

For ordinary liquids (above T m ), the relaxation toward equilibrium of any microscopic or macroscopic property f (t), after a small applied perturbation, can be usually described by an exponential time decrease. For a supercooled liquid, the response f (t) is no longer exponential and has a more sluggish behavior. It may

213

7 The Amorphous State

exp [A / (T – T0)]

Ag in g

log η log τ

Y Y

Y YY

Y

Y

Poises

Y

Y

Y

β

Cooperatively Rearranging Regions

Y

α

Y

Y

Y Y Y

YY Y

Y Y Y Y Y Y Y

13

Y

Y Y Y

Y

214

–2 1/T

1/T0

1/Tg

1/TSA

1/Tm

Figure 7.15 Arrhenius plot (log (𝜏 or 𝜂) as a function of 1000/T (K)) that summarizes the temperature evolutions of the 𝛼 and 𝛽 relaxation times and viscosity (𝜂). The 𝛼 relaxation time virtually diverges to inﬁnity at T 0 . It evolves in a non-Arrhenius way in parallel with the growth of CRRs. At T g , there is a break of the activation energy that progressively increases upon aging. The 𝛼 and 𝛽 processes seemingly decouple at T SA . The 𝛽 process has an Arrhenius behavior and lower activation energy.

be generally expressed with the Kohlrausch–Williams–Watts function [68], or “stretched exponential”: f (t) ∝ exp[−(t∕𝜏)𝛽 ]

(0 < 𝛽 < 1)

(7.12)

The smaller 𝛽, the more stretched is the relaxation. The exponential behavior is recovered for 𝛽 = 1. The stretching generally increases when temperature decreases and reaches values on the order of 0.3–0.8 at T g . It was observed [46, 69] that low values of 𝛽 are generally correlated with high fragility index m. Experimentally, it is the broadening of the 𝜒 ′′ (𝜔) peak that reﬂects the stretching of the relaxation function mentioned above. It is believed that the non-exponential character is the consequence of kinetic heterogeneities in glass-forming systems with regions of slower and faster molecular mobility that induces a distribution of relaxation times [70–72].

7.7 Molecular Mobility and Instability for T < T g 7.7.1

The Aging Phenomenon

For T < T g , the molecular motions, whose considerable slowdown gives rise to the glass transition, nevertheless remain. This mobility allows the glassy system, and all its physical properties, to evolve very slowly when trying to reach the equilibrium liquid state. This is the aging phenomenon. The lower is the

7.7 Molecular Mobility and Instability for T < Tg

Aging at 20 °C 0.9

0.7 0.6 0.5

0 1 min 5 min 30 min 60 min 3h 6h 12 h 24 h

0.8

Heat flow (mW g–1)

0.8

Heat flow (mW g–1)

Aging at 35 °C 0.9

0 1 min 5 min 15 min 30 min 1h 3h 6h 12 h 24 h 36 h

0.4

0.7 0.6 0.5 0.4 0.3

0.3 0.2 35

40

45

50

Temperature (°C)

0.2 35

55

40

45

50

55

Temperature (°C)

H

Tg

T

Figure 7.16 DSC heating scans for amorphous indomethacin aged during various times ta at two diﬀerent temperatures 20 and 35 ∘ C.

temperature T, the slower is the evolution, and the greater is the imbalance to catch up. [73] During aging, a slow decrease in enthalpy is observed. The DSC makes it possible to measure the eﬀects upon reheating [74]. Figure 7.16 shows the thermograms recorded on amorphous indomethacin after aging of variable duration (t a ) at two temperatures (T a ) below T g . On reheating, there is an endothermic peak situated immediately above the C p jump at T g . For a given T a , the peak grows as t a increases. It grows all the more, but all the more slowly, as the value of T a is low. Figure 7.18 shows a parallel between enthalpy level and speciﬁc heat. It makes it possible to phenomenologically describe the observed behaviors. After aging, reheating gives rise to a rapid catchup with a metastable equilibrium state when the molecular mobility becomes suﬃcient (i.e. slightly above T g ). On the enthalpy diagram, this gives rise to a signiﬁcant transient slope. Its value is nothing else than that reached transiently by C p during this catchup. This is manifested by a peak that is all the more marked as the energy decay during aging has been signiﬁcant. 7.7.2

Approximate Assessment of Stability

The characterization of aging kinetics for T < T g is of particular interest in the pharmaceutical ﬁeld, if it is desired to deﬁne storage conditions for amorphous drugs, and their lifetime. Analyses of this type can be found in the literature [75]. They consist in measuring, at diﬀerent temperatures, the time evolution of the enthalpy decay ΔH(t). This is often approximately achieved by measuring the surface area of

215

7 The Amorphous State

Tg – 16 Tg – 32

2000 Enthalpic relaxation (J mol–1)

216

τ ≈ 3 × 102 h

Tg – 47 1600 1200

τ ≈ 2 × 104 h 800 400 τ ≈ 3 × 106 h

0 0

2

4

6

8 10 Time (h)

12

14

16

Figure 7.17 Enthalpic relaxation of amorphous sucrose at three temperatures lower than T g . The enthalpy has been approximately evaluated from the surface of the overshoot peak as is shown in Figures 7.16 and 7.17. Source: Hancock et al. 1995 [75]. Reproduced with permission of Springer.

the endothermic bump, between the DSC curve of the aged amorphous and the extrapolated line of the liquid. The value at inﬁnite time is estimated using the relation ΔH ∞ ≈ (T g − T) ⋅ ΔC p . After each aging (of given temperature and duration), the sample is heated for DSC analysis. An example of such an investigation at three temperatures below T g is shown in Figure 7.17 for amorphized sucrose obtained by quenching the liquid. A relaxation equation deﬁned by 𝜙(t) = 1 − ΔH(t)∕ΔH∞

(7.13)

is then often adjusted to a stretched exponential (Eq. (7.12)) in order to estimate a relaxation time. Stretching exponents are generally small (𝛽 between 0.3 and 0.8), which suggests a distribution of underlying relaxation processes. It can be seen that the estimated times are of the order of 3 × 106 h at T g − 47 K. Such very high values are found frequently, which is at the origin of the empirical law according to which a glass would be stable in practice at temperatures lower than T g − 50 K. It should be recognized, however, that the stability evaluated in this way does not take into account possible recrystallization possibilities. Faster secondary relaxations, described at the end of the chapter, are additional sources of molecular mobility that are likely to play a role in these recrystallizations. 7.7.2.1

Fictive Temperature

Slow aging relaxations are often tentatively described in terms of the change in the so-called ﬁctive temperature T f [76]. T f of a nonequilibrium glassy system is deﬁned as the actual temperature of the same compound, in metastable equilibrium, whose structure is expected to be similar to that of the nonequilibrium compound. The deﬁnition is illustrated by Figure 7.18, which also shows a method (“equal area rule”) to determine T f [74]. Upon aging at a temperature T a , T f slowly decreases. Its limit value is the aging temperature itself.

7.7 Molecular Mobility and Instability for T < Tg

H Hliq

Slope = Cp

•

Hglass ass

=

d gl

Age

Cp,liq Cp ΔCp Cp,glass Tf

T

Figure 7.18 Fictive temperature: Top: deﬁnition on the H(T) curve. It shows how T f decreases when the glass is annealed. Bottom: experimental determination of T f by application of an “equal area rule” on the C p (T) curve.

7.7.3

Nonlinearity

Below T g , the rate of structural relaxation is itself dependent on the progression of the relaxation process. Thus, we should not expect that a simple stretched exponential function could describe the relaxation of 𝜙(t) at a given temperature. This is basically due to the fact that the relaxation time 𝜏 s depends on the enthalpy and free volume values, which decrease upon annealing, at a rate that is determined by 𝜏 s . The progressive densiﬁcation induces an increase in the diﬃculty for the molecules to move. At a given temperature T, below T g , the instantaneous value of H and V (depicted by T f ) determines the mobility (𝜏), whereas 𝜏 determines the rate, dT f /dt, at which T f (and therefore H, V , etc.) changes. Aging can thus be understood via the closed-loop scheme [76]:

Tf

τ @T

dTf / dt

217

218

7 The Amorphous State

The TNM (Tool, Narayanaswamy, Moynihan) expression [74] is commonly used to describe the dependence of 𝜏 on both T and T f : 𝜏 (T, Tf ) = 𝜏0 exp[xA∕(kB T) + (1 − x)A∕(kB Tf )]

(7.14)

where x is the nonlinearity parameter (0 ≤ x ≤ 1). Maximum nonlinearity for x = 0. Another equation adapted from the more physical Adam–Gibbs model and the entropy evolution [77–79] has been proposed to express the time dependence of 𝜏 in term of T f evolution. 𝜏(T, Tf ) = 𝜏0 exp[E∕T (1 − TK ∕Tf )]

(7.15)

It thus allows deﬁning an isostructural activation energy: E(Tf ) = E∕(1 − TK ∕Tf )

(7.16)

Since T f > T, E (T f ) is lower than the equilibrated value of the activation energy E(T). Aging induces a slow decrease of T f that moves toward the aging temperature T. Aging thus induces an increase of E (T f ), which slowly tends to be closer to the equilibrated value E(T) [79]. Confrontation of the two previous equations allows expressing the nonlinearity factor x ≈ 1 − T K /T g . This relation, and that linking m to 𝛽 [46], shows that the levels of fragility, non-exponentiality, and nonlinearity are connected and rise together. When comparing diﬀerent glass formers, the tendency is as follows: x decreases when m increases, 𝛽 decreases, and T K increases toward T g . 7.7.4

Secondary Relaxations

Below T g , there are many sources of mobility that can contribute to the destabilization of a glass. In addition to the fast vibrations and the very slow 𝛼 relaxations associated with the aging of the glass, there are the relatively fast secondary relaxations. It has been proposed several times that the crystallization rate of amorphous solids near T g is facilitated by secondary relaxations rather than by the main processes [80, 81]. Secondary relaxations may have diﬀerent origins and can be detected by dielectric or mechanical relaxation techniques. They are generally deduced from the values of the frequencies corresponding to the diﬀerent peaks of the imaginary parts of the susceptibility. The timescale of these secondary relaxation processes is generally several orders of magnitude lower than that of the main relaxation motions. Some of these motions (designated by the Greek letters 𝛾, 𝛿, etc.) can be attributed to the internal degrees of freedom of the molecules when the latter are ﬂexible. However, there exists another type of secondary relaxation process that can be observed even if the molecules are rigid and which is intrinsic to the glassy state. It is named Johari–Goldstein (JG) 𝛽 process (𝛽 JG ) or simply 𝛽 process. It is sometimes diﬃcult to distinguish 𝛽 JG processes from other secondary processes. Compared to other secondary processes, the 𝛽 JG process is often closer to the frequency of the main 𝛼 relaxations. Secondary 𝛽 relaxations are generally weaker than the main process and progressively weaken upon aging.

7.7 Molecular Mobility and Instability for T < Tg

Relaxation maps are Arrhenius diagrams (log (𝜏) as a function of 1000/T(K)) that allow us to locate the temperature evolutions of the relaxation times of all identiﬁed processes. Figure 7.13 shows the relaxation maps of amorphous indomethacin [59]. Figure 7.19 shows the relaxation maps of amorphous maltitol and sorbitol [82]. Confrontations of relaxation maps obtained for these last two neighboring compounds help to identify the origin of the diﬀerent relaxation processes. The curves corresponding to the 𝛼 relaxations of the two compounds are bent and shifted with respect to each other because of the diﬀerences in T g . The faster 𝛾 relaxations of both compounds have similar Arrhenius behavior and are almost identical. The 𝛽 JG relaxation is only perceptible for maltitol. It has relaxation time values intermediate between the 𝛼 and 𝛾 processes. The 1e+2 Tg

1e+1

Maltitol

Relaxation time (s)

1e+0 1e–1

β

1e–2

γ

1e–3 CH2OH O OH

1e–4 1e–5

α

OH

CH2OH HOCH COH

OH

HCOH

1e–6

HOCH

1e–7

CH2OH

(a) Tg

1e+1

Sorbitol

Relaxation time (s)

1e+0 1e–1

γ

1e–2

α

1e–3

CH2OH

1e–4

HCOH HOCH

1e–5

HCOH

1e–6

HCOH

1e–7

CH2OH

(b) 1e–8 3

4

5

1000/T

Figure 7.19 Arrhenius plot summarizing the temperature evolutions of the relaxation times of (a) amorphous maltitol and (b) amorphous sorbitol. (b) Source: Carpentier and Descamps 2003 [82]. Reproduced with permission of ACS Publications.

219

220

7 The Amorphous State

diﬀerent relaxation processes seem to converge at a temperature T SA greater than T g (Figures 7.13, 7.15, and 7.19). Above T SA , we observe a unique Arrhenian process. Below T SA , main and secondary processes seem to decouple. Molecules involved in the 𝛼 process begin to evolve more cooperatively below T SA . The 𝛽 JG relaxations are all the more clearly identiﬁed as the compound is fragile and exhibits non-Arrhenius behavior of the main 𝛼 relaxations. According to Johari [83], 𝛽 JG relaxation would correspond to molecular motions of molecules situated in local regions of low density, the so-called “islands of mobility.” They have an Arrhenius-type evolution with activation energies much lower than that of the 𝛼 process. Another type of interpretation [84, 85] considers that the main and secondary relaxation is continuous. They represent the evolution with time of a single process whose early time is not sensitive to cooperativity (𝛽 process) while the long time behavior corresponds to the main 𝛼 process.

7.8 Multicomponent Amorphous Systems: Solubility and Stability Issues The practical use of the amorphous state of a pharmaceutical compound involves interactions with one or more other components. This is the case when one considers the question of “dissolving” an amorphous active pharmaceutical ingredient (API) in water or the plasticizing eﬀect of a solvent. However, this is also the case when considering the formulation of amorphous solid dispersions (ASD) of an API in a polymer matrix, for stabilization purposes. There are speciﬁc reviews devoted to the various problems of dissolving poorly soluble drugs and stabilizing amorphous compounds or fragile biopharmaceutical compounds [86, 87]. Currently, our discussion focuses on the fundamental physical aspects that are involved in the use of amorphous multicomponent systems. The characterization of their physical properties, and stability, needs to consider the following two questions: • The limit of solubility of one compound in the other, as a function of the temperature. • The variation and the evolution as a function of the concentration of the glass transition temperature T g of the mixed amorphous system. Obtaining these data makes it possible to plot a useful state diagram that associates equilibrium and nonequilibrium information about the system. 7.8.1

Solubility: Comparison of Crystalline and Amorphous States

The formation of a molecularly homogeneous multicomponent system needs considering the solubility limit of the components, which is temperature dependent. The concept of solubility limit itself is diﬀerent for crystalline and amorphous solid states. This is so because the dissolution of a crystal, unlike an amorphous solid, needs to provide the energy that destroys the crystal lattice (endothermic process Figure 7.21). An amorphous solid is a liquid of extremely

7.8 Multicomponent Amorphous Systems: Solubility and Stability Issues

high viscosity. It is, wrongly named “dissolution,” rather a dilution. The stability condition, speciﬁc to multicomponent systems, needs evaluating the right Gibbs free energy, which now includes the mixing enthalpy ΔH mix and the mixing entropy ΔSmix as (7.17)

ΔGmix (T) = ΔHmix − T ΔSmix

where ΔH mix and ΔSmix are the diﬀerences between the enthalpy and entropy between the mixed and unmixed states, respectively. (ΔSmix > 0 while ΔH mix can be of any sign according to the type of interaction.) In the following, we use a graphical description of the binary system API–solvent (or polymer) that allows to intuitively visualizing the possible situations. The equilibrium states of a binary system can be obtained from the G(X B ) curves at a given temperature T 0 and use the common tangent construction [21, 90]. Figure 7.20a,b shows examples of G (Mixed syst.) G (API)

lut ion

ideal or hetero-interactions

o Am

so

@T0

)

us

rph

o ph

or

ous

m

(a Liquid

Xc Sol. pol.

Crys t Concentration (%)

API Tm

T0

al Tm

T

T0

Sol. pol.

Concentration (%)

API

(a)

Figure 7.20 (a) ΔHmix ≤ 0: No miscibility gap in the liquid state. Phase diagram and common tangent construction. There is a solubility limit for the crystal state of the API, but not for its amorphous state. (b) ΔHmix > 0. The green line indicates the existence of a miscibility gap in the liquid state. Phase diagram and common tangent construction. The red tangent (and the red curve in the bottom diagram) corresponds to the nonequilibrium situation in which the glassy amorphous state of the API is put in contact with the solvent. The green tangent corresponds to the equilibrated situation: X 1 corresponds to the liquid solution in which the amorphous API dissolves in the liquid solvent. X 2 corresponds to the amorphous solution in which the solvent penetrates into the amorphous API. X am is the initial apparent limit of solubility of the glassy API before penetration of solvent in it.

221

222

7 The Amorphous State

G (mixed syst.) G (API) Homo-interactions

Am us ho orp

@T0

Cryst

al

Solv. pol.

T0

Solv. pol.

Concentration (%)

API T0

X1

Xam

Concentration (%)

T

X2

API

(b)

Figure 7.20 (Continued)

free energy diagrams and common tangent constructions. There are two cases to consider: ΔH mix ≤ 0. No solubility (strictly speaking miscibility) limit for the amorphous API: It is the case where A (solvent or amorphous polymer) and B (API) molecules like each other (ΔH mix < 0 exothermic solutions) or are indiﬀerent to each other (ΔH mix = 0 ideal solution). The Gibbs energy curve, at T 0 , for the liquid solution (Gsol (X B )) is U-shaped. For X B = 1, its value coincides with that of the amorphous solute: GAm (X B = 1). It is possible to draw a common tangent between Gsol (X B )) and the Gibbs free energy curve of the crystalline API: Gcryst (X B ). This determines the value of the limit of solubility (X c ) of the crystalline API at T 0 . At the opposite, there is no limitation of the mutual solubility between A and the amorphous API (BAm ) in the liquid states as it is obviously impossible to draw a tangent to G(X B ) starting from GAm (X B = 1). ΔH mix > 0. Existence of a miscibility gap in the liquid (amorphous) state: It is the situation where A and B molecules “dislike” each other. At low enough temperature, the Gsol (X B ) curve assumes a W-shape with a negative curvature in the middle. This is due to the fact that the enthalpic term overwhelms the entropic one. In that case, the most stable liquid solution is a mixture of two liquid-like phases of diﬀerent compositions. These compositions are given by the common tangent rule applied to the W-shape curve. The two phases are, respectively, a liquid solution where the amorphous compound BAm dissolves in the liquid solvent

7.8 Multicomponent Amorphous Systems: Solubility and Stability Issues

(concentration X 1 ) and an amorphous solution where the solvent penetrates into BAm (concentration X 2 ). X 1 is the limit of solubility for BAm . As the amorphous glassy state is out of equilibrium, the eﬀective limit of solubility X am depends on its eﬀective level of free energy. It varies with the way to prepare the amorphous state, the aging conditions, the penetration of the solvent water in the glass, etc. X 1 is only a limit value as the penetration of water in the amorphous API is extremely slow. 7.8.2

T g of Amorphous Multicomponent System

A very important question concerning the nonequilibrium properties of amorphous multicomponent systems is that of the T g of a mixture. Because T g is an indicator of molecular mobility, its value has an evident impact on the stability of a mixed system. The presence of two T g ’s indicates a two-phase system. A single T g is often taken as evidence of a miscible blend. The addition to an API, of an amorphous polymer that has a high T g , can be used to increase the overall T g value, and, thereby, decrease the molecular mobility at the storage temperature (anti-plastiﬁcation). On the contrary, the absorption of water in amorphous solid has for eﬀect to decrease the T g (plastiﬁcation). Several equations have been proposed to express the T g ’s of homogeneous molecular blends as a function of the T g ’s of its individual components, e.g. those of Fox [91], Gordon and Taylor [92], Couchman and Karasz [93], to mention only the one most often used. The simplest ones are based on the assumption of a simple weighted average of the T g ’s of the components or of the additivity of the free volumes. Tg,mix = (𝑤API Tg,API + K ⋅ 𝑤solv Tg,solv )∕(𝑤Api + K ⋅ 𝑤solv )

(7.18)

where w represents the weight fraction of the component and K is a constant. K is often taken as a simple ﬁtting parameter. In a prediction concern, several expressions of K, as a function of characteristics of the individual components, have been proposed: That of Gordon–Taylor is given by K = Tg,API 𝜌API ∕Tg,solv 𝜌solv

(7.19)

That of Couchman–Karasz is given by K = ΔCp,API ∕ΔCp,Sol

(7.20)

where ΔC p is the speciﬁc heat capacity change across the glass transition for the components. These equations are only able to predict T g -composition curves that show negative deviation from the rule of mixture prediction. Experimental studies show both negative and positive deviations from a simple weighted average of the two T g ’s of the components. The nature of the deviation from ideality has been attributed to the nature of speciﬁc interactions in the API–solvent system. In particular, positive deviation occurs in systems with strong intermolecular interactions and formation of complexes. That has been tentatively taken into account in several approaches based on mainly thermodynamic arguments

223

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7 The Amorphous State

[94, 95]. Considering the large variety of possible interactions between pharmaceutical components, it has been realized that no simple equation can be applied universally [96]. The link between the T g ’s value and molecular mobility changes in a mixed system can be understood on the basis of the simple AG expression and the magnitude of the conﬁgurational entropy (Eq. (7.10)): The increase in the disorder induced by the mixing of the components causes an increase in conﬁgurational entropy, a decrease in the main relaxation time, and thus a decrease in T g . On the contrary, the formation of molecular complexes induces a decrease in entropy, an increase in relaxation time, and thus an increase in T g and a positive deviation from ideality. 7.8.3

Improved Dissolution Properties

One approach to improve dissolution of poorly soluble drugs is to prepare them in an amorphous form. There are many examples of this in the literature. Figure 7.21a shows the dissolution proﬁles of amorphous and crystalline indomethacin (𝛾 phase) [88, 89]. The amorphous form clearly shows a peak of higher apparent solubility (spring eﬀect). At longer times, the concentration in water slowly decreases (parachute eﬀect) partly because of the formation of the crystalline form. But the concentration remains signiﬁcantly higher than that of the crystalline form. Figure 7.21a,b can be used to follow the dissolution process in the solvent. Starting from the amorphous state allows a super-saturated solution to be rapidly prepared. The crystallization that requires the crossing of a nucleation barrier occurs only slowly in a second stage. The addition of a polymer in the initial formulation (ASD) often allows the parachute eﬀect to be further extended. The diﬀerence in the nature of the two dissolution processes is illustrated in Figure 7.21b. It shows the dissolution behavior in water, of crystalline anhydrous trehalose, and amorphous trehalose. Crystalline sample presents an endothermic enthalpy of dissolution. It is associated with the energy that must be provided for the solvent to break the intermolecular bonds of the crystal. Conversely, that of trehalose in the amorphous state shows an exothermic response, which is associated with the natural tendency of molecules of water and amorphous lactose to mix together. Figure 7.21 also shows that the dissolution of an aged amorphous sample presents a signiﬁcant change in the enthalpy of dissolution (less exothermic). This is linked to the increase in densiﬁcation for the molecules of the aged sample. 7.8.4

Mixing and Stabilization

If the solubility is improved when the drug is amorphous, it is also less stable and its recrystallization propensity cannot aﬀord to guarantee the therapeutic characteristics of the material during storage. A possible strategy for stabilizing an amorphous drug against crystallization is to disperse it molecularly into a polymeric matrix in order to hinder drug re-precipitation and crystallization. The increase in stability is linked to the low molecular mobility and an increase in T g

7.8 Multicomponent Amorphous Systems: Solubility and Stability Issues

Aqueous solubility (mg/100 ml)

3.0 25 °C

Spring 2.5 2.0

Pa

ra

ch

ut

1.5

e

Amorphous

1.0 0.5

γ-Crystal 0.0 0

20

(a)

40

60

80

100

120

Time (min) Isothermal dissolution calorimetry (C80/Sétaram) Quenched liquid (–53.6 J/g)

Quenched liquid aged 10 h at Tg – 10°C (–45.5 J g–1)

Heat flow (a.u.)

exo

Crystal (60.5 J g–1)

20 (b)

40

80 60 Time (min)

100

120

Figure 7.21 (a) The in vitro experimental aqueous solubility proﬁles of indomethacin (measured at room temperature). Comparison of the behaviors of the most stable crystalline form 𝛾 and of the amorphous form obtained by quench cooling of the melt. Source: Adapted from Murdande et al. [88] and Hancock and Parks [89]. (b) Dissolution behavior, in water, of crystalline anhydrous trehalose and amorphous trehalose. Crystalline sample presents an endothermic enthalpy of dissolution. That of trehalose in the amorphous state shows an exothermic response. The dissolution of an aged amorphous sample is less exothermic.

provided by the polymer, if API and polymer molecules are intimately mixed [97]. This technique necessitates a good knowledge of the solubility of crystalline drugs in polymeric matrixes. This property is, in particular, important for selecting appropriate polymers for formulations as it deﬁnes the maximal drug loading without a risk of recrystallization. Figure 7.22 shows a schematic state diagram of an API and a polymer. It allows locating the concentration–temperature domain where molecular level mixing can be achieved in a stable glassy solution (left part

225

226

7 The Amorphous State

T

T

Tg

Tm

it

ility lim

Solub

Anti-p

lastic

izatio

n Tg

Polymer

%

API

Figure 7.22 Schematic state diagram of an API and a polymer. It allows to locate the concentration–temperature domain where molecular level mixing can be achieved in a stable glassy solution (left part of the diagram). Melting point depression of the API arises because the drug in the amorphous molecular level solid dispersion has a chemical potential equal to that of the crystalline drug at a lower temperature than the melting temperature of the pure drug.

of the diagram). Measuring the drug/polymer solubilities is, however, a diﬃcult task, which arises from the high viscosity of polymers. That makes the solubility equilibrium diﬃcult to reach and the determination of solubility curves very time-consuming [87, 98, 99]. A new method, which is based on the preparation of molecular solid solutions by mechanical alloying, allows to save a lot of time [100]. However, the low API concentration domain, which is the most important to know, is in practice very diﬃcult to explore experimentally. Many reports have been made to estimate numerically API–polymer miscibility [98, 99]. The Hildebrand solubility parameter approach [97] and the group contribution methods [101] are often used. These methods must be considered when choosing the polymer carrier. However, a number of problems remain for a quantitative estimation, especially since the API’s solubility in polymer is often rather limited (in the range of 2–8%). Predictive methods for the thermodynamic properties of liquid mixtures (such as COSMO-RS [102]) which combine statistical thermodynamic approaches with a quantum mechanical calculation are emerging. A number of applications have been already reported for predicting the free energy of mixtures of small molecules. Predicting the solubility of the polymer and solvent requires special treatments [103]. In the present, the COSMO-RS method treats polymer as a liquid solvent of monomer repeat units. It still needs some improvement to predict high solute loading with a high degree of accuracy.

7.9 Methods of Amorphization There are numerous methods for obtaining an amorphous state and several possible choices for classifying these methods. One could, for example, imagine classifying them according to the initial state of the compound to be amorphized:

7.9 Methods of Amorphization

gaseous, liquid, or crystalline. We will classify them according to the fundamental physical mechanisms involved. There are three main ways of amorphization (Figure 7.23): • The thermal route that consists in cooling the liquid state of a compound or of a solution while avoiding crystallization • The mechanical path that is a mechanism of direct amorphization in the solid state and consists in destroying an initial crystal order. The mechanical action can be static as in the case of applying pressure or dynamics during grinding. The mechanical destruction of a crystalline order can also result from rapid desolvation of a crystalline solvate • The concentration without crystallization from a diluted form, which may be gaseous (condensation of a vapor on a cold surface) or liquid (concentration of a solute in a solution). In practice, vitriﬁcations obtained by laboratory or industrial processes often combine these diﬀerent routes. In lyophilization, for example, cooling is applied to a solution that induces phase separation and an increase in the concentration of the compound to be amorphized. In hot melt extrusion (HME), a thermal cycle is combined with shearing. From the point of view of pharmaceutical applications, it is important to distinguish cases where amorphization is accidental or intentional. If it is intentional, it is useful, in practice, to know whether the method used is adaptable to large-scale production. At the preclinical level, where it is suﬃcient to prepare a few hundred milligrams or at most a few grams of amorphous substance, several techniques may be used, which are not necessarily transposable on an industrial scale.

Undercooling of a liquid

Glassy state amorphous solid

Mechanical perturbation of a crystal:

Concentration of a diluted form:

– Milling – Pressure – Desolvation of a solvate

– Vapor deposition – Precipitation – Drying

Figure 7.23 Principal routes for the formation of pharmaceutical glasses.

227

228

7 The Amorphous State

The amorphization may involve a pure API or a combination thereof with a pharmaceutically acceptable excipient in the form of an ASD. An ASD is used to enhance the stability of an active compound of low molecular weight, which is intrinsically unstable in the amorphous state [104–106]. In this case, the excipient (often a polymer [107]) should be selected so that the API–excipient interaction and its T g value are appropriate to provide suﬃcient physical stability to the ASD. It must not impair the degradation of the API and prevent its recrystallization. It is also necessary that it can be processed by the chosen route, which requires knowing its physical and chemical response to the speciﬁc perturbations of the process (high shear, high temperatures, etc.). The main methods for preparing amorphous materials are brieﬂy described below. One or the other is used depending on the type and amount of active substance to be formulated. • Thermal quenching from the liquid is a useful technique for producing small amounts of amorphous phase for preliminary evaluations. It requires the prior melting, on heating, of the API or of the components of the solution. The quenching of the liquid must be carried out to temperatures below T g and be fast enough to avoid the recrystallization of the liquid under cooling. This easy-to-use method makes it possible to test the stability of an amorphous compound in early preclinical work. It can only be used in the case where the compounds do not degrade chemically during heating. At the industrial level, a large number of methods combine this thermal eﬀect with other processes using mechanical actions or allowing the samples to be dispersed. • High-energy milling of crystalline materials [108, 109] is useful for producing small amounts of amorphous materials. Milling is also one of the main sources of accidental amorphization suﬀered during the formulation of the compounds in crystalline form. The nature of the ﬁnal product depends on both the milling intensity and the milling temperature [109]. To obtain amorphization, it is necessary that milling be carried out at a temperature lower than the glass transition temperature (T g ) of the substance [110]. From this point of view, cryogenic grinding performed at liquid nitrogen temperature may be more eﬃcient in producing an amorphous material. The milling duration must be meticulously controlled. Particular attention should be paid to the fact that the remaining crystalline residues can seed the part of the product that has been amorphized. This may lead to more or less rapid recrystallizations. For the same reason, the analysis of the physical state of the ground material may be distorted if it is not carried out quickly enough after grinding. It is, therefore, important to know how to identify small proportions of crystalline products within an essentially amorphous material. Amorphization by milling is of particular interest for compounds that are not thermally stable. This is the case, for example, of lactose or glucose, which caramelizes upon heating and undergoes mutarotation upon melting or dissolution. Mechanical grinding is then the only amorphization method that makes it possible to obtain these compounds in an anomerically pure and non-caramelized form [111–113]. This method of amorphization allowed to analyze in detail the coupling of the anomerization mechanism with the relaxation mobility of the amorphous

7.9 Methods of Amorphization

compound [114, 115]. The co-milling of crystalline compounds also makes it possible to force the formation of homogeneous amorphous alloys of immiscible compounds [100, 116–118]. • Dehydration of crystalline hydrates (or solvates) may in some cases be used to produce an amorphous material. The amorphization is then induced by the departure of the water or solvent molecules that mechanically disorganizes the initial crystal lattice. In the case of trehalose dihydrate, it has been shown that anhydrous amorphous form can be obtained if the dehydration is fast enough [119–121]. This requires careful control of the dehydration temperature [122]. Li et al. [123] investigated the amorphization of crystalline carbamazepine dihydrate upon dehydration. This method is, of course, not applicable to produce an amorphous dispersion. • Hot melt extrusion (HME) is a frequently reported method for preparing ASDs, especially for poorly soluble drugs such as ketoprofen, felodipine, itraconazole, etc. [124]. It is a continuous process that is solvent free. Unlike the methods mentioned before, which can be diﬃcult to apply on a large scale, HME is easily scaled up. It involves mixing, melting, and homogenizing and allows to easily use several additives. The diﬃculty mainly lies in the limited choice of usable excipients. Given the combination of thermal and mechanical disturbances imposed on the multicomponent system, it remains diﬃcult to understand the behavior of the material during the HME process and to predict its ﬁnal state. The perturbations applied in the amorphization methods (grinding, heating, etc.) are also used in the formulation of crystalline materials. This can lead this time to accidental amorphization, which may compromise the stability of the compounds. For example, Lefort et al. [125] demonstrated with solid-state NMR that the amorphous content of trehalose samples increased from 20% to 48% after ﬁve minutes of milling. It is, therefore, important this time to be able to identify small proportions of the possible amorphous product and to control the parameters of the process in order to obtain compounds having the desired physical purity. The methods mentioned above do not require a solvent. Another type of amorphization method is based on solvent evaporation, which poses the problem of its complete elimination. Spray-drying [126] converts a liquid solution into a powder in one step: Concentrated liquid is broken into small droplets, which are dried in a hot gas. It has been widely used to prepare formulations that contain a large variety of active ingredients. The method is fast and easily scaled up so that half of the commercialized solid dispersions were prepared by spray-drying. The method is adapted when molecules are not too heat sensitive. Freeze-drying [127–129] is a more complex method to implement because it involves several steps. The principle is to remove ice from a frozen aqueous solution and then drying the residual nonfrozen water. The formulation mainly consists of a glassy matrix composed of carbohydrate molecules or water-soluble polymers. The method is used when drug molecules have poor storage stability in an aqueous solution. Freeze-dried solid dispersions are characterized by a high

229

7 The Amorphous State

porosity and amorphous nature. They allow rapid dissolution of the product for reconstitution before administration. Coprecipitation and ﬁlm castings are other solvent evaporation-based methods that have not been so widely used. New processes and manufacturing technologies for the preparation of ASDs are emerging in the pharmaceutical ﬁeld. It is, for example, the spin coating that uses very fast solvent evaporation. Others are electro-hydrodynamic techniques such as electrospinning and electrospraying in which a strong electrical potential is applied to a liquid. Depending on the composition of the liquid, hyperquenching and (or) fast desolvation can thus be applied. Other techniques such as inkjet and 3D printing are in an early stage development. Detailed reviews and discussions of the classical and emerging techniques for the preparation of glassy pharmaceuticals are available elsewhere [130, 131].

7.10 Inﬂuence of Processing on Properties

40 mW g–1

As it is a nonequilibrium state, the amorphous form of a drug varies depending on the way it has been processed and stored. The value of T g is generally not signiﬁcantly altered; however, the eﬀect is easily identiﬁable on the shape of the DSC scan in the vicinity of T g . Figures 7.16 and 7.18 have shown how aging modiﬁes the DSC scan. It modiﬁes it through the growth of an overshoot peak that reﬂects the progressive decrease in apparent enthalpy of the amorphous compound. On the contrary, the eﬀect of actually hyperquenching a glass, by one

As cooled Aged 6 days @ 25 °C

Heat flow

230

10

Cryomilled 15 mn after aging

20

30

40

50

60

Temperature (°C)

Figure 7.24 Illustration of the impact of the history of a glassy sample on the DSC heating scan. DSC heating scans (2 ∘ C/min) of indomethacin recorded in the glass transition domain. Dotted line: quenched melt. Full line: quenched melt after a six day annealing at 25 ∘ C. Dashed line: quenched melt after six days of annealing at 25 ∘ C followed by a 15-min cryo-milling. Source: Adapted from Descamps and Willart [108] and Descamps et al. [132].

7.11 Concluding Remarks

Fast cooling Slow cooling Amorphous

100

Crystalline

% dissolved

80 60 40 20

5

15

30

60 Time (min)

Figure 7.25 Dissolution of felodipine in water–ethanol. Crystalline felodipine is indicated by Δ. Glassy felodipine prepared by cooling under ambient conditions is indicated by •. Glassy felodipine prepared by quenching in liquid nitrogen is indicated by ○. Source: Kerc et al. 1991 [135]. Reproduced with permission of Elsevier.

process or another (very fast cooling, high-energy grinding, fast drying, etc.), is to trap it in a very-high-energy situation. Upon reheating at the normal rate, the DSC thermogram then shows speciﬁc sub-T g events: exotherm and sub-T g peaks [108, 132–134] (Figure 7.24). Depending on the energy level of the glass, marked changes in the dissolution rate can be expected. Figure 7.25 shows the inﬂuence of cooling rate on the “dissolution” of amorphous felodipine [135].

7.11 Concluding Remarks In a book devoted to polymorphism, the glassy amorphous state has a somewhat speciﬁc situation because it is not a phase in the thermodynamic sense but rather a state. It corresponds to a situation of nonequilibrium that causes considerable physical problems. It is an unstable state and not a metastable one. It is inexorably subjected to an aging eﬀect, which induces more or less rapid changes in its physical properties. For the same reason, it depends on how it was prepared. Not being in equilibrium, its physical state cannot be described by a restricted number of variables and state functions. This is related to the intrinsic diﬃculty of patenting a compound in the glassy state [55]. One cannot strictly reduce its description to a few characteristic values. Despite these diﬃculties, the use of the amorphous state currently raises considerable interest, for various practical reasons, in ﬁelds as diverse as metallurgy, polymer science, food, medicine, and pharmaceutical science. In all these areas, the problems related to its use are the same. They are mainly associated with the formation and stability of glasses as well as with a need to classify glassy states and if possible to predict behaviors. The problem of the glass transition, in the broad sense, is the object of an intense fundamental activity in condensed matter physics. Great progress has been made

231

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7 The Amorphous State

in its understanding. This should help pharmaceutical scientists to have a positive and critical attitude to the use of this state, which is the subject of opinions that are too often a matter of fantasy rather than science. The aim of this chapter is to try to bridge the gap between the concerns of pharmacy practitioners and condensed matter physicists.

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Wiley-VCH 522 pages. 2 Reiner, M. (1964). The Deborah Number. Physics Today 17 (1): 62–62. 3 Guinier, A. (1994). X-Ray Diﬀraction in Crystals, Imperfect Crystals, and

Amorphous Bodies. Dover. 4 Wright, A.F., Fitch, A.N., and Fender, B.E.F. (1986). How disordered can a

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crystallized glass be? Annals of the New York Academy of Sciences 484 (1): 54–65. Gaskell, P.H. (1986). How ordered can a glass be? Annals of the New York Academy of Sciences 484 (1): 66–80. Wikipedia (2017). Scherrer equation. https://en.wikipedia.org/wiki/Scherrer_ equation (accessed April 2017). Shalaev, E. et al. (2016). Crystalline mesophases: structure, mobility, and pharmaceutical properties. Advanced Drug Delivery Reviews 100: 194–211. Descamps, M. et al. (2005). Plastic and glassy crystal states of caﬀeine. Journal of Physical Chemistry B 109 (33): 16092–16098. Descamps, M. and Decroix, A.A. (2014). Polymorphism and disorder in caﬀeine: dielectric investigation of molecular mobilities. Journal of Molecular Structure 1078: 165–173. Srinivasan, A. et al. (1996). Evidence for a supercooled plastic-crystal phase in solid ethanol. Physical Review B 53 (13): 8172–8175. Descamps, M. et al. (1997). “Pre-peak” in the structure factor of simple molecular glass formers. Progress of Theoretical Physics Supplement 126: 207–212. Morineau, D. and Alba-Simionesco, C. (1998). Hydrogen-bond-induced clustering in the fragile glass-forming liquid m-toluidine: experiments and simulations. Journal of Chemical Physics 109 (19): 8494–8503. Bordet, P. and Martinetto, P. (2016). Use of the pair distribution function analysis in the context of pharmaceutical materials. In: Disordered Pharmaceutical Materials (ed. M. Descamps). Wiley-VCH. Bordet, P. et al. (2016). Solid state amorphization of β-trehalose: a structural investigation using synchrotron powder diﬀraction and PDF analysis. Crystal Growth & Design 16 (8): 4547–4558. Terban, M.W. et al. (2016). Recrystallization, phase composition, and local structure of amorphous lactose from the total scattering pair distribution function. Crystal Growth & Design 16 (1): 210–220. Debenedetti, P.G. (1996). Metastable Liquids – Concepts and Principles. Princeton University Press.

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17 Andronis, V. and Zograﬁ, G. (2000). Crystal nucleation and growth of

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8 Approaches to Solid-Form Screening Rolf Hilﬁker1 , Fritz Blatter1 , Martin Szelagiewicz1 , and Markus von Raumer2 1 Solvias AG, Römerpark 2, 4303, Kaiseraugst, Switzerland 2

Idorsia Pharmaceuticals Ltd., Hegenheimermattweg 91, 4123 Allschwil, Switzerland

The fact that a particular active molecule may be crystallized in a host of diﬀerent forms (polymorphs, salts, and co-crystals) presents at the same time a huge opportunity and a challenge. The opportunity is that one may be able to obtain a solid form with optimal properties, such as high solubility, low hygroscopicity, good chemical and physical stability, good ﬂow properties, etc. The challenge is to ﬁnd a way to prepare and characterize the relevant forms. This means that a sound screening strategy for solid forms is required. A scheme for a sensible screening and selection strategy is depicted in Figure 8.1. The whole process is divided into two stages, i.e. “screening” where the various forms are made and “selection” where the forms are characterized in order to understand their relative stability and where it is assessed if they are suitable for further development. The ﬁrst question to ask is whether it may be possible to form a salt of the active molecule (free drug), i.e. if the molecule has reasonably strong acidic or basic groups. If salt formation is not feasible, then it may still be possible to create co-crystals (see Chapter 3) with improved properties relative to the free molecule. If salt formation is possible, solid forms with very diﬀerent properties may be produced (see Chapter 2), which is a reason why almost half of small-molecule drugs are administered as salts. Sometimes, only amorphous solids are obtained at ﬁrst in a salt or co-crystal screen. If physical data suggest that these amorphous solids represent a precursor to a crystalline substance (if, for example, the solids obtained in a salt or co-crystal screen are amorphous, but the Raman spectra show signiﬁcant line shifts relative to the amorphous free drug, this is an indication for an interaction between the free drug and the acid/base/co-crystal former), crystallization screens have to be performed. Thus, in the most extensive screening approach, one would screen for various salts and co-crystals for free drugs with acidic or basic groups and follow that up with polymorphism screens for selected salts, co-crystals, and the free drug. It is a diﬃcult decision how extensively one should screen for solid forms. Very extensive screens lead to a better and safer product and broad patent protection while increasing development costs. Therefore, intelligent design of screens is vital, so that a large parameter space is explored with minimal experimental eﬀort. Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development, First Edition. Edited by Rolf Hilﬁker and Markus von Raumer. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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Free drug

Candidates: · Free drug · Co-crystals

No

pKa(s) ?

Yes

Candidates: · Free drug · Salts · Co-crystals

Salt and/or co-crystal screening Crystallization screening

Crystalline candidates ?

No

Yes Polymorphism screening Screening

Characterization

No Selection

Good solid forms ? Yes Select suitable solid form

Figure 8.1 Scheme for form selection process.

In the selection phase, these various forms will then be characterized in depth and the optimal form will be chosen. In practice, this procedure is often abbreviated. If, for example, the free drug has suﬃciently good properties in terms of solubility and stability, salt and co-crystal screens may be omitted and only a polymorphism screen has to be carried out.

8.1 Screening for Salts and Co-crystals As making a salt or a co-crystal will normally involve an additional step in the synthesis and as the molecular weight of a salt or co-crystal will always be higher

8.1 Screening for Salts and Co-crystals

than that of the neutral molecule, salts or co-crystals will only be chosen if they promise to have clear advantages compared to the free acid/base. As a rule, a salt is chosen if the free acid/base has at least one of the following undesirable properties: very low solubility in water low melting point high hygroscopicity low chemical stability problematic solid forms, such as channel hydrates or enantiotropic polymorphs with a transition temperature close to room temperature • other undesirable properties such as unfavorable habit • intellectual property (IP) issues • • • • •

The potential acids or bases that might be able to form a salt with the API (active pharmaceutical ingredient) under investigation are chosen based on pK a diﬀerences, counterion toxicity (preferably generally recognized as safe (GRAS) status, see also the classiﬁcation scheme in [1, 2]), etc. As a rule of thumb, a pK a diﬀerence of 2–3 is suﬃcient for salt formation (see Chapter 2). It is advisable to perform salt screening and salt selection in stages, starting on the microscopic scale (e.g. a 96-well plate format) where a large number of salts is produced and characterized using a limited number of methods (e.g. birefringence, Raman spectroscopy, and X-ray powder diﬀraction (XRPD)) in order to identify a few promising candidates. Suitable methods for producing salts in such a high-throughput format include very slow evaporation of stoichiometric quantities of the acid and base in a variety of solvents where the solubilities of the acid and the base are suﬃciently high and slurrying of the acid and base in solvents where the solubility of the salt is not very high. In the second stage, the successful candidates of the high-throughput screening (HTS) are then produced on the scale of a few hundred milligrams and characterized in more detail in order to select the best ones. Desirable properties of the salts include crystallinity, high water solubility, low hygroscopicity, good chemical stability, and a high melting point. The relative importance of these properties may vary from project to project. Co-crystals can oﬀer valuable alternatives, especially for very weak bases or acids. Reasons for attempting to make co-crystals are the same as for salts.

8.1.1

Example of a Co-crystal Screen

A certain API had a needle-like morphology with an extremely large aspect ratio (Figure 8.2). Because of the corresponding low bulk density, this posed considerable problems during formulation and processing, as the API required a high dosage strength. Attempts to change the morphology by changing crystallization conditions and the solvents for crystallization failed, and salts were not an option because the API was neither acidic nor basic. Therefore, co-crystal formation was attempted.

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100 μm

Figure 8.2 Microscope image of an API with an unfavorable needle-like morphology.

The API had an amide group that can form very strong interactions with carboxylic acids by forming H N O eight-membered rings with two hydrogen bonds (see R R Figure 8.3), making carboxylic acids promising candidates for co-crystal formation. O O H The following 24 compounds were selected as Figure 8.3 Possible potential co-crystal formers based on their poteninteraction motif between tial interaction with the API and their toxicity: an amide and a carboxylic acetylsalicylic acid, l-aspartic acid, benzenesulfonic acid. acid, benzoic acid, citric acid, ethanedisulfonic acid, fumaric acid, gentisic acid, l-lactic acid, maleic acid, l-malic acid, malonic acid, l-mandelic acid, methanesulfonic acid, oxalic acid, pamoic acid, saccharin, succinic acid, l-tartaric acid, ethyl maltol, methyl 4-hydroxybenzoate, urea, l-proline, and l-tryptophan. In order to optimize the chances of success of a co-crystal screen, an understanding of phase diagrams of the co-crystal former, API, and solvent is very beneﬁcial [3–5]. However, it should always be kept in mind that each individual compound behaves diﬀerently and that the scientist has to become familiar with the properties of the compound. This requires a ﬂexible strategy that is adapted to molecular properties. In this particular case, equimolar amounts of the API and co-crystal former were mixed in four diﬀerent solvents where the API and co-crystal former had similar solubilities. These 96 (4 × 24) solutions were then evaporated very slowly under a controlled nitrogen stream in a 96-well plate. The resulting solids were analyzed by Raman spectroscopy and XRPD. In a second set of experiments, equimolar amounts of the API and co-crystal former were mixed in four diﬀerent solvents that did not dissolve the API and co-crystal former. These slurries were temperature cycled for four days, then the solvent was evaporated, and the solids were analyzed in the same way. The XRPD and Raman spectra of the H

8.3 Screening for Polymorphs, Hydrates, and Solvates

192 samples showed that, in many cases, crystalline API and/or crystalline co-crystal former was obtained in the end. For benzoic, ethanedisulfonic, maleic, l-malic, l-tartaric acid, and ethyl maltol, Raman spectra and XRPD were recorded, which diﬀered from the components, i.e. they were promising candidates for co-crystal formation. These were then scaled-up to about 100 mg and ﬁrst characterized by Raman spectroscopy and XRPD in order to verify that the same form was obtained in the scale-up experiment as in the microscopic high-throughput experiment. They were further characterized by nuclear magnetic resonance (NMR), elemental analysis, diﬀerential scanning calorimetry (DSC), thermogravimetry-Fourier transform IR (TG-FTIR), dynamic vapor sorption (DVS), aqueous solubility, and light microscopy in order to judge if their physical properties were favorable. It turned out that co-crystals with benzoic acid and maleic acid had good physical properties (high melting point, low hygroscopicity, and suﬃcient aqueous solubility) and fulﬁlled the target of the study, i.e. they had a much more desirable morphology.

8.2 Polymorphs, Hydrates, and Solvates Polymorphism is a very common phenomenon in connection with drug substances where the API is a small organic molecule with a molecular weight below 600 g mol−1 [6–10]. Literature values for the prevalence of polymorphs, solvates, and hydrates vary. Figure 8.4a is the result of 180 focused polymorph screens carried out at a contract research organization [11], and Figure 8.4b shows the statistical evaluation of entries in the European Pharmacopoeia with regard to solid-state information [12]. It is not surprising that the prevalence of diﬀerent solid forms found in the European Pharmacopoeia is lower than that for the recently carried out polymorph screens, as some of the API in the Pharmacopeia were discovered a long time ago, when polymorph screens were not always carried out thoroughly. These data show that the prevalence of substances that can exist in various solid forms is high and that if considerable eﬀort is put into polymorph screening, several solid forms will be discovered for the vast majority (>85%) of substances. The importance, implications, and investigation of polymorphism are described in depth in several recent monographs and edited books [13–17]. Excellent books about salts and co-crystals in the pharmaceutical industry are also available [1, 2, 18].

8.3 Screening for Polymorphs, Hydrates, and Solvates Screening for polymorphs and other relevant solid forms is not an easy task and requires a lot of experience, as it has to be ensured that the largest possible variety in crystallization conditions is used, both in terms of the type of crystallization methods and solvent choice. The identiﬁcation of solvates is also important, not because they might be used in the dosage form but because it is generally advisable not to use solvents that can form solvates with a particular compound in

245

8 Approaches to Solid-Form Screening

Figure 8.4 Frequency of occurrence of solid forms of organic molecules: (a) result of 180 focused polymorph screens; (b) from data in the European Pharmacopoeia.

60% 52%

38%

40%

32%

20%

13%

(a)

Solvates

Hydrates

Polymorphs

Only one form described

0%

60% 43% 40%

36% 29%

20%

(b)

Solvates

Hydrates

0%

Polymorphs

10%

Only one form described

246

a crystallization process to produce that compound. Also, if the only accessible crystalline form is a solvate, then a solvate may be very useful for puriﬁcation. Furthermore, solvates are interesting starting materials that can lead to new crystal forms that were missed during the initial polymorph study [19]. The fact that diﬀerent polymorphic forms can be obtained when the crystallization conditions are changed can be explained by Ostwald’s rule of stages which states that, “When leaving a given state and in transforming to another state, the state that is sought out is not the thermodynamically stable one, but the state nearest in stability to the original state” [20]. The rule implies that during a crystallization process, several forms may crystallize in sequence starting from the least stable form and ending up in the stable form. Or, in other words, if a very fast crystallization method, such as a rapid precipitation, is applied, one is likely to obtain a metastable form, while a very slow crystallization process, such as a

8.3 Screening for Polymorphs, Hydrates, and Solvates

slow cooling or slurry ripening, would yield the stable form. But, true to its name, Ostwald’s rule of stages is a rule and not a law, and many violations of this rule have been reported. Nevertheless, it is a useful concept for the design of polymorphism screens. US Patent 7892354 [21] provides a method to use the amorphous form to access lower energy forms and thus favors formation of new forms in a downhill strategy. As stated above, solvates can play a similar role because a solvate is inherently unstable when solvent activity is zero or falls below a critical value. A more mechanistic view of the formation of diﬀerent polymorphs takes cluster formation, nucleation, and crystal growth into account [22, 23]. This model also readily explains the inﬂuence of the solvent (if crystallization is performed from a solution) and additives in addition to the crystallization speed. Clusters and nuclei are small, and therefore, the surface free energy signiﬁcantly inﬂuences the value of the total free energy of the cluster or nucleus. This is depicted schematically in Figure 8.5. The free energy of individual molecules, i.e. very small clusters, is equal to the free energy in solution (Gsolution − Gnucleus = 0). Because of the surface energy, the free energy then increases with increasing cluster radius up to a critical cluster radius (r*) and the corresponding free energy (Gnucleus ). Further growth of the nucleus leads to a decrease in free energy and is therefore spontaneous. Solvent and/or additive molecules can preferentially adsorb on the surface of the nuclei and can therefore change the interfacial energy between nucleus and solvent and hence alter the heights of the activation barriers ΔGI * = Gnucleus,I − Gsolution and ΔGII * = Gnucleus,II − Gsolution for polymorph I and II, respectively. Because the surfaces of diﬀerent polymorphs may be diﬀerent, this preferential adsorption may also depend on the polymorph. Therefore, a situation may be encountered where ΔGI * is larger than ΔGII * in a certain solvent A, whereas in another solvent B, ΔGII * is larger than ΔGI *, such that polymorph II is kinetically favored in solvent A, whereas polymorph I preferentially forms in solvent B. A type of additive that can have a particularly Figure 8.5 Energy barriers for polymorph crystallization.

r*(II) ∆G*(II)

G(nucleus) –G(solution)

0

Polymorph I Polymorph II

Radius of nucleus

247

248

8 Approaches to Solid-Form Screening

large eﬀect is impurities [24–26] with a similar structure to the main component, as they may adsorb very strongly on the surface of certain nuclei because of their chemical similarity. Such impurities are often formed during the ﬁnal steps of the synthetic process. It is therefore crucial to perform crystallizations with a variety of solvents in order to increase the chance of successful competition of solvent molecules with impurity molecules for preferential adsorption. Although impurities are generally unwanted additives, there is a growing interest in designing new processes for the preparation or stabilization of metastable forms by deliberate addition of additives, for example, hydroxypropyl methyl cellulose (HPMC) or polyvinyl pyrrolidone (PVP) [27]. A much more detailed discussion of nucleation kinetics is given in Chapter 9, where it is also shown that depending on the solvent chosen, one polymorph can preferentially nucleate at any super saturation, whereas in another solvent, diﬀerent polymorphs nucleate preferentially depending on the super saturation chosen. This again emphasizes the importance of choosing both diverse solvents and diverse supersaturations in a polymorphism screen. In contrast to the kinetics of formation, the relative thermodynamic stability of polymorphs of nonsolvated forms is independent of the solvent it is formed in, as the solvent can only contribute to the surface free energy of the crystal. Although the surface free energy is an important contribution to the total free energy of nuclei, which are less than a few nanometers in diameter, the surface free energy is negligible compared to the bulk free energy if the crystal size is larger than about 100 nm. The formation and stability of solvates, however, is of course inﬂuenced by the choice of solvent. This is yet another reason why various solvents should be used in a polymorph screen. Thus, in order to ﬁnd all possible polymorphs and solvates, a large number of crystallization methods in a large number of diverse environments have to be carried out [10, 28, 29]. 8.3.1

Crystallization Methods

The choice of crystallization method has a major inﬂuence on which form is produced, and it therefore clearly makes sense to perform crystallizations using various methods when looking for polymorphs [29–32]. Classical crystallization methods have been reviewed by Guillory [33]. They are listed in Table 8.1, together with the degrees of freedom available for each process [34, 35]. Many of these processes (i.e. (i)–(v), (xi)) are also inﬂuenced by the initial solid form (i.e. polymorph, solvate, hydrate, or the amorphous form) that is used as this can aﬀect the solubility and hence the degree of super saturation. In (i)–(v), appropriate solvents or solvent mixtures have to be chosen. It must be ensured that the substance is chemically stable in the given solvent or solvent mixture and that the solubility lies in an appropriate range for the given method. At the same time, the solvent properties should be as diverse as possible. For (i), the solubility should ideally be in the range of 10–100 mg mL−1 . If the solubility is too low, yields will be impracticably small, and if it is too high, the viscosity might get so large that crystal growth is very slow or the resulting product becomes gel-like and hard to handle. Occasionally, there are very few individual

8.3 Screening for Polymorphs, Hydrates, and Solvates

Table 8.1 “Classical” crystallization methods. Method

Degrees of freedom

(i)

Crystallization by cooling a solution

Solvent/solvent mixture type, cooling proﬁle, temperature at start, temperature at end, concentration

(ii)

Evaporation

Solvent/solvent mixture type, initial concentration, evaporation rate, temperature, pressure, ambient relative humidity, surface area of evaporation vessel

(iii)

Precipitation

Solvent, antisolvent, rate of addition, order of mixing, temperature

(iv)

Vapor diﬀusion

Solvents, rate and extent of diﬀusion (i.e. vapor pressure of nonsolvent), temperature, concentration

(v)

Suspension equilibration (often also called “slurry ripening”)

Solvent/solvent mixture type, temperature, ratio of solvent to solid, solubility, temperature programs, stirring/shaking rate, incubation time

(vi)

Crystallization from the melt

Temperature programs (min, max, gradients)

(vii)

Heat-induced transformations

Temperature programs

(viii)

Sublimation

Temperature hot side, temperature cold side, gradient, pressure, surface type

(ix)

Desolvation of solvates

(x)

Salting out

(a) “dry”: temperature, pressure (b) in suspension: see (v) Type of salt, amount and rate of addition, temperature, solvent/solvent mixture, concentration

(xi)

pH change

Temperature, rate of change, acid/base ratio, method: acid/base added as solution or in gaseous form

(xii)

Lyophilization

Solvent, initial concentration, temperature, and pressure programs

solvents that fulﬁll these conditions. In such cases, solvent mixtures are highly advisable. Evaporation requires preferably solubilities >10 mg mL−1 , whereas for precipitation, generally a solvent with a solubility >10 mg mL−1 and a second one with a solubility 1 mg mL−1 but 0.1 Pa. According to Kuhnert-Brandstätter [36], this applies to about two-thirds of drug substances. For modern drug substances, this number is signiﬁcantly smaller as the average molecular weight of drug substances has increased over the years with concomitant decrease in vapor pressure. Obviously, (ix) requires the existence of a solvate and (x) is only useful for compounds that are charged in solution. In (i)–(vi) and (x), seeds may be used very eﬃciently. They could either consist of the desired solid form, a crystalline form of a similar compound, or inorganic, organic, or polymeric heteroseeds [37–42]. Of course, because of regulatory requirements, heteroseeds would never be used for production of a drug substance. However, they can be used for producing seed crystals, which can subsequently be puriﬁed by a series of crystallizations. In view of later processing and formulation steps, crystallization under pressure plays an important role, too. Often, it is observed that grinding can change the polymorphic form [25]. Pressure-induced changes can be brought about by, e.g., subjecting the sample to pressure in an IR-press, or grinding it in a mortar, a ball mill, or a small-scale jet mill. Grinding a mixture of two components can also be an eﬃcient way to produce co-crystals even in the absence of solvent [43–46]. In addition to these classical methods, newer methods such as capillary crystallization [47], laser-induced nucleation [48], supercritical ﬂuid crystallization [49], epitaxial matching [50, 51], ultrasound [52], and mechanochemistry [53] have been successfully used to create elusive metastable as well as stable polymorphs. 8.3.2

Choice of Solvent

The importance of the solvent for the outcome of the crystallization process has been discussed above, and one of the ﬁrst questions one has to answer when performing a polymorphism screening is which solvents should be used. Ideally, solvents as diverse as possible should be included, which leads to the question of which solvent parameters are relevant. Clearly, in addition to molecular solvent–solute interactions, bulk properties of solvents may play a role. Gu [54] examined 96 solvents in terms of 8 relevant solvent properties: hydrogen bond acceptor propensity, hydrogen bond donor propensity, polarity/dipolarity, dipole moment, dielectric constant, viscosity, surface tension, and cohesive energy density (calculated from the heat of vaporization). Based on all the 8 properties, the 96 solvents were sorted into 15 groups based on their statistical similarity. Some groups only contain one solvent (e.g. water), some several (e.g. N-methyl-2-pyrrolidone, dimethylformamide, dimethylacetamide, and dimethylsulfoxide), whereas others contain up to 16. Molecules with the same functional groups were often grouped together as one would intuitively assume. Such an approach can be of great help for designing experiments and might suggest that it is advisable to use solvents from each group in order to maximize diversity. As certain crystallization methods can only be used if the solvents meet certain solubility or boiling point requirements, groups containing several solvents are more likely to be utilized. If the classiﬁcation is made by neglecting viscosity and surface tension, a slightly diﬀerent grouping is obtained [54]. This demonstrates that it is important to choose the “right” parameters for

8.3 Screening for Polymorphs, Hydrates, and Solvates

the classiﬁcation. Other solvent descriptors such as molecular volume, shape, density, vapor pressure, melting point, boiling point, miscibility, solubility parameters, etc., may play a role, too. Recently, a method for classiﬁcation of solvents based on atomic electronegativity has been proposed [55], which allowed researchers to predict the outcome of certain crystallization experiments in terms of polymorphic form. Other approaches to solvent clustering have been suggested [56, 57]. Blomsma and van Langevelde used an approach where they characterized 413 solvents with 46 descriptors each, from which 16 principal components were derived. The matrix was then further reduced to 5 principal components and 22 solvents [58]. Clearly, some solvent properties play a larger role than others in terms of inﬂuencing the outcome of crystallization experiments, and hydrogen donor and acceptor propensities seem to be of particular importance [59]. In summary, we believe that the classiﬁcation of solvents into groups is a valuable approach for rational polymorphism screening. On top of that, it is also advisable to include solvents that are intended to be used in the formulation process (e.g. polyethylene glycol). 8.3.3

Types of Polymorph Screens

Given the fact that it is likely that the more solid forms are found, the more eﬀort is invested in the search and that one can never be sure that all relevant forms are experimentally discovered, two questions arise immediately, i.e. how extensive a search should be carried out and when in the development process a polymorph screen should be carried out. The answers to these questions must take both economic and safety criteria into account. Regulatory authorities have set some criteria in order to ensure the safety and eﬃcacy of drug products. Therefore, the ICH (International Conference of Harmonization) guidelines [60] demand that a polymorph screen has to be carried out in order to obtain regulatory approval for pharmaceutical products. There is, however, no guideline given on how such a screen should be performed. Economic criteria would suggest that a polymorph screen is conducted late in the development process of a drug, as the attrition rate of drugs during clinical development is large. Only on the order of 10–20% of the drugs entering Clinical Phase I will gain ﬁnal approval as drug products [61]. On the other hand, it would be an unacceptable risk to develop a dosage form without knowing which polymorphic form is thermodynamically stable under certain conditions of temperature and humidity. Therefore, a good strategy that balances economic considerations and risk is to carry out several polymorph screens during the development process that are appropriate for the corresponding phase. By the time when the formulation used in the clinical phase is close to the market formulation of the drug, the optimal solid form should have been identiﬁed with a reasonably high probability. A limited polymorph screen in the preclinical phase or Clinical Phase I will therefore generally have the aim of identifying the thermodynamically stable polymorph and hydrates with a reasonable conﬁdence level. If the drug is successful in Clinical Phase II, this conﬁdence level should be increased and the search should be extended to metastable forms, as they are

251

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8 Approaches to Solid-Form Screening

generally important to know for the development of a crystallization process of the desired stable form and they may also improve the patent protection of the drug. The relevance of metastable forms for the development of a crystallization process stems from the fact that metastable forms might be produced inadvertently if their existence and their properties are not known and no appropriate measures are taken so that they are not formed. A polymorph screen should proceed in a well-structured and standardized way, while recognizing that the procedure has to be tailored with respect to the substance under investigation. An approach that is not adapted to the substance is prone to ineﬃciency and overlooking relevant forms. The procedure used should also be tunable to permit various degrees of thoroughness as stated above. In essence, a polymorph screen should at least contain the following elements: • Characterization of the starting material by methods such as powder or single-crystal X-ray diﬀraction (XRD), DSC, TG-FTIR or thermogravimetrymass spectrometry (TG-MS), DVS, Raman or IR, magic-angle spinning (MAS) NMR, solubility measurements, microscopy, and HPLC (purity). • If the substance does not degrade at the melting point, hot-stage microscopy or hot-stage Raman microscopy can be a very eﬃcient way for creating other polymorphs [62]. • Crystallization experiments from solution, using several techniques with a variety of solvents and solvent mixtures. Because of the practical relevance of hydrates, water and water/solvent mixtures should always be included. Suspension equilibration and slow cooling experiments have particular importance in ﬁnding the thermodynamically stable form, which is often the most important aim of a polymorph screen. • All new forms have to be characterized by the methods used to characterize the starting material and their thermodynamic relationships have to be elucidated. • Other techniques such as desolvation of solvates and mechanical stress (pressure, grinding) are necessary to obtain the information needed for the processing and manufacturing steps. Very useful tools for polymorphism (and salt and co-crystal) screens are HTS systems [63–66], where crystallization experiments are carried out in an array format, using, e.g., 96-well plates. Such systems have been developed by research foundations [67], big pharmaceutical companies [68–70], and companies specializing in solid-state research and development [39, 71–74]. They commonly allow crystallization by cooling, evaporation, precipitation, and slurry conversion. Primary characterization of the solid is generally performed by Raman microscopy and/or XRPD. High-throughput screens should always be complemented by larger scale experiments, however, where more of the corresponding form is produced in order to allow a full physicochemical characterization. It may also be necessary to subject the substance to conditions that are not accessible in a HTS system. Experimental screening may be further enhanced by computational methods [75, 76]. If calculations and experiments yield the same stable form, a very high

8.3 Screening for Polymorphs, Hydrates, and Solvates

conﬁdence level that this particular form is the thermodynamically stable one is achieved. 8.3.4

Characterization and Selection

Identiﬁcation of the polymorphic forms, solvates, and hydrates of a substance through a HTS (possibly complemented by additional experiments inspired by computation or intuition) is only the ﬁrst step in understanding a drug’s solid-state behavior. Of equal importance are the physical properties of the various forms. A thorough characterization of these forms generally requires more material than is available in a HTS. HTSs are therefore typically followed by laboratory-scale experiments designed to produce 50–100 mg of each polymorph, solvate, and hydrate. The results obtained in the HTS generally provide a good indication of what types of experiments can produce a given form and even what that form is likely to be (e.g. forms that only appear when water is present in the solvent mixture are likely to be hydrates). In some unfavorable cases, it might happen that it is almost impossible to reproduce forms encountered during HTS experimentation. It should to be realized, however, that microscopic experiments represent somewhat special conditions, and that if it is not possible to obtain macroscopic amounts of a solid form encountered during an HTS with reasonable eﬀort, such a form would probably be considered to be irrelevant for practical purposes. Once a sample of each polymorph has been obtained, the forms are generally characterized using a variety of physicochemical methods. Important parameters include the form’s crystallinity (as determined by XRD and DSC), melting point (also determined by DSC), hygroscopicity (determined by DVS), and bioavailability (inferred by solubility and/or dissolution rate measurements along with measurements of log(D) and pK a ). XRPD and spectroscopic methods (Raman, IR, and/or NMR) provide a ﬁngerprint of each form, reveal fundamental structural information, and are very useful for patent ﬁling. TG-FTIR is useful for determining whether a solid is a solvate or hydrate, and both TG-FTIR and DSC provide information about thermal stability and decomposition. Particle-size distribution measurements and identiﬁcation of possible crystal habits for a given polymorph can give an indication of whether this polymorph can be easily processed and manufactured. These techniques should be supplemented by HPLC purity analysis. Single-crystal structures of the various forms may help to elucidate their solid-state behavior. The formation of isomorphous solvates or the moisture sorption behavior can, in favorable cases, be explained by knowing the three-dimensional arrangements of the constituent molecules. Channel or sheet-like structures, for example, might easily form nonstoichiometric solvates and hydrates. Single-crystal structures also permit simulation of the powder XRD patterns of the respective crystals and comparison of such a pattern with patterns obtained from the polymorph screening. Thermal measurements, suspension equilibration experiments, and solubility/dissolution rate measurements can all provide information about the relative stabilities of the diﬀerent forms. Such information can be used to

253

254

8 Approaches to Solid-Form Screening

construct ET (energy vs temperature) diagrams, which identify which form is thermodynamically stable at a given temperature. Monotropic and enantiotropic relationships between pairs of forms can be discerned, and such diagrams can be used as guidelines for directed crystallization of a speciﬁc form. If a metastable form is to be developed (i.e. for intellectual property reasons or because of undesirable properties of the thermodynamically stable form), such studies must be supplemented by an investigation of the kinetics of polymorph conversion. Once the solids are characterized, the intellectual property aspect becomes important. The choices of whether and when to apply for patent protection for selected or for all polymorphs encountered should be carefully made, and well analyzed, and any decision for patent life cycle management should be taken with all relevant data in hand. Finally, all characterization data and information on the solid-state behavior of a molecule will have to enter the ﬁnal decision matrix, where on a side-by-side basis, the solid forms of all entities of interest, i.e. the uncharged molecule and the various salts (or co-crystals), are listed with their respective proﬁles. Besides physicochemical data gained by characterization of the solid forms, data concerning chemical stability, pharmacokinetics, and, e.g., the patent situation enter into such a matrix (Figure 8.6). Which of the parameters are most important will depend on the particular drug and the intended application of the drug. It makes sense to list the relevant properties for a particular drug in descending order of importance and then to compile the corresponding values of the available polymorphs, salts, and co-crystals. The respective property of each form could then be graded with colors or shades of gray as “good,” “intermediate,” or “bad,” so that a look at the corresponding matrix would allow for choosing the optimal form. In terms of polymorph selection, stability is generally the dominant property for the pharmaceutical industry, such that in most cases, the stable polymorph will be chosen for development. Having the lowest free energy, the stable form also has the generally undesired property of being the least soluble one, but that is often considered a smaller problem than the potential conversion of a metastable form to the stable form during storage. If hydrates exist, the decision becomes more diﬃcult, as the thermodynamic stability then depends on humidity. Knowledge of the critical water activity, the kinetics of conversion, the conditions of use, etc., are then crucial in order to be able to select the optimal form. Free drug, polym. Free drug, polym. α β

Salt A, polym. I

Salt B, polym. I Co-cr X, Polym. A Co-cr Y, Polym. A

Solubility

0.01

0.04

1

0.08

0.5

0.7

Thermodynamic stability

Yes

No

Yes

Yes

Yes

Yes

Hygroscopicity Melting point (°C)

…..

+0.1% @ 70%r.h. +0.1% @ 70%r.h. +0.1% @ 70%r.h. +2.0% @ 70%r.h. Channel hydrate +1.5% @ 70%r.h. 80

70

150

170

150

60

…..

Figure 8.6 Scheme for selecting the optimal form. White indicates good, light gray intermediate, and dark gray bad properties. Therefore, “Salt A, Polymorph I” would be the optimal choice here.

8.4 Conclusion

8.4 Conclusion If an active ingredient is formulated as a solid dosage form, it is possible to choose the form of the API in the drug product from a very large number of possible forms. Which one of these forms is chosen may have a tremendous impact on the quality of the drug product. Bioavailability may be aﬀected, which will have an impact on both drug eﬃcacy and safety. Varying physical and chemical stability as well as hygroscopicity will aﬀect the required storage conditions and maximal storage life. Nonstoichiometric hydrates may lead to problems in terms of API content, as the drug substance may contain various amounts of water, i.e. API content may not be proportional to mass. Parameters such as bulk density, ﬂowability, compressibility, the inﬂuence of mechanical stress on the solid form, and melting point will aﬀect the formulation process. The taste of the drug product may even be inﬂuenced (e.g. salt forms). Finally, the cost of the drug product may be inﬂuenced, as the eﬃciency of the crystallization process (yield, purity, speed, and removal of residual solvents) may be diﬀerent for diﬀerent forms. Identifying and characterizing all relevant solid forms is therefore a very important step in the integrated approach to solid-state issues discussed in this book. The search for new solid forms should be systematic and ﬂexible at the same time. Diﬀerent stages of development and product maturity may require a diﬀerent degree of thoroughness for such a search. Although it is generally the goal to enter the clinical development Phase I with the thermodynamically stable form under ambient conditions, it is highly advisable to identify all relevant polymorphic forms during further pharmaceutical development. Intellectual property aspects as well as the design of robust larger scale crystallization processes rely on an exact understanding of the polymorphic behavior of a drug substance. A good strategy for polymorph screening should encompass the characterization of the starting material, thermoanalytical investigations of the solid, a solvent-based crystallization screening with both fast and slow crystallization techniques, and the search for hydrates. Microscopic, multiparallel approaches allow for rapid, low substance consuming and eﬃcient ways of identifying the tendency of solids to show polymorphism. In addition, such approaches can, in general, be used for combined salt and polymorph screenings. But even though it may be very easy to carry out a very large number of experiments quickly, the quantity of experiments should not replace the quality of careful experimental planning. Very often, additional rational crystallization methods are needed in order to get a complete picture of the behavior of the substance. Polymorph screening, while being a very important step, is only a ﬁrst step. Almost equally important and, at least in some cases, challenging is polymorph characterization and polymorph landscape understanding as it is the basis of every selection process. Characteristics of all solid forms of interest of the potential drug substances, i.e. the neutral molecule and the various salts and co-crystals, have to be compared. Physicochemical data, data on chemical stability and pharmacokinetics, assessment of the patent situation, etc., enter into the process of deciding which solid form to promote for further development. The ﬁnal selection of the optimal solid might be a tedious exercise in some cases, and the pros and cons of each form have to be considered in a well-balanced way as

255

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they will gravely inﬂuence the future of the drug. This decision should be made early in the development process (Chapter 1) in order to avoid the necessity of making changes in the solid form later on in the process, which would lead to both additional costs and delays in market introduction. In the end, only the answers to the following three questions matter, i.e. • Which form should be developed? • How can that form be produced reliably? • How can it be assured that no undesired changes occur during formulation and the shelf life of the product? And the quality of a polymorphism screening and characterization process can be judged on its ability to answer these questions reliably.

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Properties, Selection, and Use. Weinheim: Wiley-VCH. 2 Stahl, P.H. and Wermuth, C.G. (ed.) (2011). Handbook of Pharmaceutical

Salts, Properties, Selection, and Use. Zürich: Wiley-VCH. 3 Rager, T. and Hilﬁker, R. (2009). Z. Phys. Chem. 223: 793–813. 4 Rager, T. and Hilﬁker, R. (2010). Cryst. Growth Des. 10 (7): 3237–3241. 5 Rager, T. and Hilﬁker, R. (2012). Pharmaceutical Salts and Co-crystals, RSC

Drug Discovery Series No. 16 (ed. J. Wouters and L. Quéré), 280–299. 6 Griesser, U.J. and Stowell, J.G. (2003). Solid-state analysis of polymorphism.

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In: Pharmaceutical Analysis (ed. D.C. Lee and M.L. Webb), 240–294. Oxford: Blackwell Publishing Ltd. Lipinski, C.A., Lombarda, F., Dominy, B.W., and Feeney, P.J. (2001). Adv. Drug Delivery Rev. 46 (1): 3–26. Stahly, G.P. (2007). Cryst. Growth Des. 7: 1007–1026. Bernstein, J. (2011). Cryst. Growth Des. 11: 632–650. Cruz-Cabeza, A.J., Reutzel-Edens, S.M., and Bernstein, J. (2015). Chem. Soc. Rev. 44: 8619–8635. Stahly, G.P. (2004). Presentation at 22nd SCI Process Development Symposium (December 2004), Cambridge. Griesser, U.J. (2006). The importance of solvates. In: Polymorphism in the Pharmaceutical Industry (ed. R. Hilﬁker), 221–234. Weinheim: Wiley-VCH. Brittain, H.G. (1999). Polymorphism in Pharmaceutical Solids. New York: Marcel Dekker, Inc. Brittain, H.G. (2009). Polymorphism in Pharmaceutical Solids, 2e. New York: Informa Healthcare. Byrn, S.R., Pfeiﬀer, R.R., and Stowell, J.G. (1999). Solid-State Chemistry of Drugs, 2e. West Lafayette: SSCI Inc. Bernstein, J. (2002). Polymorphism in Molecular Crystals. Oxford: Oxford Science Publications. Hilﬁker, R. (2006). Polymorphism in the Pharmaceutical Industry. Weinheim: Wiley-VCH.

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(2014). Cryst. Growth Des. 14: 513–522. 20 Ostwald, W. (1897). Z. Phys. Chem. 22: 289–330. 21 Blatter, F., Szelagiewicz, M., and von Raumer, M. (2011). Process for the

parallel detection of crystalline forms of molecular solids. US 7892354 B2. 22 Myerson, A. (2002). Handbook of Industrial Crystallization, 2e. Boston, MA:

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9 Nucleation Marco Mazzotti1 , Thomas Vetter2 , David R. Ochsenbein1 , Giovanni M. Maggioni1 , and Christian Lindenberg3 1 2

ETH Zürich, Institute of Process Engineering, Switzerland University of Manchester, School of Chemical Engineering and Analytical Science, United Kingdom

3 Novartis Pharma AG, Switzerland

9.1 Introduction The term “nucleation” is used to describe the onset of the formation of a new phase from a parent phase [1, 2]. Examples of nucleation processes include the formation of vapor bubbles in a liquid phase, the formation of droplets from a vapor phase, or from another liquid, as well as the formation of crystalline particles from vapor, liquid, or even another solid. In the following, we will focus on the formation of new crystalline particles from solution exclusively. Apart from the breakage of an already existing particle into two or more pieces, nucleation is the only mechanism generating new crystals and is therefore of fundamental interest. From a processing perspective, it is notoriously a phenomenon hard to control in batch crystallizers, a fact that increases the importance of process design strategies that avoid or minimize nucleation through the addition of previously prepared seed crystals. It is useful to classify the events leading to the formation of nuclei into diﬀerent types [3, 4]: primary homogeneous nucleation refers to the formation of nuclei from clear liquids; primary heterogeneous nucleation occurs when nuclei are formed with the participation of foreign surfaces (such as stirrers, crystallizer walls, or crystals of another form); and secondary nucleation describes the formation of nuclei of one crystal form with the participation of already-present crystals of the same crystal form. Although much of what is described in the following sections applies to all three types of nucleation, there are slight diﬀerences that need to be accounted for. It is noteworthy that these diﬀerent nucleation mechanisms can occur simultaneously and to varying degrees throughout a crystallization process; moreover, the nucleation rates of diﬀerent solids, e.g. polymorphs, may compete with each other. For instance, starting from a clear solution containing a solute, it is possible that mixtures of diﬀerent polymorphs are obtained during the crystallization process when the nucleation kinetics of the diﬀerent crystal forms Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development, First Edition. Edited by Rolf Hilﬁker and Markus von Raumer. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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are comparable. However, as diﬀerent crystal forms exhibit diﬀerent stability, all forms will ultimately convert into the stable form upon reaching thermodynamic equilibrium. Nevertheless, all pathways for nucleation share the fact that the formation of nuclei involves the concomitant creation of a new bulk phase and of an interface. When there is a driving force for crystallization, the former leads to a decrease in free energy of the system, whereas the latter increases it. This interplay of contributions often leads to the presence of a substantial energy barrier for the creation of a nucleus. In such cases, the original state of the parent phase is not thermodynamically unstable, but rather metastable and the rate of formation of nuclei, i.e. the nucleation rate, is ﬁnite. This implies that a purely thermodynamic understanding of the system, albeit essential, is insuﬃcient to describe nucleation; a kinetic understanding of the system is additionally required in order to answer questions pertaining to the dynamics of the system. Furthermore, the eﬀect of the operating conditions on both aspects needs to be understood. Theories of nucleation aim at achieving this goal and a brief overview of the most important theoretical frameworks, experimental characterization tools, and applications shall be given in the following. Finally, this chapter will also highlight how the use of seed crystals in a crystallization process allows obtaining a desired crystal form, which is of importance when the performance of a product strongly depends on the manufactured crystal form.

9.2 Homogeneous Nucleation In order to describe the formation of nuclei, we must ﬁrst deﬁne the driving force for crystallization. We can express it as the diﬀerence in chemical potential between a solute molecule in the solution at its current state, 𝜇𝓁 , and in the solution’s equilibrium state, 𝜇𝓁∗ . In practical applications, it is more convenient to express this driving force in terms of the supersaturation S. These quantities can be related by ( ) ( ) a𝓁 c ∗ (9.1) ≈ kT ln Δ𝜇 = 𝜇𝓁 − 𝜇𝓁 = kT ln S = kT ln ∗ a𝓁 c∗ where k is the Boltzmann constant, T is the temperature, a𝓁 represents the activity of the solute in the supersaturated solution, and a∗𝓁 is the activity of the solute in the solution’s equilibrium state (note that a𝓁 = c𝛾, where c is the concentration and 𝛾 its activity coeﬃcient). Although the last step introduced in Eq. (9.1) using concentrations instead of activities is only accurate for ideal solutions, where 𝛾 ≈ 𝛾 ∗ ≈ 1, or when 𝛾∕𝛾 ∗ ≈ 1 (which is a much less stringent requirement), it represents a useful approximation as concentrations are experimentally accessible quantities. Concerning the thermodynamics and kinetics of homogeneous nucleation, two theories are of particular importance. The ﬁrst one is the oldest and probably best known theory of nucleation: classical nucleation theory (CNT). Originally developed for the nucleation of droplets and bubbles, the CNT is also extensively applied to crystals, which, in stark contrast to droplets/bubbles, exhibit a strong supramolecular structure. The second theory we will discuss in this chapter

9.2 Homogeneous Nucleation

represents a reﬁnement of the CNT, which recognizes this diﬀerence. It is often referred to in the literature as two-step nucleation theory (2-SNT) [5–7]; its development took place mainly during the last three decades and was fueled by considerable progress in measurement devices allowing for the observation of ever smaller entities in solution [8–10]. We will ﬁrst introduce the two theories on a conceptual level before putting them on a more rigorous theoretical footing. A schematic illustration of the two theories is shown in Figure 9.1, where diﬀerent key states Number of molecules in new phase(s)

Free molecules and disordered, liquid-like cluster

Free molecules and crystalline cluster in liquid-like cluster

Free molecules and crystalline cluster

...

...

Number of molecules with crystalline order

Molecules in solution

Free molecules and crystalline nucleus

Free molecules and crystalline nucleus inside disordered cluster

Macroscopic crystal

Figure 9.1 Conceptual picture of the mechanisms of nucleation according to classical nucleation theory (CNT; blue arrows) and to two-step nucleation theory (2-SNT; orange arrows). Both theories consider a supersaturated solution as their starting point. According to both theories, clusters are forming/disintegrating through the attachment/detachment of building units. In the CNT, clusters are assumed to exhibit the ﬁnal crystal structure immediately when building units attach. In contrast, the 2-SNT assumes that nucleation proceeds through the formation of disordered, liquid-like clusters in a ﬁrst step, whereas the formation of structured clusters occurs from these droplets in a second step. Upon reaching a critical cluster size – the so-called nucleus size – the attachment of further building units is energetically favored, ultimately leading to the formation of a macroscopic crystal.

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of the solution and of the newly forming phase are depicted. We depict these states in relation to the number of molecules that are contained in the new phase and the number of molecules with crystalline order in this phase. In both theories, the initial state for primary homogeneous nucleation is a clear supersaturated solution (S > 1) containing a number of solute molecules that exhibit no crystalline order (top left corner in Figure 9.1) and a ﬁnal state consisting of one or more macroscopic crystals (bottom right corner). However, the pathways connecting the two states are rationalized in diﬀerent ways in the CNT (blue arrows) and the 2-SNT (orange arrows); key states along the two pathways are discussed in the following. CNT states that crystalline clusters are forming from the supersaturated solution through simultaneous ﬂuctuations in density and order. Building blocks of crystals (assumed here to be solute molecules) can attach to or detach from a cluster in a step-by-step manner. When molecules are attaching/detaching, the blue pathway laid out in Figure 9.1 is traveled reversibly depending on the rates of molecule attachment and detachment. We will show in Section 9.2.1 that the attachment of molecules to a cluster is energetically unfavorable until a critical number of molecules are reached while it is favored beyond this number. 2-SNT, on the other hand, treats the evolution of density and structure of the newly formed phase independently from each other. Namely, the 2-SNT postulates that density ﬂuctuations ﬁrst lead to the formation of disordered, liquid-like clusters (or droplets), which exhibit a higher density than the original clear liquid. Only after this step, crystalline order is achieved through rearrangement of the molecules within that cluster. 9.2.1

Classical Nucleation Theory

CNT dates back to the work of Gibbs, Becker and Döring, Volmer, and many others [11, 12]. The interested reader can ﬁnd the full derivation, historical details, and various technical aspects of CNT in the classical works of Kashchiev and Debenedetti [1, 13]. In order to describe the thermodynamic aspects of CNT, we derive the energy diﬀerence between a solution and a solution containing a cluster of n molecules. As hinted at in the introduction, the total change in the system free energy, ΔGn , that is, the work of cluster formation, is given by the sum of two terms: an energy gain due to formation of a crystalline bulk phase and an energy loss caused by the formation of an interface between the new and the parent phase. We may thus write ΔGn = −nΔ𝜇 + 𝜎An

(9.2)

where the bulk contribution has been expressed using the crystallization driving force, Δ𝜇 (Eq. (9.1)), and the surface contribution is expressed through the surface energy 𝜎 and the surface area of the cluster An . We may assume that the cluster geometry can be characterized by a characteristic length L. The volume and the area of the cluster are then expressed as V = kv L3 , and A = ka L2 , respectively. kv and ka are the volume and surface shape factors (for cube of side L, kv = 1 and ka = 6; for sphere of diameter L, kv = 𝜋∕6 and ka = 𝜋). The Gibbs free energy of

9.2 Homogeneous Nucleation

a cluster of size L, at given temperature T and supersaturation S, can then be expressed as ΔG(L) = −

kv 3 k L3 L Δ𝜇 + 𝜎ka L2 = − v kT ln S + 𝜎ka L2 𝑣c 𝑣c

(9.3)

where 𝑣c is the molecular volume. From this equation, it is clear that ΔG is zero for L = 0, goes through a maximum and decreases monotonically afterward. This behavior is shown in Figure 9.2 for several supersaturations. The maximum on each curve represents an unstable equilibrium, implying that a cluster of such a critical size, Lc , has an equal probability of growing into a full crystal and of dissolving back into solvated molecules. A cluster of critical size is typically referred to as a nucleus. Lc may be computed from Eq. (9.3) by setting dΔG∕dL = 0, thus yielding Lc =

2ka 𝜎𝑣c 3kv kT ln S

(9.4)

The value of the corresponding free energy change is ( 3 ) 4ka 𝜎 3 𝑣2c (9.5) ΔGc = 27kv2 k 2 T 2 ln2 S The term between brackets in Eq. (9.5) is a constant dependent on the nucleus geometry: for a sphere, it equals 16𝜋∕3; for a cube, it is 32. Analogous to the reaction coordinate used in chemical systems, the cluster size L can be interpreted as the characteristic coordinate for nucleation, which describes the evolution of the system energy, ΔG, during the formation and evolution of a cluster. Using this analogy, we can interpret ΔGc as the activation barrier to nucleation and the nucleus as a transition state. As already visible from Figure 9.2, we see that Eqs. (9.4) and (9.5) indicate that higher supersaturations lead to lower energy barriers for nucleation and smaller nuclei sizes. This ﬁnding is crucial because according to transition state theory, the rate of passing through a transition state is proportional to the exponential of the height of the energy barrier that needs to be

S Free energy (ΔG)

Figure 9.2 Free energy required according to classical nucleation theory to form a cluster of size L. Each curve is drawn at constant values of supersaturation and temperature; the symbol on each curve marks the maximum of the free energy and the corresponding critical size Lc .

0

Cluster size (L)

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crossed. In other words, the nucleation rate J, i.e., the number of nuclei formed in a solution per unit time and unit volume, is found to be ( ) ( ) ΔGc B J = AS exp − = AS exp − 2 (9.6) kT ln S with ( 3 ) 3 2 𝜎 𝑣c 4ka (9.7) B= 2 27kv k 3 T 3 The pre-exponential factor, J0 = AS, in this equation is typically seen as a product of the number of nucleation sites and the frequency of building block attachment to the cluster. Within the literature discussing the CNT, several limiting cases have been considered when deriving the attachment frequency [1, 14], leading to slightly diﬀerent functional dependencies of the pre-exponential factor on the operating conditions. However, the resulting expressions share their linear dependence on the concentration in solution (and hence the supersaturation, as explicitly written in Eq. (9.6)). The number of nucleation sites is, however, notoriously hard to predict, often leading to discrepancies of several orders of magnitude between experimentally measured data and theoretical predictions. This is often attributed to the presence of small (sub-micron) particles or other impurities in solutions that act as nucleation sites, but other explanations exist as well (see Section 9.2.2). Although the eﬀect of such “dust” particles and other heterogeneous surfaces (stirrers, crystallizer walls) is often most pronounced on the kinetic parameter A, it is also known to aﬀect the thermodynamic parameter B in Eq. (9.6). This will be discussed in Section 9.3.1. Practitioners are therefore often content to gather experimental data and treat A and B as ﬁtting parameters. Nevertheless, it is important to realize that CNT has delivered some mechanistic insight on the functional form of the nucleation rate, which can prove invaluable for process design. For instance, the observation of a metastable zone, i.e. a zone in the phase diagram where nucleation is not observed within a speciﬁed time frame, is consistent with the nucleation rate law outlined in Eq. (9.6): the nucleation rate is rapidly increasing only after a certain threshold supersaturation is reached – before this threshold, considerable time can pass before nucleation is observed. Note that the metastable zone is a purely kinetic phenomenon and should not be thought of as a thermodynamic boundary. 9.2.2

Two-Step Nucleation Theory

As shown in Figure 9.1, according to 2-SNT, the system evolves from an initial state (the clear solution) to the ﬁnal state (the crystals and the solution) passing through an intermediate metastable state. The diﬀerence between the reaction paths described by CNT and 2-SNT has also a profound eﬀect on the energetics of the two processes, as one can readily see in Figure 9.3. This ﬁgure shows the Gibbs free energy change along a reaction coordinate 𝜂, which represents both the cluster’s size and its structural properties. From the initial state (ΔG = 0), i.e. the clear solution, the system has to overcome two energy barriers of height

Free energy (ΔG)

9.2 Homogeneous Nucleation

ΔG*1

Liquid-like cluster ΔG*2

0 Solution Crystal

Nucleation coordinate (η)

Figure 9.3 A qualitative representation of the energy proﬁle of a cluster as a function of a nucleation coordinate, 𝜂, in 2-SNT. The nucleation coordinate encompasses both the cluster size and its degree of crystallinity. Source: Pan et al. 2005 [15]. Reproduced with permission of AIP publishing.

ΔG1∗ and ΔG2∗ before ultimately reaching the ﬁnal state. After the ﬁrst energy barrier, a metastable state is located, which represents the liquid-like cluster. It should be noted that the energy level of the liquid-like cluster is not necessarily higher than that of the solution, as in Figure 9.3, but could also be lower. 2-SNT was originally developed to describe the crystallization of proteins in aqueous solutions, such as lysozyme in water [16] for which CNT did not agree well with experimental observations. Speciﬁcally, for these systems, liquid-like clusters were observed in supersaturated solutions before the formation of crystals. The qualitative picture of the Gibbs free energy is diﬀerent from the one obtained from CNT, which suggests that the mathematical form of the nucleation rate J may be diﬀerent as well. For crystal nucleation of proteins in aqueous solutions, a phenomenological model has been derived under system-speciﬁc assumption, and the corresponding nucleation rate has been estimated [15, 16]. Just as for CNT, also for this phenomenological model, accurate ab initio calculations of the involved energies are diﬃcult; hence, the authors took them as ﬁtting parameters [15]. Although the theory was initially conceived to describe nucleation of proteins in solution [7, 16–19], recent evidence and its formal generality suggest that two-step nucleation could also describe the crystallization of amino acids, small organic molecules, and even inorganic compounds, some of which exhibit features of a two-step process [20–22]. It should be pointed out that the nature of the intermediate species formed (density, concentration, structure, etc.), as well as a consistent formulation that applies to all systems, is still a topic of debate.

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9.3 Heterogeneous and Secondary Nucleation 9.3.1

Heterogeneous Nucleation

Forming nuclei through homogeneous nucleation entails crossing substantial energy barriers, i.e. it is an energetically unfavorable process; hence, it constitutes a “rare event” even when a considerable driving force for crystallization exists. However, the presence of interfaces can promote nucleation. Industrial crystallizers can rarely – if ever – be considered free from foreign surfaces (such as impellers, microscopic “dust,” crystallizer walls, liquid–air interfaces/bubbles, etc.). Nucleation occurring in the presence of such foreign surfaces is referred to as heterogeneous nucleation. The adsorption of crystallizing material on these surfaces lowers the critical free energy required for the formation of a nucleus. The extent of this reduction is often rationalized to depend on the structural similarity between the foreign surface and the crystal to be formed on it [3]. This is often assumed to lead to a reduction in surface energy, i.e. the surface energy 𝜎 in Eq. (9.5) is replaced with an eﬀective surface energy 𝜎ef = Ψ𝜎, with the eﬀectiveness factor Ψ being between 0 and 1. Clearly, this leads to a decreased value of B in Eq. (9.6) and hence an increased nucleation rate. In fact, this is a general behavior and the presence of any heterogeneous surface increases the nucleation rate in comparison to the case of homogeneous nucleation. In other words, the supersaturation required to reach a certain threshold nucleation rate is lower; hence, the metastable zone for heterogeneous nucleation is narrower than for homogeneous nucleation. The nuclei formed through heterogeneous nucleation may either stick on the surface on which they formed or they might be forcibly detached from the surface if suﬃcient shear or mechanical force is exerted on them. In the former case, heterogeneous nucleation is generally a nuisance as it is a source of scaling and encrustation, whereas in the latter case, the nuclei can grow into well-deﬁned crystals suspended in the solution. Unfortunately, the current state of the art does not allow to predict heterogeneous nucleation rates in a quantitative manner from measured or simulated surface characteristics. In practice, this means that the parameters in Eq. (9.6) ought to be estimated from experimental data if a quantitative nucleation rate is desired and that the presence of any material providing surfaces at which heterogeneous nucleation can occur needs to be controlled to gain meaningful and reproducible results. 9.3.2

Secondary Nucleation

Primary nucleation produces new nuclei of the substance being crystallized independently of the presence of such crystals in the system. Secondary nucleation, on the contrary, is the phenomenon leading to the formation of new nuclei because of the prior presence of fully grown crystals in the suspension. It is interesting to note that nuclei formed through secondary nucleation exhibit the same crystal structure as the parent crystal [23, 24]. Over the years, multiple mechanisms have been proposed to describe secondary nucleation and the debate regarding the mechanistic interpretation and the mathematical description of the phenomenon

9.3 Heterogeneous and Secondary Nucleation

(a)

(b)

(c)

Figure 9.4 Conceptualization of diﬀerent secondary nucleation mechanisms: (a) boundary layer mechanisms, (b) crystal–crystal collision, and (c) crystal–impeller collision.

is far from being settled [25]. Nevertheless, most authors agree on its qualitative features and that there are a couple of distinct pathways leading to the formation of nuclei through secondary nucleation; they are conceptually depicted in Figure 9.4. In the ﬁrst mechanism (depicted in Figure 9.4a), secondary nuclei form in the boundary layer surrounding each crystal in suspension, or on the crystalline surface itself [25–27]. The details are governed by the speciﬁc physicochemical properties of the system considered and by the crystallization conditions. In the boundary layer, new nuclei form through an activated process similar to nuclei formed through primary nucleation. The energy barrier for this process, however, is believed to be much lower as the particle surface acts as a catalyst for nuclei formation and the surface exhibits the same crystal structure as the new crystals being formed. Once formed, the nuclei might be removed from the boundary layer by ﬂuid shear or collisions of the crystal with impeller, walls, or other crystals. Alternatively, they might stick on the surface of the parent crystal, just as in the case of heterogeneous nucleation. A diﬀerent set of mechanisms occurs when the particle surface is the direct source of new nuclei. It is noteworthy that the mechanical forces needed for these other mechanisms are signiﬁcantly higher than the one required for the boundary layer removal [28]. The new nuclei are then generated by initial breeding, dendritic growth, and attrition. Of these three mechanisms, attrition is likely the most common in industrial processes and was hence drawn in Figure 9.4b,c. Initial breeding, typically observed in seeded crystallization, assumes that ﬁnes have been produced during previous stages of crystallization, adhered to the larger seeds, and are eventually removed from the seeds due to ﬂuid shear and/or collisions. Dendritic growth occurs when the diﬀusion of solute molecules to the surface of a crystal is limiting the growth rate; it results in dendrites (“needles”)

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protruding from the original surface and can result in multiply branched structures when undisturbed. However, in stirred conditions, the thin dendrites are easily broken oﬀ, thus forming new nuclei. As diﬀusion-limited crystal growth is a necessary part of this mechanism, high supersaturations are usually required for its occurrence, which can be avoided by process design (e.g. slow cooling or antisolvent addition), see also Section 9.6. Finally, attrition describes the formation of nuclei due to abrasion. The parent particle, upon collision with other crystals (Figure 9.4b) or with parts of the crystallizer (Figure 9.4c), produces ﬁnes so small that the particle itself can be considered unchanged by each individual abrasion event. Clearly, multiple abrasion events on the same crystal lead to its destruction, unless the abraded crystal can heal through growth. From the conceptual description of these mechanisms, it is clear that the ﬂuid dynamics and several aspects of the crystals inﬂuence the rate of secondary nucleation. Relevant aspects of the crystals include their underlying crystal structure, their morphology, as well as the mechanical and chemical state of the exposed surfaces. Additionally, the supersaturation of the liquid phase plays a decisive role in all the mentioned mechanisms: in the solute layer removal mechanism, the thickness of the layer increases with supersaturation [25], supersaturation governs whether dendritic growth occurs, and whether the attrition fragments survive in solution. The latter depends on whether they are larger or smaller than the critical size (cf. Eq. (9.4)). All these considerations point at an increase in secondary nucleation rate with increasing supersaturation. The discussion presented above clearly highlights that obtaining a quantitative and predictive description of secondary nucleation is considerably diﬃcult and has not yet been achieved. Nevertheless, the present qualitative understanding has helped to formulate empirical and semiempirical rate expressions of secondary nucleation that are able to describe speciﬁc sets of data [25]. The expressions can be summarized as Jsec = k𝜀a (S − 1)b g(𝜙i , G)

(9.8)

where 𝜀 is the speciﬁc power input into the crystallizer, S is the supersaturation, and g is a function of the ith-moment 𝜙i of the crystal size distribution and of the crystal growth rate G, while a, b are ﬁtting parameters. The functional form of g is system speciﬁc as well.

9.4 Characterization of Nucleation 9.4.1

Deterministic Nucleation Rates

CNT and 2-SNT provide a theoretical framework for describing nucleation kinetics and expressing nucleation rates. Each theory depends on a certain number of parameters; although some of the parameters can be predicted from theory, it is customary to estimate all of them by ﬁtting experimental data. However, the estimation of nucleation kinetics suﬀers from an important limitation: in most systems, nuclei are small and their formation cannot be directly observed or otherwise detected. Indeed, one can easily calculate that an astonishing number of

9.4 Characterization of Nucleation

clusters with critical size would be needed to aﬀect a system’s experimentally accessible properties, such as turbidity or concentration. Hence, only once the nuclei have grown larger, nucleation events that happened earlier can be detected. The time elapsed between the attainment of initial supersaturation and the detection of crystals is deﬁned as the detection, or induction time, tD . Conceptually, this time can be thought of as the sum of the nucleation time, tN , and the growth time, tG , i.e. the time necessary to grow the new nuclei to a suﬃcient size. Hence, we can write tD = tN + tG . As a consequence, the information contained in such experiments depends not only on the nucleation rate but also on the crystal growth rate, G. It is thus clear that one cannot estimate the nucleation rate J from detection experiments without a model or some simplifying assumptions concerning crystal growth. The detection time also depends on the property that is monitored, as well as the technique and the detection limit of the speciﬁc instrument that is used to measure this property. The typically measured quantities in crystallization from solution are conductivity, turbidity, and infra-red intensity, which can be correlated with some property of the crystals (e.g. number of particles, average size, and crystal volume fraction) or of the solution (concentration). For instance, a typical formula relating the detectable volume fraction of crystals in solution, 𝛼v , deﬁned as the ratio between solid and system volume to the induction time reads as [1, 29, 30]: ( ) 4𝛼v 1∕4 (9.9) tD = kv JG3 where kv is the volume shape factor. In Eq. (9.9), supersaturation and temperature are assumed to be constant during the experiment. For the former assumption to be valid, the detectable volume fraction 𝛼v must be suﬃciently small. Note that this threshold value is also dependent on the speciﬁc experimental setup used and on the substance system monitored. Several alternative deﬁnitions of detection time are possible as well, based on diﬀerent monitored properties, e.g. the number of particles. As the detection threshold is a volume fraction, Eq. (9.9) implies that the detection time should be scale invariant. This property is interesting because small systems allow for better mixing and more uniform temperature and also require smaller amounts of substances to carry out induction time experiments. The induction time method has been applied to estimate the nucleation kinetics of many systems, particularly in lab-scale crystallizers (100 ml–10 l), see for example [29, 30]. In this type of studies, induction times were measured at diﬀerent supersaturations, as shown in Figure 9.5. For each supersaturation, a limited number of repetitions are usually carried out, and signiﬁcant scatter is observed in the detection times. The average value of the induction time at each supersaturation can then be converted to a nucleation rate (using Eq. (9.9) and a previously determined growth rate), which can be used to estimate parameters in a nucleation rate expression, e.g. Eq. (9.6). The data scattering observed in the example is typical in this type of experiments, and a rather poor reproducibility of detection time experiments has been consistently reported in the literature. Some theories concerning the origin

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Figure 9.5 A typical example of detection time experiments in a 500 ml crystallizer. 𝛼-L-Glutamic acid was crystallized in water at constant supersaturation, at three diﬀerent temperatures: ∘ ∘ 25 C (black), 35 C (blue), and ∘ 45 C (red). The bars associated with each point are given by the standard deviation. Source: Lindenberg and Mazzotti 2009 [30]. Reproduced with permission of Elsevier.

2000

1500 Detection time, tD (s)

272

1000

500

0

0

2

4 6 Supersaturation, S (–)

8

and the eﬀects of such scattering have been provided, and they are discussed in Section 9.4.2. 9.4.2

Stochastic Nucleation Rates

One possible cause of poor reproducibility worth investigating is the ﬂuid dynamic problems related to mixing, as well as heat and mass transfer limitations. These issues are well known in chemical reactor design, and it is known that strong local gradients can cause uncontrolled and nonreproducible phenomena, e.g. hot spots where the supersaturation, and thus the nucleation rate, is lower. In order to avoid or at least minimize local gradients, induction time experiments have been performed in increasingly smaller volumes over the past 30 years. Today, a considerably large record of data collected in crystallizers from 5 ml to droplets as small as nano- or even pico-liters is available in the literature. Concentration and temperature gradients, which might be uncontrolled sources of variability in larger scale experiments, are negligible in such systems. However, the stochasticity observed in the induction time measurements increases with decreasing volumes, instead of decreasing. As an example, two data sets collected in 1 ml isothermal reactors are shown in Figure 9.6, which clearly indicate that – even in the absence of gradients – the detection times are widely scattered. Indeed, comparing these results with those of Figure 9.5 highlights an even broader distribution of detection times. Similar observations have been reported for many other systems, both organic and inorganic, at diﬀerent operating conditions, and, usually, with a broadness of

9.4 Characterization of Nucleation

1

Probability, P (–)

0.8

0.6

0.4

0.2

0

0

1

(a)

2 3 4 Detection time, tD (s × 103)

5

1

Probability, P (–)

0.8

S

0.6

0.4

0.2

0 (b)

0

0.5

1

1.5

2

2.5

3

Detection time, tD (s × 104)

Figure 9.6 Typical examples of detection time distributions observed in small volumes: (a) acetaminophen crystallized in water in 1 ml vials by employing a constant cooling rate but diﬀerent solution concentration (red higher than blue). Source: Kadam et al. 2012 [31]. Reproduced with permission of Elsevier. The diﬀerent curves correspond to two diﬀerent ∘ ∘ saturation temperatures (diﬀerent solution concentrations): 60 C (red) and 30 C, (b) p-aminobenzoic acid crystallized in acetonitrile in 1.5 ml under isothermal conditions but diﬀerent initial supersaturations. Source: Sullivan et al. 2014 [32]. Reproduced with permission of ACS Publications.

273

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9 Nucleation

induction time distribution inversely proportional to the size of the system. The evidence has convinced researchers that such statistical behavior is not merely an experimental accident but an intrinsic feature of nucleation. In fact, nucleation should be interpreted as a stochastic phenomenon whose nondeterministic nature becomes keenly apparent at small system scales. CNT, and also 2-SNT, describes nucleation as an activated process in which an energy barrier needs to be overcome to go from the metastable, supersaturated solution to the stable, crystalline state. When the energy barrier to be overcome between the two states becomes substantial (larger than about 1 kT or roughly 2.5 kJ mol−1 at room temperature), nucleation becomes a “rare event.” The energy barriers for nucleation lie well beyond this threshold, which can be inferred from experimental data and has also been shown in molecular dynamic simulations [22]. Rare events exhibit an intrinsically stochastic nature, i.e. each realization of an event occurs at a random time, but the ensemble of all possible realizations follows a statistical distribution, as it is observed in detection time experiments. Various models have hence been proposed to reconcile theory and experiments, to identify the statistical distributions describing the data, and to use such distributions to establish reliable nucleation kinetics from the experimental data [16, 31, 33–36]. There are strong theoretical arguments that primary nucleation should be described by Poisson statistics and many experimental dataset exhibit these statistics. In the Poisson model, for constant temperature and supersaturation, the probability P of having formed at least one nucleus up to time tN , in a system of volume V and of nucleation rate J, is P(tN ) = 1 − exp(−JV tN )

(9.10)

The distribution of nucleation times is described by Eq. (9.10), and its mean value and its standard deviation are inversely proportional not only to the volume of the system but also to the nucleation rate; because the latter increases with the supersaturation, this equation may explain why the data at lower supersaturation appear more scattered than those at higher supersaturation (see Figure 9.6, but also Figure 9.5). To prove the stochastic hypothesis of nucleation and to estimate nucleation rates, not only for the case of Poisson distribution considered here but for any statistical distribution, the detection time experiments and their analysis must satisfy some important requirements: First, the diﬀerent experimental repetitions must be carried out under the same conditions; only then, can they be assumed to form part of the same statistical distribution. Second, as one can only measure detection times, whereas the stochastic hypothesis concerns nucleation times, one must be able to link the detection times to the nucleation times. Hence, a mathematical model describing stochastic nucleation must also account for the growth of the nuclei into fully developed crystals. Third, a representative sample of the stochastic process must be gathered, i.e. a large enough number of experimental points must be collected, so that they form a representative sample of the detection time distribution underlying the stochastic process [37].

9.5 Order of Polymorph Appearance – Ostwald’s Rule of Stages

9.5 Order of Polymorph Appearance – Ostwald’s Rule of Stages One of the goals in many manufacturing processes is to consistently obtain a speciﬁc polymorph. However, many substances exhibit multiple polymorphs. It is therefore no surprise that there is an extensive body of work dealing with the order in which the diﬀerent forms emerge in a process. Most prominently, Ostwald was the ﬁrst to note that – conspicuously often – the least stable polymorph appears to be the ﬁrst to nucleate in a system, followed by the second-most unstable form, etc. [38]. This empirical observation, made by many researchers for a large set of additional compounds, has since been named Ostwald’s rule of stages (OSR). Although OSR does not represent a physical law and several counter examples exist (e.g. [39]), there have been various theories attempting to explain the underlying cause of this phenomenon. Thermodynamic arguments have been brought forward [40], as well as arguments that claim properties of the solution structure to be relevant for polymorph selection [41]. Here, we shall brieﬂy present a line of reasoning based on nucleation kinetics favored by a majority of authors [42–44], which has the advantage of being compatible with the observed supersaturation dependence encountered in various systems [45], and of revealing a clear, systematic path for process design. Fundamentally, this interpretation implies that depending on the solution environment, certain precritical cluster conﬁgurations associated with particular polymorphic forms are favored. Assuming that the nucleation kinetics of a given compound may be described by Eq. (9.6), the logarithm of the ratio of the nucleation rates for two competing polymorphs is given by ( ) ( ∗) ( ) B Au c B J − 2 u (9.11a) + ln ∗s + 2 s ln u = ln Js As cu ln (c∕c∗s ) ln (c∕c∗u ) The labels u and s here refer to the less stable and more stable form, respectively, Eq. (9.11a) can be recast in a more compact form by deﬁning 𝛼 = ln(Au ∕As ), 𝜆 = ln(c∗s ∕c∗u ) and 𝛽i = Bi ∕ln2 Si . ( ) J ln u = 𝛼 + 𝜆 + 𝛽s (c) − 𝛽u (c) (9.11b) Js In Eq. (9.11b), we have highlighted those terms that depend on changes in the liquid concentration, c. The behavior of the system is visualized in Figure 9.7; note that, by deﬁnition, c∗s < c∗u and 𝜆 < 0. It is easy to see that Eq. (9.11) approaches negative inﬁnity for c → c∗u and that it tends toward (𝛼 + 𝜆) for large supersaturations. In other words, at concentrations approaching the solubility of the unstable form, the nucleation of the stable form is more likely, whereas at higher concentrations, the dominant form depends on the value of the kinetic parameters. If, for example, we have that (𝛼 + 𝜆) > 0, higher supersaturation will eventually always lead to preferred nucleation of the

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Bs / Bu

α+λ>0

α+λ 0; the nucleation of the unstable polymorph always dominates for increasing concentrations; (b) 𝛼 + 𝜆 < 0; the nucleation of the unstable polymorph may dominate only if Bs is suﬃciently larger than Bu and within intermediate concentrations. Cornel et al. 2009 [46]. Adapted with permission from ACS Publications.

unstable form; see Figure 9.7a. If, on the other hand, this inequality does not hold (cf. Figure 9.7b), the unstable form can only dominate nucleation if Eq. (9.11) has a maximum (only the case when Bu ≤ Bs ), and if that extremum lies above zero, (Bu must be suﬃciently smaller than Bs ); the particular conditions can be found easily by solving the associated system of equations. Naturally, the behavior of the system will be aﬀected by temperature, and an analogous analysis can be performed to determine its eﬀect. To make an example, if 𝛼 is found to exhibit a strong negative correlation with temperature, that is, 𝜕𝛼∕𝜕T ≪ 0. For a given solute concentration and assuming the solubility ratio 𝜆 is only a weak function of T, it would then be beneﬁcial to operate at elevated temperatures to produce the stable form and at lower temperatures to manufacture the unstable polymorph. In summary, given primary nucleation kinetics of two or more polymorphs, it is comparably easy to identify operating conditions at which the nucleation of a particular form is favored based on some simple analysis of the system; knowledge of the prefactors and the relative stability (𝛼 and 𝜆) alone may even be suﬃcient to decide upon a strategy for production. Furthermore, the variety of possible cases is rather limited for simple kinetics, as can be seen from Figure 9.7. The above type of analysis retains its usefulness regardless of the type of process under consideration, i.e. batch or continuous crystallization. Similar approaches can be used for other types of nucleation kinetics that are dependent on other factors, including the choice of solvent, additives, templates, or the mixing rate in the case of reactive crystallization [47, 48]; the eﬀect of these properties on the polymorph selectivity may be much greater than that of supersaturation or temperature alone. Nevertheless, this approach hinges on the fact that nucleation rates are assumed to be known. If this is not the case, some prior kinetics estimation work – as, e.g. outlined in Section 9.4 – is necessary. If such studies lead to unsatisfactory results or nucleation during the crystallization step is ruled out as a viable option for other reasons, the logical response

9.6 To Seed or Not to Seed?

is to attempt suppressing nucleation entirely, making instead use of seed crystals to drive the production of a speciﬁc polymorph.

9.6 To Seed or Not to Seed? Seeding is widely used in the chemical and pharmaceutical industry to control crystal properties and to ensure constant product quality such as crystalline form, particle size distribution, and purity. Compared to their unseeded counterparts, seeded crystallization processes can be performed at relatively low supersaturations, which are favorable for control of the afore-mentioned properties. 9.6.1

Process Control

As mentioned above, the metastable zone is the region in the phase diagram in which the supersaturation is suﬃciently low to avoid spontaneous nucleation (of a given polymorph), illustrated, e.g. by the blue and red regions in Figure 9.8. In seeded crystallization processes, the seed crystals should be added within the metastable zone in order to avoid spontaneous nucleation; values of S at the seeding point in industrial crystallization of organic compounds range from 1.1 to 1.5. The seed crystals may be added as suspension to enable quick dispersion in the vessel and to avoid formation of lumps; furthermore, they should be smaller than the desired product crystals. Therefore, a particle comminution step, such as dry milling or sieving, is often required in the preparation of seeds, if these have been diverted from the product crystals of a previous batch. In industrial practice, it is also important to use seed crystals with reproducible particle size distribution, in order to ensure low product variability. 12

Concentration, c (%)

10 8 6 4 2 0

0

20 40 Temperature, T (°C)

60

Figure 9.8 Solubility and metastable zone of a stable polymorph (blue) and a metastable polymorph (red) for the case of a monotropic system. Solid lines: solubility; dashed lines: limit of the metastable zone. The blue diamond depicts the seeding point for obtaining the stable polymorph and the red triangle the seeding point for the metastable polymorph.

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The optimum amount and size of the seed crystals depends on the desired particle size of the product. Assuming the crystal size increases only by crystal growth and secondary eﬀects such as agglomeration, breakage, and secondary nucleation are negligible, the mean particle size of product crystals, Lp , can be approximated by ) ( 1 + Cs 1∕3 Ls (9.12) Lp = Cs where Ls is the size of the seed crystals and Cs is the seed loading, deﬁned as Cs =

ms (Seed mass) = (Yield) mp − ms

(9.13)

In Eq. (9.13), ms represents the mass of seed crystals and mp that of product crystals [49]. The total surface area of the seeds, which, in turn, depends on their size and amount, also determines the maximum rate of cooling or antisolvent addition to keep supersaturation at a level suﬃciently low to avoid secondary eﬀects. Kubota and coworkers proposed an experimental method to determine the optimum conditions for seeded crystallization. First, experiments using a diﬀerent amount and size of seed crystals are conducted. Secondly, the experimental values of Lp ∕Ls are plotted vs the seed loading Cs and compared to the ideal growth line given by Eq. (9.12), see Figure 9.9. Experimental values of Lp ∕Ls below the ideal growth line may be caused by nucleation (low amount seeds, large seed crystals, or high supersaturation caused by fast cooling or antisolvent addition) or breakage (brittle crystals and intense stirring) [50]. Values above the ideal growth line may be a result of agglomeration (high supersaturation, insuﬃcient stirring, or high concentration of relatively small crystals) [51].

Lp /Ls (–)

278

101

10–4

10–3 10–2 Seed loading, Cs (–)

10–1

Figure 9.9 Seed chart. Solid line: ideal growth line; diamonds: product following the ideal growth line; triangles: product particle size below ideal growth line as a result of nucleation; squares: product particle size above ideal growth line as a result of agglomeration.

9.6 To Seed or Not to Seed?

Despite the fact that seeded crystallization processes are generally robust and deliver constant product quality, variability may be introduced by impurities having an eﬀect on solubility and growth rate [52], or by changes in the equipment or process parameter such as stirrer type or stirring rate. It is also known that the growth rate of crystals may not be constant over time and is impacted by defects in the crystal lattice as well as relative surface area of diﬀerent crystal facets of the seed crystals [53]. 9.6.2

Polymorphism Control

Seeding can also be employed to control the polymorphic form of a compound produced by crystallization. In principle, there are four possible situations that may occur in practice [54]: 1. The desired polymorph is stable and identical to the polymorph generated by primary nucleation. In this case, seeding may be mainly utilized to improve process robustness as described above, but not to control the polymorphic form. 2. The required polymorph is stable and the polymorph generated by primary nucleation is metastable. As outlined in Section 9.5, this case, which follows OSR, is relatively common. Seeding with the stable polymorph at low supersaturations and below the solubility of the metastable polymorph avoids occurrence of the metastable polymorph in the process, see Figure 9.8. 3. The required polymorph is metastable and is that which is also generated by primary nucleation. Seeding with the metastable form may avoid the occurrence of the stable form. However, there is a high risk of a polymorph transformation during the process because the supersaturation of the stable form is always higher (for monotropic systems or below the transition temperature for enantiotropic systems), see Figure 9.8. 4. The required polymorph is metastable and the polymorph generated by primary nucleation is stable. Seeding cannot be employed to ensure only the metastable polymorph is obtained, if the solubility of the metastable polymorph is higher than the concentration at which the stable polymorph precipitates spontaneously. “Disappearing” polymorphs, that is, those that have been manufactured until a certain point in time but subsequent attempts to produce this polymorph result in a diﬀerent form, are linked to situations 3 and 4, i.e. the desired form is a metastable polymorph. Their disappearance can be explained by the occurrence of a new more stable polymorph and the unintentional or universal seeding, which describes the presence of small amounts of the new more stable polymorph in all laboratories or production facilities [55]. 9.6.3

Impurity Control

Crystallization is a very eﬃcient separation process theoretically leading to fully pure material in a single process step. In reality, however, impurities, by-products, or solvents can still be found in the crystallite. There are multiple reasons why

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the particle may not be pure, including adsorption of impurities on the crystal surface, incorporation into the crystal lattice, entrapment of impurities between agglomerated crystals, precipitation of the impurity as separate crystals, or amorphous particles. Impurities may be incorporated as point defects into the crystal lattice at equilibrium conditions and the incorporation can be characterized by a segregation coeﬃcient [56, 57]. In industrial crystallization, the amount of impurities found in the crystallite can exceed the amounts predicted by the segregation coeﬃcient and is related to nonequilibrium growth processes resulting in inclusions or defects. The tendency to form inclusions or defects increases with supersaturation [56]. Therefore, seeded crystallization processes operated at low supersaturation may be employed to improve the puriﬁcation eﬀect.

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10 Crystallization Process Modeling Marco Mazzotti1 , Thomas Vetter2 , and David R. Ochsenbein1 1 ETH Zürich, Institute of Process Engineering, Switzerland 2

University of Manchester, School of Chemical Engineering and Analytical Science, United Kingdom

10.1 Introduction The properties of crystalline products are not only deﬁned by their composition and crystal structure but also by their size and shape. The inﬂuence of these features is particularly important for downstream processing operations, such as ﬁltration, drying, milling, granulation, blending, etc. For instance, one can surmise that thin needle-like crystals are more prone to break in an agitated dryer than compact crystals of the same material, or that the time required to separate mother liquor from crystals by cake ﬁltration depends on how tightly crystals in the ﬁlter cake are packed, which, in turn, depends on the crystal size and shape. Crystals owe their characteristic sizes and shapes to an interplay between crystal structure, thermodynamics, and kinetics – in short: to some inherent properties and to the process they were manufactured in. In fact, at the level of individual crystals, it is a particle’s history, the environments, and events it has encountered that determine those features. Given the variety of possible trajectories within a process, it is no surprise that crystals also exhibit a diversity of sizes and shapes, typically described by a particle size and shape distribution (PSSD). Simple approaches to modeling crystallization processes, e.g. a yield calculation solely based on thermodynamics, are not able to successfully describe, much less predict, the properties that are connected to the crystal size and shape distribution. Yet, as illustrated in the drying and ﬁltration example above, this capability would be highly desirable. The remainder of this chapter is therefore focused on introducing modeling concepts for crystallization processes that allow keeping track of the properties of the liquid phase and of the solid phase, speciﬁcally the PSSD. After brieﬂy deriving the underlying concepts in the following paragraphs, selected case studies showcasing applications of this modeling methodology are presented. Among the examples covered are polymorph transformations, crystal growth, and agglomeration rate estimation, as well as examples of model-based process optimization.

Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development, First Edition. Edited by Rolf Hilﬁker and Markus von Raumer. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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10.1.1

Population Balance Equations

For the purpose of an accessible introduction to crystallization process modeling, we ﬁrst assume that crystals can be described by a single characteristic length L. This implies the existence of a one-dimensional particle size distribution (PSD), denoted here as f (L). Formally, f is a number density function, so that f (L)dL corresponds to the number of crystals per volume of suspension with characteristic lengths between L and L + dL. The evolution of this distribution over time can be described using population balance models [1–3]. The corresponding equations account for changes in the number of particles within a given control element, i.e. they describe how many particles are in the control element, how many are entering it, and how many are leaving it. To illustrate this concept, we derive the population balance equation (PBE) for an idealized tubular crystallizer with constant cross section A (cf. Figure 10.1a). We will then show how this model can be modiﬁed to also apply to continuous stirred tanks as well as batch crystallizers. In the tubular crystallizer considered here, we assume that its content is perfectly mixed in radial direction, but that no mixing in axial direction occurs. Collectively, these assumptions lead to a “plug ﬂow” behavior; however, we highlight that these simplifying approximations are by no means a necessary criterion for the modeling framework, i.e. nonidealities could easily be accounted for if necessary. Regardless, here, the PSD is hence not only a function of the time t, and of the internal coordinate (characteristic crystal size) L, but also of the external coordinate (the position along the crystallizer axis) x, that is f (t, x, L). We consider a control element stretching from x to x + Δx and stretching from L to L + ΔL (cf. Figure 10.1). In the external coordinate, the control element can be visualized as a slice of the plug ﬂow crystallizer (drawn as the gray disk in Figure 10.1a), whereas the internal coordinate is not visible in this representation. Acknowledging this, the control element is redrawn in Figure 10.1b to visualize both internal and external coordinates. A PBE is obtained by accounting for all ﬂuxes, drawn as arrows in Figure 10.1b, and possible source or sink terms. In abstract terms, we can write for the control element: Accumulation = In − Out + Birth − Death

(10.1) Particles leaving due to growth

L+ΔL

Flow in, Q

A x

(a)

Flow out, Q x+Δx

External coordinate x

Particles entering due to flow

Particles in control element AΔxΔLf

Particles leaving due to flow

L

Particles entering due to growth

(b)

x

x+Δx

Figure 10.1 (a) Conceptual drawing of a plug ﬂow crystallizer with control element highlighted as a slice of the reactor in gray; (b) drawing of the control element and ﬂuxes into and out of it.

10.1 Introduction

Fluxes in x-direction represent the transport of ﬂuid and particles along the axial coordinate of the crystallizer, while ﬂuxes in L-direction account for crystal growth or dissolution. Nucleation, breakage, and agglomeration are important examples of mechanisms that can be described using birth and death terms. For the case of a plug ﬂow crystallizer with volumetric ﬂow Q, Eq. (10.1) can be written as AΔxΔL([f ]t+Δt − [f ]t ) = QΔL([f ]x − [f ]x+Δx )Δt + AΔx([Gf ]L − [Gf ]L+ΔL )Δt

(10.2)

+ AΔLΔx(B − D)Δt where we have deliberately omitted the arguments of f as well as those of the growth (or dissolution) rate G for brevity’s sake. The subscripts in Eq. (10.2) indicate at which point the terms in square brackets have been evaluated. By dividing Eq. (10.2) by ΔL, Δt, Δx, and A and by letting ΔL → 0, Δt → 0, and Δz → 0, we obtain 𝜕f 𝜕(Gf ) Q 𝜕f + + =B−D 𝜕t A 𝜕x 𝜕L

(10.3a)

However, the above considerations do not yet describe changes in concentration in the liquid phase, a crucial property due to its inﬂuence on the driving force for nucleation and growth. The necessary material balance for the solute yields dm 𝜕c Q 𝜕c + =− c 𝜕t A 𝜕x dt

(10.3b)

where mc is the crystal mass per volume of suspension, typically given by mc = kv 𝜌c 𝜙3 , kv is a shape factor, and 𝜌c is the crystal density. Here, 𝜙3 is the third moment of the PSD, in general deﬁned as ∞

𝜙i =

∫0

Li f dL.

(10.4)

Equation 10.3 forms the general description of a plug ﬂow crystallizer with a known temperature proﬁle, both in transient phases and during steady state. In a similar manner, the equations describing a (well-mixed) continuous stirred tank reactor (CSTR) with volume V can be derived, yielding 𝜕(fV ) 𝜕(Gf ) +V = +V (B − D) + Qin fin − Q f 𝜕t 𝜕L d(cV ) d(mc V ) + = Qin cin − Qc dt dt

(10.5a) (10.5b)

which in the case of clear input stream ( fin = 0) and at steady state reduces to the well-known mixed suspension mixed product removal (MSMPR) formulation: 𝜕(Gf ) Q + f =B−D 𝜕L V Q Q (c − cin ) = − mc V V

(10.6a) (10.6b)

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10 Crystallization Process Modeling

Notably, Eq. (10.6b) is not a diﬀerential, but only an algebraic equation. Finally, we consider the case of a batch crystallizer, which we ﬁnd to be described by 𝜕(Gf ) 𝜕f + =B−D (10.7a) 𝜕t 𝜕L dm dc =− c (10.7b) dt dt In order to solve any one of Eqs. (10.3), (10.5), (10.6), and (10.7), additional information is needed. First, a set of initial and boundary conditions is required; for the case of the batch crystallizer and assuming zero-sized nuclei, these can, for example, be written as J f (t = 0, L) = f0 (L), f (t, L = 0) = (10.8a) G (10.8b) c(t = 0) = c0 where J is the rate of nucleation and f0 and c0 are a seed distribution and the initial solute concentration, respectively. Second, we need some knowledge regarding the constitutive equations that describe the kinetics of the system, that is, we need expressions for J, G, B, and D. This requires some understanding of the underlying phenomena that is often not trivial to obtain but has been accomplished – at least to some degree – for many of the major crystallization mechanisms [4], e.g. nucleation [5, 6], growth [7–9], agglomeration [10–13] and breakage [14, 15]. For the sake of simplicity, here, we assume that the necessary expressions are available. 10.1.2 10.1.2.1

Notes Regarding Population Balance Models Energy Balances and Fluid Dynamics

The models presented in Section 10.1.1 represent useful descriptions in the case of comparably slow crystallization processes, whose temperature can be adequately controlled by some low-level feedback controller. For fast processes or those that are strongly exo- or endothermic, an additional heat balance that is coupled to the other equations is necessary for a complete model. Nevertheless, it should be noted that the assumption of perfect temperature control is often a reasonable approximation, particularly for organic compounds grown at low supersaturations, as is often the case in pharmaceutical production. In a similar vein, the assumption of well-mixedness, be it partial (e.g. in the radial direction in Eq. (10.3b)) or complete (cf. Eqs. (10.5a), (10.6a), and (10.7a)) may be violated for systems where uniform mixing is diﬃcult (e.g. large tanks) or where crystallization occurs with very short characteristic times (e.g. precipitation). In these cases, mixing aspects need to be taken into consideration explicitly, resulting again in more complex descriptions of the process [11, 16, 17]. 10.1.2.2

Solution of Population Balance Equations

An application of the above models requires an accurate solution of the set of (integro-)partial diﬀerential equations derived above. Unfortunately, analytical solutions are only available for the simplest cases, and in general, numerical tools

10.2 System Characterization and Optimization

are necessary to compute model outputs. Fortunately, there exists a vast literature on the fast and eﬃcient numerical solution of PBEs [18–21], together with various strategies to reduce the complexity of the resulting model equations making simplifying assumptions. Regarding the latter, particularly the various methods of moments that have been developed deserve mention [1, 22]. 10.1.2.3

Applications

The population balance models outlined in Section 10.1 represent a ﬂexible framework to describe particulate processes and can be useful for a variety of tasks. For instance, it is possible to characterize systems whose behavior has not yet been identiﬁed by ﬁtting parameters in population balance models to experimental data; we present examples for this application in Sections 10.2.1–10.2.3. Once these kinetics are known, processes can be optimized using computational studies (cf. Section 10.2.4) and become candidates for model-based control strategies, such as model-predictive control. In addition, such systems can also be realistically investigated on a process design level, allowing the analysis of diﬀerent ﬂow sheets in terms of, e.g., reachable sets [23]. Finally, extensions to systems with multiple internal states (e.g. multiple characteristic sizes) are possible and represent an important new research direction, as highlighted in Section 10.3.

10.2 System Characterization and Optimization Identifying the kinetic parameters that form part of the constitutive equations in the population balance model is vital in order to obtain a truly predictive model of a process. To some extent, this can be done through independent experiments, whose goal is to extract information about the rate of individual mechanisms. Important examples are induction time (nucleation rate) measurements as well as growth rate studies, which may be conducted using setups that are substantially diﬀerent from a standard crystallizer. However, because of the complexity of the process, it may sometimes be more meaningful to estimate kinetics from experiments that are closer to how the crystallization process would be carried out in production, thereby taking into account nonidealities that occur because of imperfect mixing, particle–particle interactions, etc. A generally applicable pathway for system identiﬁcation is to run simulations and then compare the model output to experimental data (cf. route A in Figure 10.2). By deﬁning an objective function – for example, the sum of squared residuals between model predictions and experimental measurements – and embedding the process model in a higher order optimization routine, the diﬀerence between experimental data and model outcome can be minimized through iterative adaptation of the kinetic parameters. The necessary experimental data are typically acquired by using process analytical technology (PAT) tools, which permit online monitoring of the continuous phase (e.g. the solution concentration through infrared spectroscopy and Raman spectroscopy) and/or the particles (e.g. the PSD or some properties of the

289

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A

B Optimization routine

Kinetic parameters

Operating policy

Model

A Experimental data

Output

Compare Target outcome

Compound data

Objective function value

B

Figure 10.2 Schematic overview of parameter estimation (A) and model-based process optimization (B). Compound data (thermodynamic/crystallographic properties, etc.), kinetic parameters, and information regarding the operating parameters are generally necessary for the simulation of a crystallization process.

PSD through Raman spectroscopy, focused beam reﬂectance measurements (FBRM), imaging probes, and in situ laser diﬀraction). Although such data alone already helps to understand a process in greater detail, using them in the PBE modeling framework allows drawing more in-depth and more general conclusions regarding the process behavior. Analogous to parameter estimation, one can optimize the outcome of processes whose kinetics are already known, the main diﬀerence lying in the fact that the comparison is then made by comparing the model output with some target outcome (B route in Figure 10.2) rather than the experiments and that the decision variables are related to the operating policy instead of the kinetic parameters. Critically, it must be noted that – because of the nature of the problem – there is generally no certainty supported by theory that any optimization (A or B in Figure 10.2) converges toward a local, much less a global optimum in reasonable time. Nevertheless, we will show that, even without this guarantee, valuable results can be obtained with this approach. 10.2.1

Crystal Growth

The characterization of systems under conditions for which crystal growth plays a dominant role is probably the simplest yet also most important application for the approach described in Section 10.2. One such example is given by Vetter et al. [7], in which the population balance model shown in Eq. (10.7) with zero right hand side (B = D) was used to ﬁt the growth rate of ibuprofen to measured

10.2 System Characterization and Optimization

concentration proﬁles in seeded batch desupersaturation experiments. By applying the estimation procedure to experiments at diﬀerent concentrations of a polymeric additive, the latter’s inﬂuence on the growth rate could be determined. Likewise, Codan et al. [24] used a similar system of equations and experimental procedure to determine the growth kinetics of S-mandelic acid in the presence of its counter enantiomer within the two phase region in water, indicating the applicability of the population balance framework also for chiral systems. The growth-inhibiting eﬀect of R-mandelic acid at various concentration levels was quantiﬁed and its dependence on supersaturation demonstrated. As for continuous crystallizers, similar strategies can be used to obtain information regarding the process kinetics. An important simpliﬁcation occurs for MSMPRs: in the absence of agglomeration and breakage, the identiﬁcation of both nucleation and growth rates simultaneously for a single operating condition can be done rapidly by comparing the obtained PSD with the one computed from Eq. (10.6a). In fact, under the above assumptions and assuming the growth rate is size independent, that equation possesses a simple analytical solution, given by ( ) J −LQ (10.9) fss (L) = ss exp Gss V Gss which indicates that, ideally, nucleation and growth rates at the steady state (ss) can be computed from the y-intercept and slope of the line drawn by a plot of ln( fss ) vs L. An important discussion regarding the usefulness of such experiments is provided by Garside and Shah [25]. 10.2.2

Polymorph Transformation

The modeling of solvent-mediated polymorph transformation can be achieved by extending the standard formulation in Section 10.1, which considers only one crystal species, to the case where there exist multiple solid-state forms. In particular, PBEs for all relevant species in the system need to be written and solved in parallel, taking into account the fact that the equations for the diﬀerent solid forms are coupled through the concentration of the solute, which is one and the same for all of them. For the case of a well-mixed batch reactor with m diﬀerent polymorphs and no source or sink terms (B = D = 0), Eq. (10.7a) becomes 𝜕fi (t, L) 𝜕[Gi (L, Si )fi (t, L)] + = 0 i = 1, … , m (10.10a) 𝜕t 𝜕L Note that growth, dissolution, and nucleation kinetics diﬀer for diﬀerent species and are typically expressed as functions of the corresponding supersaturation Si = c∕c∗i . The associated material balance, too, is rewritten to account for changes in the solution concentration due to the various polymorphs ∑ dmc,i dc =− dt dt 1 m

(10.10b)

The system of partial and ordinary diﬀerential equations formed by Eqs. (10.10a) and (10.10b) is valid regardless of the underlying thermodynamics and can be solved in a similar way as in the case of a single species. A number of authors

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10 Crystallization Process Modeling

ti

tp

50

α form

β form 40

80 60

30 Solute

α solubility

40

20 β solubility

20

10

Solute concentration (g kg−1)

100 Solid composition (wt %)

292

0 0 0

2

4

6

8

10

12

Time (h)

Figure 10.3 Evolution of solid composition and liquid concentration over time for an unseeded polymorph transformation experiment. Markers indicate experimental data (composition: Raman; solute concentration: ATR-FTIR), whereas solid lines show model ﬁts. Source: Cornel et al. 2009 [28]. Reprinted with permission from ACS Publications.

have reported system characterization results using this model and its variants (e.g. for continuous systems) [26, 27]. In particular, Cornel et al. [28] have investigated the solvent-mediated polymorph transformation from α to the monotropically stable β l-glutamic acid, that is, a system for which m = 2. In particular, they performed seeded experiments and solved the above equations to ﬁt the secondary nucleation kinetics of the β form; nucleation rate of α l-glutamic acid as well as the growth and dissolution rates had been determined or estimated independently [29, 30]. The results obtained from the seeded experiments were further used to predict the behavior of the system in the unseeded case with acceptable success as illustrated in Figure 10.3. The model ﬁnally demonstrated its ability to forecast total transformation times for experiments starting from clear solutions at diﬀerent supersaturation levels. It is important to highlight the role of the two spectroscopic techniques used in that work: in situ attenuated total reﬂection Fourier transform infrared (ATR-FTIR) and Raman. The two PAT tools allowed insight into the main mechanisms even before the rigorous kinetics determination. Namely, the fact that the dissolution of the metastable α form is not the rate-determining step was established through qualitative analysis of the data alone [31]. 10.2.3

Agglomeration

The characterization of systems that exhibit eﬀects besides nucleation and growth has been performed in the literature as well. Focusing on the case of

10.2 System Characterization and Optimization

agglomeration, it is convenient to ﬁrst rewrite Eq. (10.7a) in the volume-based form, where the characteristic length L is replaced by a characteristic volume 𝑣 = kv L3 . In the case of a well-mixed batch reactor, this yields 𝜕f (t, 𝑣) 𝜕[Γ(𝑣, S)f (t, 𝑣)] + = B(t, 𝑣, S) − D(t, 𝑣, S) (10.11) 𝜕t 𝜕𝑣 where the length-based growth rate G was further replaced by its volume-based 1∕3 equivalent, Γ = 3kv 𝑣2∕3 G. Clearly, the mass balance as well as the initial and boundary conditions previously presented in Eqs. (10.7b) and (10.8b) can be easily rewritten to reﬂect this change in internal coordinate. If it is assumed that agglomeration is an irreversible process, that is, agglomerated particles are cemented together via a stable bridge that is strong enough to withstand all forces acting on it, the birth term can be written as (see, e.g. [3] for a detailed derivation) B(t, 𝑣, S) =

𝑣

1 𝛽(𝑣 − 𝑣′ , 𝑣′ , S)f (t, 𝑣 − 𝑣′ )f (t, 𝑣′ )d𝑣′ 2 ∫0

(10.12)

while the death term is given by ∞

D(t, 𝑣, S) = f (t, 𝑣)

∫0

𝛽(𝑣, 𝑣′ , S)f (t, 𝑣′ )d𝑣′

(10.13)

The newly included kinetics are governed by the agglomeration kernel 𝛽, itself often assumed to be the product of two factors: a collision frequency 𝛽c and an agglomeration eﬃciency (or sticking probability) Ψ. Although diﬀerent derivations and expressions exist for the two factors [10, 11, 32–36], there is a general consensus that the agglomeration kernel depends on ﬂuid viscosity, energy dissipation rate, as well as supersaturation; theoretical derivations further predict a dependence of the agglomeration rate on particle size, although several authors have chosen to neglect this eﬀect, being still able describe experiments satisfactorily [12, 37, 38]. The above model as well as variations thereof has been used to describe or characterize multiple agglomerating systems in the literature [39–42]. Lindenberg et al. [12] tested diﬀerent models for 𝛽c and Ψ together with Eqs. (10.11)–(10.13) to describe the agglomeration behavior of α l-glutamic acid in water under varying process conditions. The ﬁtted model showed excellent agreement with the experimental results with respect to its prediction of the supersaturation proﬁles and the PSD (cf. Figure 10.4). It is hence suitable for further use during process design and development. The same work, in which additional computational ﬂuid dynamics (CFD) simulations were performed to investigate shear rate variations in the stirred batch vessel (cf. Figure 10.5), further serves to demonstrate a number of key issues that play a role in the modeling of agglomeration. First, process characterization for these systems becomes inherently more cumbersome because of the increased complexity of the process. Second, the understanding of the ﬂuid dynamics of suspensions in stirred vessels and its role in agglomeration is still limited, particularly for the higher suspension densities and larger vessel sizes that are of industrial interest. Third, there is a diﬃculty to experimentally distinguish agglomeration from other processes acting on the

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PSD, such as growth. The reason for this is that typically only a total PSD is measured, that is, a distribution that includes both agglomerates and primary particles. The problem is compounded by the fact that sample preparation, such as sonication, can aﬀect the PSD by breaking up otherwise stable particles. In response to the former two issues, a trend toward reduced models, whose lower computational cost allows for faster computation of process outcomes able to be integrated in CFD software, is evident [22]. With regard to the third point, image analysis approaches have shown potential in distinguishing agglomerates

Mass density (1/m)

8000 Seed Experiment Simulation incl. agglomeration

6000

Simulation w/o agglomeration

4000

2000

0 0.0000

0.0001

(a) Run 2, S = 4.24

0.0002

0.0003

0.0004

0.0005

0.0006

Particle size (m)

8000

Mass density (1/m)

294

Seed Experiment Simulation incl. agglomeration

6000

Simulation w/o agglomeration

4000

2000

0 0.0000

0.0001

(b) Run 3, S = 5.74

0.0002

0.0003

0.0004

0.0005

0.0006

Particle size (m)

Figure 10.4 Comparis on of experimental (markers) and ﬁtted modeling (solid lines) results. (a) & (b): Eﬀect of supersaturation; (c) & (d): Eﬀect of seed particle size. Source: Lindenberg et al. 2008 [12]. Reprinted with permission from ACS Publications.

10.2 System Characterization and Optimization

Seed Experiment Simulation incl. agglomeration

Mass density (1/m)

20 000

15 000

Simulation w/o agglomeration

10 000

5000

0 0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

Particle size (m)

(c) Run 7, F1

12 000 Seed Experiment Simulation incl. agglomeration

Mass density (1/m)

10 000 8000

Simulation w/o agglomeration

6000 4000 2000 0 0.0000

0.0001

(d) Run 10, F3

0.0002

0.0003

0.0004

0.0005

0.0006

Particle size (m)

Figure 10.4 (Continued)

from primary particles, a step that might help to obtain the higher resolution data sets necessary for experimental validation [43–47]. 10.2.4

Optimization

Here, we shall give a brief introduction to model-based optimization in the ﬁeld of crystallization, although it should be noted that several model-free approaches to optimize or control processes exist as well (e.g. [48–50]). A more comprehensive review of the current state of the art in both ﬁelds can be found elsewhere [51–53]. Schematically, model-based optimization of a (crystallization) process with respect to some generic objective, Φ, can be viewed as the following

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10 Crystallization Process Modeling

6.26e–01 5.95e–01 5.64e–01 5.33e–01 5.01e–01 4.70e–01 4.39e–01 4.08e–01 3.77e–01 3.46e–01 3.14e–01 2.83e–01 2.52e–01 2.21e–01 1.90e–01 1.59e–01 1.27e–01 9.62e–02 6.51e–02 3.39e–02 2.74e–03

(a) 140 120 100 80 f (ε)

296

60 40 20 0 0.001

0.01

0.1

ε (W kg–1)

(b)

Figure 10.5 a) Contour plot of velocity magnitude in ms−1 for a stirring rate of 200 rpm; (b) distribution of energy dissipation in the stirred reactor for the same stirring rate. Source: Lindenberg et al. 2008 [12]. Reprinted with permission from ACS Publications.

generic problem minimize/maximize Φ subject to Model equations Constraints

(10.14)

10.3 Multidimensional Population Balance Modeling

where the objective function Φ generally depends on the time (for batch systems often the end-time only), the state of the system (e.g. density function and its moments or nucleation/growth rates), and the inputs (temperature, antisolvent addition rate, etc.), as indicated also in Figure 10.2. Further, the model equations (e.g. Eqs. (10.7a) and (10.8b)) deﬁne the dynamics of the system, while constraints are set to make sure the solution remains within a physically and potentially economically sensible domain (feasible cooling rates, limited supersaturation, etc.). The mathematical problem stated in Eq. (10.14) is extremely diﬃcult because of its nonlinearity and nonconvexity, which allows for the existence of many local extrema. Consequently, there is no single pathway that guarantees successful convergence to an optimum, nor is there a simple way of demonstrating in general global optimality of an already found solution; diﬀerent authors have hence used diﬀerent numerical methods to optimize Eq. (10.14) with no single strategy showing clear superiority. Regardless, the optimization of crystallization processes can yield insights that are well worth the additional eﬀort. Sheikholeslamzadeh and Rohani [54] conducted an investigation of the optimal control policy for the polymorphic transformation of l-glutamic acid based on kinetics identiﬁed using the procedure outlined in Section 10.2.2. In another study, Lindenberg et al. [55] performed multiobjective optimization to improve process time and ﬁne fraction for the combined cooling and antisolvent crystallization of aspirin in an ethanol–water mixture. By allowing temperature and antisolvent fraction to change simultaneously, the reachable set of possible outcomes is expected to be signiﬁcantly larger [56]. Speciﬁcally, the following objective function was used: ] [ tp (10.15) Φ= tp ∫0 J dt with the ﬁrst element of Φ referring to the total process time and the second row referring to the number of new crystals formed during the process. The solubility, nucleation, and growth kinetics were identiﬁed beforehand as function of T, S, and antisolvent concentration. In the case of multiobjective optimization, the objective function Φ is not scalar but rather a vector-valued function, whose elements are to be optimized simultaneously. This leads to a set of so-called Pareto optimal solutions, for which none of the objectives can be improved without degradation of another; an example of such a Pareto front for the above work is shown in Figure 10.6. Focusing on one point within the Pareto set, the authors could demonstrate the superiority of the resulting cooling and antisolvent proﬁle as compared to two alternative strategies (“cooling ﬁrst” and “antisolvent ﬁrst”; cf. Figure 10.7), highlighting that the overall parameter estimation and process optimization strategy was successful.

10.3 Multidimensional Population Balance Modeling Although one-dimensional population balance models have served researchers well in the description of many systems, it is widely recognized that in many cases, the properties of the solid are not well characterized by a single descriptor. Particularly, this is the case for systems where dynamic impurity incorporation and

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1e+11 T (°C) or Q (g min–1)

1

1e+10

2 1e+9 Number of nuclei (m–3)

298

1e+8

30 Temperature T 20

10

Flow rate Q

1e+7 0

1e+6

0

500

1000

1500

2000

Time (s)

1e+5 3

1e+4 1e+3 1e+2 1e+1 1200

1400

1600 Process time (s)

1800

2000

Figure 10.6 Pareto optimal set of the two-objective optimization problem treated in [55] (solid line). The dashed line is obtained with constant antisolvent addition and cooling rate (see inset for operating policies). The region below the Pareto set is not feasible and the set is limited at low processing times because of the constraints on the maximum cooling rate. The empty circles represent diﬀerent process alternatives shown in detail in Figure 10.7: antisolvent addition ﬁrst, then cooling (case 1) or the reverse (case 2). The ﬁlled circle is a Pareto optimal point that was experimentally implemented (case 3). Source: Lindenberg et al. 2009 [55]. Reprinted with permission from ACS Publications.

evolving crystal shapes are observed. Indeed, in order to capture crystal shape or impurity content in particles, one requires additional internal states in the model. The resulting, generalized form of the PBE with n internal states, e.g. for the case of a well-mixed batch reactor, is given by ∑ 𝜕[Gi (x, S) f (t, x)] 𝜕 = B(t, x, S) − D(t, x, S) f (t, x) + 𝜕t 𝜕xi i=1 n

(10.16)

The main diﬀerence between the above equation and Eq. (10.7b) is the substitution of L with the more general n × 1 state vector x and the corresponding use of the summation operator. As in the 1D case, the mechanisms that aﬀect the population can be modeled through G, B, and D, although the former has become an n × 1 vector, too. In the important case where particle shape alone is of interest, the internal state vector corresponds to the vector of characteristic sizes, i.e. x = L, and Gi = dLi ∕dt, typically the normal growth rate of facet i. Although the larger number of internal states in Eq. (10.16) grants the ability to simulate processes in greater detail, the availability of techniques to accurately measure properties such as particle shape for a statistically signiﬁcant sample of particles – preferably in real time – is limited. Furthermore, even though multidimensional population balance models have been used in multiple instances for

10.3 Multidimensional Population Balance Modeling

1 3

400

300

26

45

wt fractio

60

n water (%

(a)

Te m

30

pe

30 28

°C

100

re (

34 32

)

200

rat u

Concentration (g kg–1)

2

)

6.0e+3

Mass density (1/m)

5.0e+3

3

4.0e+3 2 1

3.0e+3 2.0e+3 1.0e+3 0.0 0

(b)

200

400 600 Particle size (μm)

800

Figure 10.7 Diﬀerent combined cooling and antisolvent processes as investigated in [55]; (1) antisolvent ﬁrst, (2) cooling ﬁrst, (3) optimized process. (a) Process trajectories in the phase diagram, (b) particle size distribution obtained at the end of each process. The ﬁgures highlight that the nonoptimized processes result in an uncontrolled supersaturation proﬁle, which leads to undesirable particle size distributions, whereas the optimized process results in a unimodal particle size distribution of medium-sized particles. Source: Lindenberg et al. 2009 [55]. Reprinted with permission from ACS Publications.

parameter estimation and system characterization [57–59], multidimensional population balance modeling, and in particular appropriate and fast solution techniques, are an ongoing topic of research [60–65]. It is mostly for these two reasons that the use of multidimensional modeling has been very limited outside of academia, despite the fact that it represents an important research direction for the future of the application of population balances to crystallization processes.

299

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10 Crystallization Process Modeling

10.4 Conclusion Having provided the theoretical background as well as a broad outline of potential applications in this chapter, a brief discussion of the beneﬁts and drawbacks of crystallization models together with an outlook is in order. Population balance modeling can be a powerful and versatile tool that allows a deep and quantitative understanding of crystallization processes. However, this insight typically comes at the cost of a time- and labor-intensive examination of individual systems; with guidelines for transferability of the lessons learnt being rarely investigated in detail. Similarly, issues of model distinguishability and an incomplete understanding of statistics on the side of experimenters lead to parameterized models whose predictive capabilities outside of an often narrow operating region may be unsatisfactory. All these problems are being compounded by the fact that real processes often deal with complex mixtures with signiﬁcant batch-to-batch variations. Consequently, population balance models have not yet met with widespread acceptance in industry. Nevertheless, we believe that a turning point has been reached for several reasons. First, the presence of a mathematical framework intrinsically provides a structure that facilitates systematic analysis and understanding of the process. This stands in contrast with a more qualitative understanding, which lacks organization and is more prone to misinterpreting or completely missing important interactions. Undoubtedly, this approach brings with it a larger dependency on the know-how and experience of the person evaluating the results and varying interpretations between diﬀerent experts are hence to be expected. Second, with growing availability of fast computational methods and software tools, accurate solutions to the complex set of equations presented here become more and more accessible to nonmodelers. This frees up time that can be used for devising shorter and more statistically robust experimental plans. Third, once a satisfactory description of a process has been established, process models possess crucial advantages over experiments: simulations can be obtained at virtually no cost and process models can be easily integrated into higher order hierarchies. This means that novel ideas or process designs can be tested quickly and without great ﬁnancial investment, thus allowing to explore a much larger set of alternatives than can be done in a laboratory or pilot scale. Crystallization processes are determined by the behavior of myriads of solid particles interacting with at least one ﬂuid phase and with each other. Although studies on single particles, such as studies on growth mechanisms, are necessary and important to gain fundamental insight, a single crystal does not make a crystallizer. To believe that this is suﬃcient for an understanding of the entire process is to fool oneself, as the variability in the history of particulates must not be neglected. Population balance modeling represents a scientiﬁc and mathematically sound pathway of dealing with these properties while providing suﬃcient ﬂexibility to deal with problems of varying complexity. Thus, it remains an indispensable instrument for those seeking to further improve or develop crystallization technology.

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turbulent ﬂow: part I. Chem. Eng. Res. Des. 67: 301–307. 37 Wójcik, J. and Jones, A. (1997). Experimental investigation into dynamics

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and stability of continuous MSMPR agglomerative precipitation of CaCO3 crystals. Chem. Eng. Res. Des. 75: 113–118. Collier, A.P. and Hounslow, M.J. (1999). Growth and aggregation rates for calcite and calcium oxalate monohydrate. AIChE J. 45: 2298–2305. Iggland, M. and Mazzotti, M. (2011). A population balance model for chiral resolution via Viedma ripening. Cryst. Growth Des. 11: 4611–4622. Tavare, N.S. and Patwardhan, A.V. (1992). Agglomeration in a continuous MSMPR crystallizer. AIChE J. 38: 377–384. Ilievski, D. and White, E.T. (1994). Agglomeration during precipitation: agglomeration mechanism identiﬁcation for Al(OH)3 crystals in stirred caustic aluminate solutions. Chem. Eng. Sci. 49: 3227–3239. Zauner, R. and Jones, A. (2000). Determination of nucleation, growth, agglomeration and disruption kinetics from experimental precipitation data: the calcium oxalate system. Chem. Eng. Sci. 55: 4219–4232. Ros, F., Guillaume, S., Rabatel, G., and Sevila, F. (1995). Recognition of overlapping particles in granular product images using statistics and neural networks. Food Control 6: 37–43. Alander, E.M., Uusi-Penttila, M.S., and Rasmuson, Å.C. (2003). Characterization of paracetamol agglomerates by image analysis and strength measurement. Powder Technol. 130: 298–306. Faria, N., Pons, M.N., Feyo de Azevedo, S. et al. (2003). Quantiﬁcation of the morphology of sucrose crystals by image analysis. Powder Technol. 133: 54–67. Terdenge, L.-M., Heisel, S., Schembecker, G., and Wohlgemuth, K. (2015). Agglomeration degree distribution as quality criterion to evaluate crystalline products. Chem. Eng. Sci. 133: 157–169. Ochsenbein, D.R., Schorsch, S., Vetter, T. et al. (2015). Agglomeration of needle-like crystals in suspension: I. Measurements. Cryst. Growth Des. 15: 1923–1933. Griﬃn, D.J., Grover, M.A., Kawajiri, Y., and Rousseau, R.W. (2015). Mass-count plots for crystal size control. Chem. Eng. Sci. 137: 338–351. Saleemi, A.N., Rielly, C.D., and Nagy, Z.K. (2012). Comparative investigation of supersaturation and automated direct nucleation control of crystal size distributions using ATR-UV/vis spectroscopy and FBRM. Cryst. Growth Des. 12: 1792–1807. Abu Bakar, M.R., Nagy, Z., Saleemi, A.N., and Rielly, C.D. (2009). The impact of direct nucleation control on crystal size distribution in pharmaceutical crystallization processes. Cryst. Growth Des. 9: 1378–1384. Braatz, R. (2002). Advanced control of crystallization processes. Annu. Rev. Control 26: 87–99. Nagy, Z.K. and Braatz, R.D. (2012). Advances and new directions in crystallization control. Annu. Rev. Chem. Biomol. Eng. 3: 55–75.

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53 Nagy, Z.K., Fevotte, G., Kramer, H., and Levente, S.L. (2013). Recent advances

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11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective Andrei A. Zlota The Zlota Company, LLC, 15 Fairbanks Rd., Sharon, MA 02067-2858, USA

11.1 Introduction Crystallization process scale-up remains to be one of the more signiﬁcant challenges for process scientists. For this review, process scale-up refers to the technology transfer and execution of a process at a scale by approximately one order of magnitude larger than the previous experimentation scale, with a focus on the execution of the process in a pilot or in a manufacturing plant. There are several reasons for the diﬃculty of crystallization process scale-up, including the stochastic nature of nucleation and the signiﬁcant impact the equipment has on crystallization process results. The crystallization equipment addressed herein is the actual crystallizer; however, ﬁltration or centrifugation, cake wash, and drying are also operations that aﬀect active pharmaceutical ingredient (API) quality attributes such as particle size, particle size distribution (PSD), and chemical and optical purity. Because of such complexity, no comprehensive, ﬁrst-principles-based theory is available for all APIs to guide in the development of a robust crystallization process. The operating conditions in the plant are ﬁrst deﬁned based on the process understanding developed at small scale. Scale-up success can be deﬁned in two stages: “right the ﬁrst time,” and later passing speciﬁcations in the plant. Although luck and/or a forgiving process could be invoked for a “one-time” success, long-term robustness is based on thorough process understanding. Because of the very large number of projects that a process R&D group works on, management must decide, on a case-by-case basis, how much to invest in the development of an API crystallization process at a given time. The traditional approach to process development could perhaps be used in the early stages of a project, whereas a systematic, quality by design (QbD) [1]-based methodology is best suited for a project in an advanced stage. Companies who are already knowledgeable in the art and science of QbD are best positioned to allocate resources meaningfully. This short review is structured based on the QbD approach to process development.

Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development, First Edition. Edited by Rolf Hilﬁker and Markus von Raumer. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective

11.2 API Critical Quality Attributes (CQAs) We begin with the end in mind: the API critical quality attributes (CQAs). Polymorph is a CQA preferably known from the very beginning of crystallization process development. Occasionally, “late appearing polymorphs” complicate the process development [2]. In addition, we will know the other CQAs such as chemical and optical purity and particle size. Processability is a quality attribute that is deﬁned on a case-by-case basis. For example, it is desirable that the API ﬂows well, does not stick, and does not easily get electrostatically charged. With respect to polymorphs, we must know about the existence of other forms, their thermodynamic relationship, as well as about the kinetics of the transformation of one form into another (including solvent dependence). The Drug Product Development group informs the Drug Substance Process Development group about the desirable ranges for solid-state properties of the API, including particle size and PSD. “Perfect” spheres of 50 μm diameter, with a narrow size distribution, may be an enthusiastic starting point, with the common need to adjust it later to more realistic characteristics. It is quite surprising how broad of a PSD a robust formulation process can often tolerate. We must clarify that the solid-state properties of the API obtained at the bench are rarely completely reproduced upon scale-up. Other than polymorph that must be exactly as decided, most of the other properties, especially particle size and PSD, do change upon scale-up. Success will be measured by the capability of the crystallization process to produce API that passes speciﬁcations. Another part of the “end in mind” relates to the crystallizer to be used in the plant. Given the multipurpose nature of the reactors used in the pharmaceutical industry, and the busy schedules of the plants, chances are less that we will know in advance exactly which reactor will be used for a process; however, with some experience, and with some cooperation from the plant staﬀ, one can have a reasonable idea about a small number of options. The scale-up section below addresses this issue in some detail.

11.3 Statistical Design of Experiments (DoE) for Crystallization Process Development The QbD approach encourages us to make a clear distinction in the development process between scale-independent and scale-dependent process parameters. Because the processes we develop are multivariate, multivariate analysis, such as statistical design of experiments (DoE), is a more appropriate experimental methodology than one-variable-at-a-time investigations. It is preferred to ﬁrst deﬁne a small-scale design space1 using only scale-independent parameters. In order to accomplish this, we start with a team brainstorming eﬀort to generate an exhaustive list of all the process parameters impacting the API CQAs. Such lists tend to be relatively long, perhaps 20–30 parameters. The next step will be to execute a screening statistical DoE 1 Design Space is deﬁned as “the multidimensional combination (and interaction) of input variables and process parameters that has been demonstrated to provide quality assurance.”

11.3 Statistical Design of Experiments (DoE) for Crystallization Process Development

matrix to determine the most statistically signiﬁcant parameters impacting the API CQAs. To keep the screening DoE matrix at a practical size, we will ﬁrst need to prioritize the brainstormed list and select a suitable number (dictated by the resources available) of parameters to be included in the screening DoE study. This ranking step also contributes to the preliminary risk analysis. Several methods can be used to rank the process parameters, with Kepner-TregoeTM and FMEA (failure mode and eﬀects analysis) being among the most popular. Although FMEA tends to be more familiar to process scientists from hazards analysis, Kepner-TregoeTM [3] tends to be faster. As a result of this preliminary risk analysis, a subset of the brainstormed parameter list is included in the screening DoE investigation. We must clarify that parameter ranking, although systematic and executed by a team of process scientists, does have a subjective component. The ensuing DoE experimentation will conﬁrm the validity of the ranking or, occasionally, it will show that a certain process parameter was wrongly excluded from the screening study. Frequently used types of DoE-screening matrixes are fractional and full factorial designs, with occasional use of more aggressive designs such as Plackett-Burman [4]. The statistically signiﬁcant parameters identiﬁed in the DoE screening study can then be included in an optimization or RSM (response surface methodology) study in order to develop a small-scale design space. A separate set of experiments, described in more detail below, aims at the understanding of the equipment impact on process results. During such scale-up investigations, we attempt to understand the controlling mechanism for mixing and identify a scale-up factor.2 With the rare exception of mixing insensitive crystallizations, a complete process model includes both scale-independent and scale-dependent factors. 11.3.1 Example: DoE Methodology to Develop a Robust Crystallization Process, a Case of an API Developed as a Polymorphic Mixture GlaxoSmithKline (GSK) identiﬁed casopitant mesylate (Figure 11.1) as a potent NK1 antagonist with potential activity in several therapeutic areas. The manufacturing process was developed using a QbD approach. Late in the development process, it was understood that what was considered to be API pure form I was in fact a mixture of form I (major form) and form III of casopitant mesylate [5]. During the polymorph investigations, it was never possible to crystallize either pure form I or pure form III, with form I “appearing” to be the thermodynamic stable form (no complete conversion of one form into the other was ever observed). After careful evaluation of the clinical historical data, form III was deﬁned as an API CQA, and its amount in the API was capped at 27%, which was the amount of form III present in the API used in the preclinical and clinical studies. The process was a seeded reactive crystallization, which converted the casopitant-free base into the mesylate API. The process was initially conducted in ethyl acetate, and later in a mixture of ethyl acetate, acetone, and isooctane. 2 Scale-up factors are deﬁned as process parameters that are either maintained constant or changed in a controlled way upon scale-up.

307

308

11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective

Figure 11.1 Casopitant mesylate.

COCH3 N CH3SO3H

N

N F

O

N CF3

CF3 Casopitant mesylate 1

An extensive series of DoE matrixes were executed, ﬁrst at 50 ml scale and later at 2 L scale. The 2 L reactor used was a scaled-down geometrically similar version of the crystallizer used in manufacturing. After a risk assessment, a relatively long list of 10 parameters was included in a DoE “scoping study.”. The process parameters investigated in the scoping study are listed below (they were taken at two levels; a small number of center point replicates were also executed): • Casopitant impurity proﬁle (initially a categorical factor, it was later converted into a numerical one); impurities were spiked at controlled levels • Mixing conditions (described as power per volume, P/V); using chemical engineering calculations, the agitation speed and the ﬁll level in the reactor were determined in order to get to a certain P/V value • Ethyl acetate amount • Acetone amount • Isooctane amount • Seed quantity • Seed attributes; either a “parent” (representative API batch produced during development) or a mixture of the “parent” and micronized seed • Seeding temperature • Ageing time after seed addition • Isooctane addition time At the appropriate stage, the seed contained a controlled amount of form III. One of the challenges of this process was the diﬃculty to quantify form III; only transmission XRPD and solid-state NMR could be used to quantify form III in the API. Based on the learnings from the scoping study, several additional DoE investigations were conducted, one of which is discussed in more detail in this chapter. This follow-up matrix included six process parameters and ﬁve process results (Table 11.1); this was a 14 experiment fractional factorial study. All the parameters are listed with their natural variables, with the exception of the casopitant impurity proﬁle that is presented in coded ranges (−1, +1).

Table 11.1 One of the DoE matrixes used to develop the casopitant mesylate crystallization process.

Run

Casopitant impurity proﬁle (numerical)

1

−1

Ethyl acetate amount (vol)

Acetone amount (vol)

Seeding temperature (∘ C)

Isooctane amount (vol)

Impurity 3 (%a/a)

Impurity 11 (%a/a)

D10 (𝛍m)

D50 (𝛍m)

D90 (𝛍m)

3.5

3.5

50

0.5

0.24

0.41

4.1

17.5

2

0

2.5

4.5

40

3

1

0.21

0.23

3.5

13.4

48.3

3

1

3.5

3.5

30

2

1.5

0.42

0.08

1.6

5

12.3

1.5

5.5

30

4

Isooctane addition time (h)

4

0.5

2.9

11

61

4

1

0.29

0.08

5

−1

1.5

5.5

50

2

1.5

0.1

0.27

6.8

31.5

75.6

6

1

1.5

3.5

50

2

0.5

0.22

0.06

2.8

10.4

38.6

7

0

2.5

4.5

40

3

1

0.2

0.22

3.3

12.5

41.7 16.8

8

−1

1.5

3.5

30

4

1.5

0.28

0.4

1.9

6.3

9

−1

3.5

5.5

30

2

0.5

0.26

0.44

2.9

11.2

37.7

40.1

10

1

3.5

5.5

50

4

1.5

0.15

0.07

5.3

23.6

69

11

−1

1.5

5.5

50

2

0.5

0.14

0.31

6.5

32

79

12

−1

1.5

3.5

50

2

1.5

0.16

0.29

4

15.6

52

13

−1

1.5

3.5

30

4

0.5

0.29

0.41

1.9

6.4

17

14

−1

1.5

5.5

30

4

1.5

0.23

0.4

3.8

15.8

Source: Cimarosti et al. 2010 [5]. Reproduced with permission of ACS Publications.

53.4

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11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective

The parameters that had been investigated in prior DoEs and were not included in the matrix above were ﬁxed at the center points of the ranges employed in the scoping study. The study was a “combination” DoE, where both scale-independent and scale-dependent factors were included. From scale-up investigations, it was determined that the scale-up factor for this crystallization was power/volume. Using chemical engineering models, the various mixing conditions, described by certain power/volume values, were obtained using calculated agitation conditions (agitator type, agitation rate, baﬄes, and reactor ﬁll level). Because the mixing conditions associated with the “rpm” entity will depend on several factors, including the type and size of the agitator, “revolutions per minute” (rpm) is not a scalable factor, and the use of agitation speed (rpm) as a factor in a DoE matrix is not recommended. There are two possible objectives for such fractional factorial studies: screening the experimental space and robustness assessment. In a fractional factorial matrix, parameters are taken only at two levels (notwithstanding the center point experiments) and therefore cannot lead to predictive models, and thus to a design space. In this case, the fractional factorial study was considered an additional screening of the experimental space, aimed at establishing the statistical signiﬁcant factors impacting the crystallization process results. Modern DoE software platforms include several tools that allow us to determine the statistical signiﬁcant factors.3 For example, in Design Expert [6], from the half normal probability plot (Figure 11.2), we understand that for the response Impurity-11, the impurity proﬁle (factor A), temperature (factor D), and the amount of ethyl acetate (factor B) mostly inﬂuence the amount of impurity-11 produced. A chemical interpretation supports this ﬁnding. An identical list of inﬂuential factors is obtained with other software platforms. The model used by Design-Expert to establish the sequence described above is a linear model exhibiting an excellent R2 adjusted = 0.96. Other statistical parameters calculated indicate that the model used is statistically signiﬁcant, albeit without predictive power as discussed above. Predictive models are preferably quadratic, best with factors varied at ﬁve levels. In each DoE software platform, there are several visualization tools that assist the user in interpreting the statistical analysis. For example, with Fusion PRO [7], for the D90 particle size response (for which the desired range is 15–60 μm), we learn from the bar graph in Figure 11.3 that seeding temperature is the most statistically signiﬁcant factor for the D90 response (as it is for the D10 and for the D50 responses as well). In the course of typical QbD implementation, a screening investigation is followed by an optimization (RSM) study that allows the development of a quadratic, predictive model, and of a design space. In such a DoE matrix, we incorporate the statistically signiﬁcant factors identiﬁed in the screening study. The size of RSM matrixes is very sensitive to the number of factors included; for example, three factors require at least 15 experiments, whereas four factors require at least a 27 experiment matrix. The inclusion of a fourth factor must be

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3 We also executed the analysis of the data in Ref. [5], and present it herein.

11.3 Statistical Design of Experiments (DoE) for Crystallization Process Development

Half-normal plot

Half-normal % probability

99

A

95 90

D

80

Error estimates Shapiro–Wilk test W-value = 0.852 p-value = 0.100 A: Impurity p. B: EtOAc C: CH3COCH3 D: T E: iC8 F: iC8 add time

B

70 50 30 20 10 0

Positive effects Negative effects

0.00

0.08

0.15 |Standardized effect|

0.23

0.31

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Figure 11.2 Half normal probability plot (Design-Expert ) showing that the impurity proﬁle (A), seed temperature (D), and the amount of ethyl acetate (B) are statistically signiﬁcant factors for Impurity-11 response, with the impurity proﬁle (A) the most statistically signiﬁcant. Note the negative eﬀect for A and for D, and the positive eﬀect of B.

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 D

C

E

A

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A×C

A×D

Figure 11.3 Model term pareto chart (Fusion PRO ) indicating that seeding temperature (factor D) and the amount of acetone (factor C) are the most statistically signiﬁcant factors for the D90 response. The associated coded variable model (R2 adjusted = 0.98) is D90 = 44.4–4.9 × A + 11.9 × C + 17.4 × D + 5.6 × E − 3.5 (A × C) − 2.9 (A × D). A = free base impurity proﬁle, B = the amount of ethyl acetate.

311

11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective

carefully justiﬁed, especially if such experiments are conducted at the preferred 2 L scale. In this speciﬁc case, it is conceivable that an RSM study including factors A (casopitant-free base impurity proﬁle), D (seeding temperature), and C (amount of acetone in the crystallization solvent) would be an eﬀective approach to develop a scale-independent process model. If based on scale-up investigation, power/volume is a scale-up factor for all the API CQAs, a process model including power/volume needs to be developed. Alternatively, mesomixing time could be evaluated as a scale-up factor, incorporating both mixing conditions as well as the isooctane addition time. Such predictive models are then veriﬁed experimentally, preferably ﬁrst at the scale at which the experiments used to generate the model were executed and then at the next experimental scale, and adjusted as needed. Once veriﬁed, an RSM model can be used to deﬁne a design space. A “sweet” space (in seeding temperature, impurity proﬁle coordinates) where the crystallized API-passing speciﬁcations can be obtained from the preliminary optimization of the model generated by fractional factorial study discussed above is shown in Figure 11.4; the graph shown here is meant to be an example of DoE software visualization capabilities. The design space could be deﬁned, for 50

48

D90: 60 D10: 5

46

44

42

T (°C)

312

40

38

36

Imp-11: 0.3 D50: 13 Imp-3: 0.18

34

32 D90: 30 30 –1.0 –0.9 –0.8 –0.7 –0.6 –0.5 –0.4 –0.3 –0.2 –0.1 –0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Impurity profile (%)

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Figure 11.4 Preliminary sweet space (Fusion PRO ) for the casopitant mesylate crystallization process (the white area); colored spaces are failure zones for the various process results indicated; failure edges are listed with the associated speciﬁcation limit.

11.3 Statistical Design of Experiments (DoE) for Crystallization Process Development

example, as a rectangle inside the white area of the graph (“sweet spot”); failure edges for the various process results are indicated in the graph, with process results of failure zones color coded. The optimization criteria used in the calculation were: Impurity-3 NMT 0.18%, Impurity-11 NMT 0.30%, D10 = 1–5 μm, D50 = 13–45 μm, and D90 = 30–60 μm (the 30 μm low limit was selected so that it appears on the graph; the actual low limit acceptable for D90 is 15 μm). The process parameters not displayed in the two-dimensional graph in Figure 11.4 were ﬁxed as follows: ethyl acetate amount 1.5 volumes, acetone 5.5 volumes, isooctane 2.1 volumes, and isooctane addition time 1.5 h. The “sweet space” identiﬁed from this calculation is relatively broad, and an RSM study is likely to prove excellent process robustness (good process capability). Using detailed chemistry information (not discussed in the reference), the failure zone identiﬁed at low impurities in the casopitant-free base can probably be explained, however counterintuitive it may appear. An example of a design space and of a control space is shown in Figure 11.5; this is also for a crystallization process where the CQA is the D90 of the PSD [8]. The coordinates are tip velocity of the impeller and temperature. The design space is well nested in the sweet space, and the control space presented is a subspace of the design space. The control space described is one of the several possible control spaces; movement inside the design space is not expected to trigger regulatory activity; however, exceptions have been reported. Note that in certain manufacturing plants, temperature could become a critical process parameter. Using Monte Carlo simulations (available in several DoE platforms, or as separate software), we can quantify the risk to be out of speciﬁcations and estimate the process capability indexes. 2.6 2.4

D90: 13

Design space 2.2

v (tip) (m s–1)

2.0 1.8 1.6

Design space

Control space

v (tip) 1.4

1.1 – 2.2 m s–1

T 13 – 26 Add time 8 – 12

1.2

°C min

1.0

Control space

0.8

D90: 5

v (tip)

1.4 – 1.9 m s–1 T 15 – 25 °C Add time 8 – 12 min

0.6 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

T (°C)

Figure 11.5 An example of a design space (green rectangle) and of a control space (blue rectangle) for a crystallization process; the CQA is D90 of the particle size (with a speciﬁcation between 5 and 13 μm).

313

314

11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective

11.4 Process Analytical Technology (PAT) for Polymorph Control An important part of the FDA QbD initiative was the PAT guidance of 2004 [9], and several reviews were published about PAT implementation, including crystallization monitoring and polymorphic transformations [10]. Because of the unavailability of suﬃcient fundamental science needed to develop crystallization processes, calculations, experimentation, and process measurements are very valuable tools for crystallization process development. Because of the signiﬁcant amount of information collected and analyzed, online measurements are considered to be more informative than end-of-the-process analytics, having a stronger capability to prove process robustness. For complex crystallization processes, several sensors are often used to monitor the process and possible polymorphic transformations, with some probes focused on the solid phases and others on the liquid phases. A typical example of the outcome of such monitoring is presented in Figure 11.6 where both the FBRM (Focused Beam Reﬂectance Method) and the PVM (Particle Vision Measurement)

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(a)

(c)

(b)

(d)

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Figure 11.6 Monitoring of a crystallization process with the FBRM and PVM probes: (a) trends for the populations of particles of various sizes (counts/s); (b) chord length distribution; (c) PVM image; (d) values for the various statistics calculated by the FBRM . Source: Courtesy of Mettler-Toledo Autochem.

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11.4 Process Analytical Technology (PAT) for Polymorph Control

probes are used.4 The evolution of the chord length distribution (CLD), a surrogate for PSD, generated by the FBRM probe, together with the pictures taken by the PVM probe provide valuable insight into the crystallization process. PAT is useful for both the development of process understanding (preferably at small scale) and for process control in the plant. Numerous examples for the use of the FBRM probe for feedback control have been published, demonstrating the use of PAT for robust process development [11]. Raman spectroscopy has proven very valuable for the monitoring of polymorphic transformations [12]. The calculation of PSD from the CLD measured in situ is challenging because of the assumptions needed in using the necessary algorithms [13]. Crystal shape, solid, and liquid optical properties impact the FBRM measurement. Nevertheless, the qualitative and semiquantitative information provided by FBRM measurements is very valuable for crystallization process development. A novel approach (quality by control, QbC) has been proposed recently, recommending a “design via control” strategy, based on the use of feedback control to determine operating strategies during the crystallization [14]. Two model-free methods were developed for particle size control: automated direct nucleation control (ANDC), which uses the FBRM probe, and supersaturation control (SSC) using UV or IR to measure solute concentration in real time. Feedback control using Fourier transform infrared (FTIR) was one of the tools employed in the development of a robust crystallization process consistently producing the stable polymorph of the desired particle size of a Merck API [15]. PAT data collection methodology is very important; theoretically, a PAT sensor can be used with any lab ﬂask or vial, as well as with any plant reactor. However, because of the heterogeneous nature of crystallization slurries, the mixing and the thermal conditions of the media aﬀect the value of the information captured by the sensor. The ability to accurately describe and control the hydrodynamic and thermal conditions in the reactor is essential for the generation of valuable PAT data. A detailed discussion regarding the theory of sampling in the PAT context was published [16]. Moreover, the position of the sensor in the reactor, especially one investigating the solid phase, such as the FBRM , is very important, and the relevance of the FBRM probe position in a large plant reactor is even of greater signiﬁcance. The use of recirculating loops was found to be a practical solution to the challenge of probe position. Suitable studies at the small scale are needed to properly design such a recirculating loop, and the associated pump that transfers the slurry from the reactor to the ﬂow-through cell where the probe is placed, and back to the reactor. An elegant example of the use of an FBRM together with a Raman probe to control the polymorph and particle size of a Bristol Myers Squibb API was reported [17]. This API had to be produced in its hemihydrate form, when an anhydrous and several solvates were also possible forms of the API. The use of

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4 With thanks to Dr. Dominique Hebrault, Mettler-Toledo Autochem, www.mt.com.

315

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11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective

a recirculating loop is discussed, together with a rotor–stator wet milling device that allowed the avoidance of dry milling.

11.5 Mixing and Scale-Up Investigations 11.5.1

Scale-Up Factors, Mass Transfer

Nucleation, growth, and agglomeration are all dependent on supersaturation, which, in turn, through concentration and temperature gradients, depends on mixing. Suitable mixing conditions are part of the control strategy to obtain API-passing speciﬁcations, that is, obtaining a certain crystal form, of desired purity, average size, and size distribution. As discussed below, mixing optimization for a crystallization process is a complex process, often with conﬂicting objectives. For polymorphs produced using antisolvent crystallizations, in addition to the impact that mixing has on crystallization processes, in general, both the addition rate and the turbulence at the point of addition can impact polymorph control [18] (see also the mesomixing time discussion below). It is worth reiterating that any generalization regarding crystallization process development is diﬃcult because such processes are compound and solvent speciﬁc. The objective of scale-up investigations is to quantify the impact of the equipment on process results. An important aspect of process robustness and its associated control strategy is the understanding of the process parameter changes needed for quality assurance when a process is transferred to a diﬀerent site or to a diﬀerent reactor (managing the variability). Ideally, such scale-up experiments are conducted in equipment which is similar to the plant equipment. Although full similarity is impossible, a reasonable compromise could be geometric similarity, however, in many instances because of the use of multipurpose plant reactors, even “just” geometric similarity is not possible. As a result, chemical engineering calculations are needed in order to bridge (scale-up and scale-down) between small- and large-scale reactors. The VisiMix software [19] is a convenient powerful software program allowing for the calculation of over 180 mixing process parameters. Such calculations allow for the design of meaningful crystallization experiments aimed at understanding the controlling mixing mechanism; they also allow the design of scale-down experiments, by determining relevant mixing conditions in the small reactor mimicking the conditions in the plant crystallizer. An example of the type of input data necessary to execute such mixing and scale-up calculations is presented in Figure 11.7. For large (plant) reactors, many process parameters exhibit signiﬁcantly diﬀerent values in diﬀerent places in the reactor. Some engineering models allow for the calculation of the average of such process parameters, as well as the unique values in certain positions in the reactor (such as at the tip of the impeller, or behind the baﬄes). The ratio of the average value of a mixing process parameter to that in a unique place depends on several factors, including the reactor geometry.

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11.5 Mixing and Scale-Up Investigations

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Figure 11.7 Selected values for input for VisiMix calculations for the case of a Büchi kilo-lab reactor, 72% full, operating at 52 rpm, handling a heterogeneous solid–liquid system.

Both mass and heat transfer phenomena depend on the ﬂow conditions in the reactor. API plant crystallizers operate almost without exception in full turbulence, characterized by Reynolds numbers larger than 10 000.5 Occasionally, the ﬂow conditions in bench reactors can be in the transitional regime (between laminar and turbulent, exhibiting Reynolds numbers in the 1 000–10 000 range) and scaling-up a process from transition to fully turbulent regime can be challenging. Systematic process scale-up requires, among others, the identiﬁcation of scale-up factors, process parameters that are either kept constant, or changed in a controlled way upon scale-up. Ideally, such scale-up factors should be dimensionless, and such dimensionless factors are used in the scale-up of certain particulate processes, such as blending. For most synthetic chemical and crystallization processes, scale-up factors with dimensions are used, such 5 The Reynolds number (Re) is a dimensionless number, describing the ratio of inertial to viscous forces; in general, it is calculated as Re = (𝜌 × v × L)/𝜇, where 𝜌 = density (kg m−3 ), v-velocity (m s−1 ), L = characteristic linear dimension (m). For stirred tanks, modiﬁed formulas are used; VisiMix calculates a Re (impeller) based on the impeller diameter, and a Re (ﬂow) based on the tank diameter.

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317

318

11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective

as power/volume, impeller tip velocity, turbulent shear rate, micromixing time, and others. Identiﬁcation of scale-up factors can be accomplished ﬁrst by executing a relatively small number of experiments at the bench, under variegated conditions, each of which being characterized with mixing and scale-up calculations such as those provided by VisiMix . The second step is a search of a correlation between CQAs and such calculated mixing process parameters. When such a scale-up factor candidate is found, experimentation at larger scale (kilo-lab, small pilot plant) is necessary to conﬁrm this hypothesis and adjust the model, as needed. We must keep in mind that such mixing calculations are semiempirical, being based on both fundamental principles and empirical models. Therefore, the absolute value of such calculations is rather limited and must be interpreted with caution. However, the relative values of these calculations are of considerable practical value; when using the same models to calculate reactors at diﬀerent scales, the parameters calculated can be used for design and troubleshooting purposes.

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11.5.2

Scale-Up Factors in Crystallization Processes

Scale-up investigations must start with the assessment of the lowest meaningful scale and mode of experimentation necessary. A detailed discussion of these topics is beyond the scope of this review; however, one comment about the mixing method is in place. Often times, the ﬁrst crystallization experiments are conducted at small scale using magnetic stirring, followed by experimentation in larger crystallizers employing overhead stirring. We developed suﬃcient industry experience to know that when changing the mixing method from magnetic stir bars to overhead stirring, there are possible changes in the crystallization process outcome. For example, the l-glutamic metastable polymorph transformation to the stable form can be up to 1 order of magnitude slower when scaling up from 50 ml (magnetic stirring) to 1000 ml (overhead mixing) [20]. A reasonable explanation for this observation is the grinding eﬀect that stir bars have, leading to increased seed surface area. Impeller tip velocity was found to be a scale-up factor in a crystallization process developed by the scientists and engineers at Merck [21]. The graph in Figure 11.8 shows the correlation between mean particle size in a crystallization process and impeller tip velocity, across several scales, including manufacturing, and when using diﬀerent types of agitators. The graph in Figure 11.9 presents the relationship between impeller tip velocity and agitation rate calculated with VisiMix for three diﬀerent reactors and agitators. The line drawn at 2.0 m s−1 shows an example of a mixing scenario characterized by the same impeller tip velocity at all three scales considered. Crystallization processes are complex, and describing them with only one mixing process parameter, however important, is not realistic. As a result, even when we do ﬁnd such scale-up factors, we are very careful about other parameters describing mixing in the reactor. Table 11.2 shows two such additional mixing process parameters characterizing the heterogeneous liquid–solid system analyzed, with the reactors at the three scales operating at the same tip velocity of the

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11.5 Mixing and Scale-Up Investigations

Mean particle size dependency on impeller tip velocity several types of agitators, at several scales 150 A-310

140 Mean particle size (μm)

130 Rushton 120 A-310

110

A-200

Rushton

100

Factory

A-200

90 80 70 60 50 0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Impeller tip velocity (m s–1)

Figure 11.8 Linear correlation between mean particle size and crystallizer impeller tip velocity for several types of agitators and at several scales. Source: Based on Ref. [22]. 10

Tip velocity of the impeller (m s–1)

9 8 Plant 7 6 5 4 Kilo-Lab 3 Lab

2 1 0 0

50

100

150

200

250

300

350

400

450

500

Agitation rate (RPM) v (tip) = π × N × D, D = Agitator diameter, N = Agitation rate

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Figure 11.9 VisiMix calculated tip velocity of the impeller for the bench (RC1), kilo-lab (Büchi), and plant (Pfaudler) reactors. The graph shows that conditions can be designed to exhibit a certain impeller velocity (e.g. 2.0 m s−1 ) for each of the reactors.

550

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11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective

Table 11.2 Handling of the crystallization slurry in the reactors at three scales operated at a tip velocity of the impeller of 2.0 m s−1 . Tip velocity of the impeller (m s−1 )

Maximum degree of axial non-uniformity (%)

Time between two strong collisions (s)

Reactor

Scale (L)

Agitation rate (rpm)

Lab

2.0

500

2.0

16.0

46.0

Kilo-Lab

78.0

150

2.0

16.0

8.0

Plant

800.0

50

2.0

66.0

72.0

Complete suspension is not achieved in the plant reactor at 50 rpm.

impeller: the quality of the suspension (as described by the maximum degree of axial nonuniformity) and the estimate for the time between two strong collisions (during which much of the crystal growth occurs). The plant reactor operating at 50 rpm is unlikely to be capable to completely suspend the slurry, having solids settled at the bottom. Based on prior knowledge, and possibly additional experiments, the process development team may decide that the calculated conditions in the plant reactor for 2.0 m s−1 impeller tip velocity must be adjusted (by a small increase of the agitation speed) in order to improve the handling of the slurry and reduce the maximum degree of axial nonuniformity. The VisiMix calculated average power per mass for the same three reactors discussed above at the three scales is shown in Figure 11.10. As discussed for the tip velocity of the impeller, using power per mass calculations, we can identify conditions at each scale characterized by the same power per mass. Should the crystallization in the lab executed at 0.45 W kg−1 be successful, we could then verify the hypothesis that power per mass is indeed a scale-up factor by executing the crystallization in the kilo-lab under the same mixing conditions of 0.45 W kg−1 . If the API passes speciﬁcations, we could design operating conditions in the plant

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Power per mass, average (mW kg–1)

320

2500 Plant

2000

Kilo-Lab

1500 Lab 1000 500 0 50

100

150

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200

250 300 350 Agiation rate (RPM)

400

450

500

Figure 11.10 VisiMix calculated average power per mass for the bench (RC1), kilo-lab (Büchi), and plant (Pfaudler) reactors. The graph shows that conditions can be designed to exhibit a certain average power per mass (e.g. 0.5 W kg−1 ) for each of the reactors.

550

11.5 Mixing and Scale-Up Investigations

Table 11.3 Handling of the crystallization slurry in the reactors at three scales operated at an average power per mass of approximately 0.45 W kg−1 .

Reactor

Scale (L)

Agitation rate (rpm)

Power per mass, average (mW kg−1 )

Maximum degree of axial non-uniformity (%)

Time between two strong collisions (s)

Lab

2.0

450

0.43

18.3

51.5

Kilo-Lab

78.0

150

0.46

16.1

7.7

Plant

800.0

90

0.46

33.3

40.0

Complete suspension is not achieved in the plant reactor at 90 rpm (however, as expected, the maximum degree of axial nonuniformity is lower at 90 rpm than at 50 rpm as indicated in Table 11.2).

reactor (see Table 11.3), perhaps with the minor adjustment of a slight increase in the plant agitator speed. Turbulent shear rate average and local values (Γturbulent , 1 s−1 ) are calculated by VisiMix using Eq. (11.1) [22]:

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Γturbulent = (𝜀∕𝜈)1∕2

(11.1)

where 𝜀 is the turbulent energy dissipation (W kg or m s ) and 𝜈 is the kinematic viscosity (m2 s−1 ). Simpliﬁed correlations [23] might suggest that for Newtonian ﬂuids, the shear rate (𝛾) can be calculated using 𝛾 = K × N (Metzner–Otto relationship), where K is an impeller-dependent constant (5–40) and N is the agitation rate. This model counterintuitively implies that the turbulent shear rate is independent of the agitator diameter, and for a given agitator (K), for constant turbulent shear rate, one might scale-up at constant agitation rate, a rare occurrence. This model tends to work for a portion of the turbulent regime, but it does not apply in highly turbulent ﬂow. VisiMix calculates three values for the turbulent shear rate: maximum, near the baﬄes, and average. In some crystallization processes, we found that the average particle size was inversely proportional with the maximum value of the turbulent shear rate, and successful scale-up was achieved operating at constant turbulent shear rate (maximum); see Figure 11.11 for the maximum turbulent shear rate in diﬀerent reactors. As can be seen in Table 11.4, agitator diameter does have an impact on shear rate; perhaps more importantly, the distribution of shear is signiﬁcantly agitator dependent, with a unique shear rate distribution for the case of an anchor-frame agitator. From a practical perspective, this means that it is desirable to use the same type of agitator upon scale-up, and when this is not possible, to use such engineering calculations to design meaningful scale-down experiments in order to understand the impact on process results. Table 11.5 describes the assessment of the suspension handling in the plant reactor operated at the same maximum turbulent shear rate as the bench and the kilo-lab reactors; in this case, at 102 rpm, the maximum degree of axial nonuniformity lower than 30% is an indication of limited particle settling. −1

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11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective

16000 Plant

14000 Turbulent shear rate, max (1 s–1 )

322

Kilo-Lab 12000 10000 Lab 8000 6000 4000 2000 0 25

75

125

175

225

275

325

375

425

475

525

Agitation rate (RPM)

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Figure 11.11 VisiMix calculated turbulent shear rate (maximum value) for the Lab (RC1), Kilo-lab (Büchi), and plant (Pfaudler) reactors mentioned in the text. The graph shows that conditions can be designed to exhibit a certain maximum turbulent shear rate (e.g. 8100 1 s−1 ) for each of the reactors (for the datasets analyzed the trends are linear).

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Table 11.4 VisiMix calculated values for several turbulent shear rate values in a plant reactor containing a slurry, as discussed in the previous calculations (800 L Pfaudler, 80% full) with various agitators. Turbulent shear rate (1 s−1 ) Diameter (m)

Agitation rate (rpm)

Maximum (impeller blade)

Baﬄe

Bulk

RCI

0.762

100

7 820

3 420

356

RCI

0.762

50

2 770

1 190

126

Agitator type

RCI

0.381

100

3 810

587

90

Anchor-frame

0.762

100

6 500

11 400

1 370

Pitched Paddle

0.762

100

4 560

3 630

528

Propeller

0.762

100

2 610

2 110

445

RCI, Retreat curve impeller. In addition to agitator type and agitation rate, agitator diameter also impacts the shear rate. The anchor frame agitator exhibits a very diﬀerent shear rate distribution than all other agitators calculated (this is due to its geometry, which leads to a unique mixing environment in the narrow space between the agitator and the baﬄe).

11.5 Mixing and Scale-Up Investigations

Table 11.5 Handling of the crystallization slurry in the reactors at three scales operated at a maximum turbulent shear rate of approximately 8100 1 s−1 .

Reactor

Scale (L)

Agitation rate (rpm)

Turbulent shear rate, maximum (1 s−1 )

Maximum degree of axial non-uniformity (%)

Time between two strong collisions (s)

RC1

2.0

485

8070

16.9

47.8

Buchi

78.0

200

8100

11.9

5.8

Pfaudler

800.0

102

8060

28.7

35.3

Little particle settling is expected in the plant reactor at 102 rpm.

When an antisolvent is used in a crystallization process, other than solvent composition (which can be optimized using DoE), addition point and addition rate must be deﬁned. A key objective in the development of such processes is the minimization of sharp antisolvent concentration gradients. Mixing at the scale of the antisolvent plume exiting the feed pipe is termed “mesomixing” and its characteristic time, the mesomixing time (𝜏 s , s), can be estimated [24] using Eq. (11.2): 𝜏s = A × (Qa ∕𝜀 × N × Da )0.33

(11.2)

where A is a constant (∼1.60), Qa the addition rate (m3 s−1 ), 𝜀 the turbulent dissipation of energy (m2 s−3 ), N the agitation rate (revolutions per second, 1 s−1 ), and Da is the agitator diameter (m). Table 11.6 presents the mesomixing times calculated for the RC1 (Bench), Buchi (Kilo-Lab), and Pfaudler (Plant) reactors under conditions leading to the same mexomixing time for the three reactors. If diﬀerent addition points are used, near the tip of the impeller at the bench, and subsurface in the plant, the mesomixing times can be diﬀerent by a factor of approximately 5 (6.6 vs 32.7 ms, respectively). When planning a DoE, if addition rate is a factor to be included, it is recommended that mesomixing time is used as a variable (which reduces the number of Table 11.6 Mesomixing times calculated for the three reactors discussed, at conditions that exhibit the same mesomixing time, when reasonably analogous addition points are used across the three scales. Mesomixing time (ms) Reactor

Bench Kilo-Lab Plant

Agitation rate (rpm)

Addition point subsurfacea)

Near the impeller tipb)

40

330

33.8

6.6

80

130

32.8

8.0

400

100

32.7

6.9

Add. rate (ml min−1 )

a) Calculated using the average turbulent dissipation of energy. b) Calculated using the maximum turbulent dissipation of energy.

323

324

11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective

factors investigated compared to the option of using addition rate and agitation rate as factors). DoE in combination with mixing investigations were employed in developing process understanding for an antisolvent crystallization [25]. The factors included in the screening design were agitation rate, feed rate, axial position of the feed, and radial position of the feed. Agitation rate and feed rate were found to be the most statistically signiﬁcant factors, with the axial position more signiﬁcant than the radial position of the feed. A DoE optimization was conducted, including the agitation rate as a factor, as well as the media volume and a dimensionless parameter (NV /Q, N = agitation rate, V = media volume, Q = addition rate). The optimization study shows that the dimensionless parameter (NV /Q) is the most statistically signiﬁcant factor, and a predictive model including the three factors was developed. Although less detailed than the mesomixing time, the dimensionless factor (NV /Q) does include both agitation rate and addition rate in its deﬁnition. Computational ﬂuid dynamics (CFD) calculations were used to map the antisolvent concentration distribution in the various reactors used. 11.5.3

Mixing Impact on the Metastable Zone Width (MSZW)

Estimating the metastable zone width (MSZW) for a crystallization is important in the development of a robust crystallization process, both for robust operation and for developing a seeding strategy. Unfortunately, because of the stochastic nature of nucleation, there are no deterministic models for the calculation of the MSZW, and experimental measurements are necessary. Moreover, MSZW is sensitive to mixing, and therefore, it is expected that it will change upon scale-up. Generalizations regarding the change of MSZW during process scale-up are compound speciﬁc and therefore diﬃcult to make. A detailed study of the impact of mixing on the MSZW for the crystallization of the three region isomers of aminobenzoic acid in water was reported [26]. 11.5.4

Disappearing Polymorphs During Scale-Up

In spite of the extensive knowledge about polymorphs accumulated during the past two decades, polymorphs continue to “surprise” us [2]. Disappearing polymorphs have been reported, and often, the change of the impurities proﬁle is considered the reason for late-appearing polymorphs [27]. Unfortunately, there is no clear evidence that in such cases, a careful analysis of the engineering scale-up strategy was conducted to evaluate the possible contribution of mixing-related phenomena to the polymorphic behavior observed. 11.5.5

Polymorph Control Methods Based on Mixing

Special methods for polymorph control are being creatively designed; an example where slow mixing in an emulsion slows crystal nucleation and growth in an antisolvent crystallization, favoring the formation of the stable polymorph has been

11.5 Mixing and Scale-Up Investigations

reported [28]. An interesting dependence of the identity of the polymorph crystallized on agitation was observed at small scale (30 ml vials using magnetic stir bars) for m-hydroxybenzoic acid polymorphs [29]. 11.5.6

Heat Transfer

The most common method for desupersaturation is cooling, often practiced, for better process control, together with seeding. Crystallization textbooks discuss in detail the various cooling protocols: natural, linear, and cubic [30]; quadratic cooling proﬁles were also proposed [31]. Natural cooling practiced at constant jacket temperature is the easiest to implement in the plant, but the least capable to control the crystallization process, and the most scale sensitive. Linear cooling is a better choice; however, a cubic cooling proﬁle (Eq. (11.3)) is much more capable to control nucleation: Tt = T0 − (T0 − Tf ) (t∕𝜏)3

(11.3)

where T 0 is the initial temperature, T f the ﬁnal temperature, t the time, and 𝜏 is the cooling time. In Figure 11.12, a cubic cooling proﬁle is demonstrated for the range 80–20 ∘ C, in 6 hours, noting that in the ﬁrst two hours, the reactor temperature changes very little (2 ∘ C). The main advantage of this cooling approach, in combination with seeding, is achieving control over the nucleation process, preventing an uncontrolled precipitation, with a higher than desired population of ﬁnes. For the same considerations, cubic addition proﬁles are recommended for antisolvent crystallizations. In certain crystallization processes, such as chiral resolutions, fast cooling could be desirable [32]. However, we must keep in mind that on scale, because of the lower heat transfer area available per media volume, attaining fast (>1 K min−1 ) cooling rates can be

90.00 80.00 70.00 60.00

Temperature (°C)

50.00 40.00 30.00 20.00 10.00 0.00 0.00

1.00

2.00

3.00

4.00

Time (h)

5.00

6.00

7.00

Time (h) T (°C) 0.00 80.00 0.20 80.00 0.40 79.98 0.60 79.94 0.80 79.86 1.00 79.73 1.50 79.09 2.00 77.84 2.50 75.78 3.00 72.71 3.50 68.42 4.00 62.72 4.50 55.40 5.00 46.25 5.50 35.08 6.00 21.68 6.05 20.21

Figure 11.12 An example of a cubic cooling proﬁle, with the temperature varied from 80 to 20 ∘ C in six hours; note that the temperature is lowered in the ﬁrst two hours by only 2.1 ∘ C, whereas for a linear cooling rate, the temperature would be lowered by approximately 20 ∘ C in the same two hours.

325

326

11 Crystallization Process Scale-Up, a Quality by Design (QbD) Perspective

Table 11.7 Cooling rates that could be attained in an 800 L plant reactor, operated at T jacket = constant, and 110 rpm (using as heat transfer ﬂuid Syltherm HF at a ﬂow rate in the jacket of 20 gal/min). T jacket (o C) −1

Cooling rate (K min )

0

−20

−50

−73

0.10

0.25

0.45

0.65

110 rpm, Syltherm XLT, 20 GPM, 60–0 ∘ C; T

jacket

= constant.

challenging. Table 11.7 shows the cooling rate that could be achieved in a plant reactor (800 L, discussed above) operating at 110 rpm at various constant jacket temperatures. Notwithstanding the diﬃculty and high cost of operating the jacket at very low temperatures, we can see that even with the jacket temperature set at −73 ∘ C, we can achieve at most a cooling rate of only 0.65 K min−1 . Moreover, even for the relatively slower cooling rate of 0.50 K min−1 , the jacket temperature must be held at a signiﬁcantly lower temperature in the plant than that used for the bench reactor: −50 vs 0 o C, respectively. When the jacket temperature must be so low, we must carefully assess the possibility of the formation of undesired metastable forms at scale, forms that were not observed at the bench because of the less cold jacket employed at small scale. Furthermore, at such low jacket temperatures, encrustation could be observed, and media viscosity increase could impact the nucleation process.

11.6 Conclusions and Outlook In addition to the fundamental understanding of the polymorphs’ kinetics and thermodynamics, a holistic, systematic approach to crystallization process scale-up can lead to successful technology transfer and manufacturing of the desired API form within speciﬁcations. QbD was ﬁrst proposed by the regulators, but it is now becoming, because of its signiﬁcant business value, an important industry initiative. QbD is good development, and its tools have proven time and again to be very valuable for the development of robust crystallization process, with the capability of controlling the solid-state properties of the API. The more QbD is practiced, the more the scientiﬁc elements of crystallization process development are reinforced, minimizing the “touch of art” occasionally invoked with such a complex scientiﬁc activity.

References 1 (a) (2007). Pharmaceutical Quality for the 21st Century: a Risk-Based

Approach. Silver Spring, MD: Department of Health and Human Services, Food and Drug Administration, Center for Drug Evaluation and Research. (b) International Conference on Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use, ICH Harmonized Tripartite Guideline, Pharmaceutical Development, Q8(R2), Step 4, 2009,

References

2 3 4

5 6 7 8

9

10

11 12 13 14 15 16 17 18

19

the ﬁrst QbD ICH Guideline; ICH Q9 and ICH Q followed; (c) Development and Manufacture of Drug Substance, ICH Q11; (d) (2015). Advancement of Emerging Technology Applications to Modernize the pharmaceutical Manufacturing Base-Guidance for Industry. Silver Spring, MD: Department of Health and Human Services, Food and Drug Administration, Center for Drug Evaluation and Research. Bucar, D.K., Lancaster, R.W., and Bernstein, J. (2015). Angew. Chem. Int. Ed. 54, 6972 and references therein. Parker, J.S. and Moseley, J.D. (2008). Org. Process. Res. Dev. 12, 1060 and references therein. (a) Montgomery, D.C. (2012). Design and Analysis of Experiments, 8e. New York: Wiley. (b) Anderson, M.J. and Whitcomb, P.J. (2015). DoE Simpliﬁed, 3e. Boca Raton, FL: CRC Press. (c) Goupy, J. and Creighton, L. (2007). Introduction to Design of Experiments, 3e. Cary, NC: SAS Press Series. (d) Eriksson, L., Johansson, E., Kettaneh-Wold, N. et al. (2008). Design of Experiments, 3e. Umea, Sweden: Umetrics AB. Cimarosti, Z., Castagnoli, C., Rossetti, M. et al. (2010). Org. Process. Res. Dev. 14: 1337. Stat-Ease, Inc. Design-Expert v.8.0.7.1 (www.statease.com, now at version 10). S-Matrix Corp. Fusion PRO v.7.32.1 (www.smatrix.com, now at version 9). Case study discussed in: Zlota, A.A. (2007–2018). Practical Quality by Design (QbD) Methods for Modern Pharmaceutical Process R&D and Manufacturing, Course provided by The Zlota Co., LLC. (2004). PAT-A Framework for Innovative Pharmaceutical Development, Manufacturing, and Quality Assurance. Rockville, Maryland: U.S. Department of Health and Human Services, Food and Drug Administration, Center for Drug Evaluation and Research. (a) Chanda, A., Daly, A.M., Foley, D.A. et al. (2015). Org. Process. Res. Dev. 19 (1): 63. (b) Bordawekar, S., Chanda, A., Daly, A.M. et al. (2015). Org. Process. Res. Dev. 19 (9): 1174. (c) Simon, L.L., Pataki, H., Marosi, G. et al. (2015). Org. Process. Res. Dev. 19 (1): 3. Hermanto, M.W., Chow, P.S., and Tan, R.B.H. (2012). Ind. Eng. Chem. Res. 51 (42): 13773. Barrett, M., Hao, H., Maher, A. et al. (2011). Org. Process. Res. Dev. 15: 681. Hermanto, M.W., Chow, P.S., and Tan, R.B.H. (2010). Cryst. Growth Des. 10: 3668. Yang, Y., Song, L., and Nagy, Z.K. (2015). Cryst. Growth Des. 15: 5839. Cote, A., Zhou, G., and Stanik, M. (2009). Org. Process. Res. Dev. 13: 1276. Esbensen, K.H. and Paasch-Mortensen, P. (2010). Process Analytical Technology (ed. K.A. Bakeev), 37. Wiley. Lo, E., Mattas, E., Wei, C. et al. (2012). Org. Process. Res. Dev. 16: 102. (a) Qu, H., Louhi-Kultanen, M., Rantanene, J. et al. (2009). J. Cryst. Growth 311 (13): 3466. (b) Barrett, M., O’Grady, D., Casey, E. et al. (2011). Chem. Eng. Sci. 66: 2523. VisiMix . The turbulent module, v.12, www.visimix.com.

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20 Ferrari, E.S., Davey, R.J., Cross, W.I. et al. (2004). Cryst. Growth Des. 4 (5):

1061. 21 Andrews, A.T. (2003). (Merck), Presentation at the AIChE Annual Meeting,

San Francisco, CA, USA, November 16–21, 2003.

®

22 VisMix . Turbulent, User’s Guide, v.12. p. 89. 23 Hemrajani, R.R. and Tatterson, G.B. (2004). Mechanically stirred vessels. In:

24 25 26 27 28 29 30 31 32

Handbook of Industrial Mixing, 1e (ed. E.L. Paul, V.A. Atiemo-Obeng and S.M. Kresta), 368. Hoboken, NJ: Wiley. Bourne, J.R. (2003). Org. Process. Res. Dev. 7, 471 and references therein. Liu, X., Hatziavramidis, D., Arastoopour, H., and Myerson, A. (2006). AIChE J 52 (10): 3621. Howard, K. (2011). PhD thesis, Loughborough University, p. 121. Prashad, X., Sutton, P., Wu, R. et al. (2010). Org. Process. Res. Dev. 14: 878. Wang, X. and Kirwan, D.J. (2006). Cryst. Growth Des. 6 (10): 2228. Liu, J., Svärd, M., and Rasmuson, A. (2014). Cryst. Growth Des. 14: 5521. Mullin, J.W. (2001). Crystallization, 4e, 392. Woburn, MA: Butterworth-Heinemann. Kleetz, T., Braak, F., Wehenkel, N. et al. (2016). Cryst. Growth Des. 16 (3): 1320. Federsel, J.J. (2000). Org. Process. Res. Dev. 4: 362.

329

12 Processing-Induced Phase Transformations and Their Implications on Pharmaceutical Product Quality Seema Thakral1,2 , Ramprakash Govindarajan3 , and Raj Suryanarayanan1 1 University of Minnesota, College of Pharmacy, Department of Pharmaceutics, 308 Harvard Street S.E.,

Minneapolis, MN 55455, USA University of Minnesota, Characterization Facility, 308 Harvard Street S.E., Minneapolis, MN 55455, USA 3 University of Iowa, College of Pharmacy, Department of Pharmaceutical Sciences and Experimental Therapeutics, 115 S Grand Ave, Iowa City, IA 52242, USA 2

12.1 Introduction The importance of physical characterization of pharmaceutical solids has been recognized for many decades [1]. It is well known that the physical form (polymorphic form, degree of crystallinity, and state of solvation) of the active pharmaceutical ingredient (API) can signiﬁcantly inﬂuence the stability and performance of the dosage form. Even though an appropriate physical form of the API may be selected, it may not be retained in the ﬁnal pharmaceutical product. Stresses experienced during processing and interactions with formulation components can result in phase transformations [2]. The behavior of the resulting pharmaceutical composition will be inﬂuenced by the extent of conversion and the properties of the transformed phase. It is, therefore, important to detect, quantify, if necessary, and understand the implications of such phase changes on product quality and performance. Physical characterization of the ﬁnal product would reveal the overall eﬀect of processing. However, multiple phase transformations can occur during the sequence of pharmaceutical processing steps. The eﬀect of each processing step on physical form and the behavior of the transformed phase can be understood only by monitoring the phases during processing. This information can then be used to design processes and optimize formulation and processing variables, with the objective of controlling the physical form, not only during manufacture but also during the shelf life of the ﬁnal product. The possible phase transitions during pharmaceutical processing have been outlined as Scheme I (Figure 12.1). Although not intended as an exhaustive summary, it lists the common transitions of interest to a drug formulator. Changes, either in the arrangement of molecules in the crystal lattice or in lattice order, can lead to physical transformations such as amorphization, crystallization, or polymorphic transitions. Incorporation or removal of solvent molecules from the crystal lattice, interconversions between salt and free acid/base forms, and the Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development, First Edition. Edited by Rolf Hilﬁker and Markus von Raumer. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

Phase transformation during pharmaceutical processing

Reduction in longrange order (amorphization)

Mechanical processing

Vitrification from solution

Melt quenching

Increase in longrange order (crystallization)

Heat induced

Plasticizer induced

Change in lattice structure (polymorphic transformation)

Solid−solid transition

Solution mediated

Solution/ solventmediated transition

Change in chemical composition

Solvate formation

Desolvation

Crystalline product

Figure 12.1 Schematic representation of processing-induced phase transformations.

Salt formation

Co-crystal formation

Free drug

Amorphous product

12.1 Introduction

formation/dissociation of co-crystals constitute changes in the chemical composition of the phase. Hence, the latter do not ﬁt under the conventional deﬁnition of “physical solid-state transformations.” However, in light of their importance, we will include these under the broad deﬁnition of processing-induced phase transitions (Scheme I) and discuss some pharmaceutically relevant examples. The product phase formed as a result of a change in the chemical composition may, in turn, undergo further transformations. For example, stoichiometric incorporation of water into the crystal lattice of an anhydrous phase results in the formation of a hydrate. Subsequent dehydration of the hydrate may result in an amorphous anhydrate. This hydration–dehydration cycling can also result in a stable or metastable crystalline anhydrate, as has been demonstrated in the case of theophylline [3]. Scheme II (Figure 12.2), based on the stress relaxation concept of Morris et al. [2], shows how thermal or mechanical stresses or interaction with other formulation components (e.g. water) can induce phase transformations. Thus, a transition may be thermodynamically favored resulting in a product phase that is stable under the stressed conditions. The transition of an anhydrate to a hydrate during wet granulation and the formation of a higher-temperature-stable polymorph on heating are instances of such conversions. The stress might also result in a kinetically stabilized metastable phase (e.g. partial or complete amorphization due to mechanical processing and vitriﬁcation of solutes in frozen solutions). These constitute “trapping” of the system under the applied stress (Figure 12.2). When the stress is partially or completely removed (e.g. when the wet-massed granules are dried, when the compression force is removed during tableting, or when a frozen solution is heated to an annealing or drying temperature), the system may “relax” back to the original state. If the phase generated under stress is metastable under the de-stressed conditions, it will tend to convert to the stable form. The kinetics of this transformation will determine the metastable phase concentration in the ﬁnal product, over its shelf life. During the manufacture of a dosage form involving several unit operations, the formulation components can undergo multiple stress relaxation cycles. Phase transformations during pharmaceutical processing have been the subject of several reviews [2, 4–6]. A comprehensive review by Wildfong highlights the importance of material-speciﬁc attributes and provides a mechanistic perspective of stresses experienced by API and excipients during various unit operations in pharmaceutical processing [6]. We have expanded our previous chapter (ﬁrst edition of this book) to incorporate the updated understanding of processing-induced phase transformations and the potential repercussions on the ﬁnal product quality [7]. Speciﬁcally, we have pointed out how such phase transitions of the drug (or excipient) can confer either desirable or undesirable properties, to the ﬁnal dosage form. Very often, the same transition can be beneﬁcial in some respects and detrimental in others, as will be evident from the discussed examples. If the original (i.e. the “as is”) form of the drug substance was intended to be retained in the ﬁnal drug product, any inadvertent changes in phase composition are undesirable. However, manufacturing processes may be designed to deliberately cause phase transformations so as to obtain a drug product

331

Initial solid phase of API/excipient Thermal Mechanical Influence of formulation components

Processing stresses

Stable phase under new conditions e.g. hydrate formation during (i) aqueous wet granulation (ii) freezing of aqueous solution

Metastable phase e.g. (i) amorphization during milling/ compression (ii) vitrification during freezing aqueous solution

Stressed state-trapping

Removal of stress-relaxation

Formation of stable phase e.g. (i) dehydration of hydrate to stable anhydrate upon drying (ii) crystallization of (a) amorphous API in tablets (b) freeze concentrate upon annealing/drying

Formation of metastable phase

Persistence of metastable phase formed

e.g. dehydration of hydrate to metastable- crystalline or amorphous anhydrate upon drying

e.g. (i) surface disorder on solid particles upon milling (ii) formation of amorphous lyophile

Kinetically controlled transformation to stable phase Figure 12.2 Schematic representation of the mechanism of phase transformations as a result of processing stresses. Source: Adapted from Govindrajan and Suryanarayanan, 2006.

12.2 Pharmaceutical Processes Causing Unintended Phase Transformations

with certain properties. An example is the generation of amorphous drug phases from crystalline starting materials by processes such as melt extrusion and spray-drying. Similarly, planned or unintended changes can occur in the excipients as well. We will discuss such phase transformations under two broad categories: (i) processes causing unintended phase transformations and (ii) processes designed to intentionally cause transformations. A prior understanding of the former is especially important as these are an “undesired” side eﬀect of the pharmaceutical processing steps involved in the conversion of an API into a drug product. These may or may not have implications on the ultimate performance of the drug product. Even when the performance of the ﬁnal dosage form is seemingly unaﬀected by the appearance of a physical form diﬀerent than the starting phase, from a regulatory perspective, a comprehensive study of these transformations is necessary.

12.2 Pharmaceutical Processes Causing Unintended Phase Transformations 12.2.1

Milling

Mechanical milling is conducted in the pharmaceutical industry, primarily to reduce particle size. The mechanical energy required to produce the desired reduction in particle size can also bring about changes in the physical form of the material. These phase transformations that are often undesirable include polymorphic changes, dehydration, and changes in lattice order. In order to have batch-to-batch consistency, it is necessary to have a thorough understanding of the eﬀect of milling on both particle size distribution and the physical form of the API [4, 8]. Milling under relatively mild conditions may also be conducted to improve blend homogeneity and is beyond the scope of this discussion. When a powder is milled, in an eﬀort to accommodate the applied mechanical stress, the system responds along the path of least resistance resulting in particle fracture or deformation [6, 9]. As drug particles are often polycrystalline aggregates, as a ﬁrst step, particle fragmentation is facilitated along grain boundaries. However, the continued application of stress can lead to displacement of molecules from their equilibrium lattice positions. If the system is able to return to its original state when the stress is removed, the response is elastic. However, pharmaceutical milling often imposes stresses beyond the elastic limit of the material and leads to plastic deformation. The displacement of molecules from their equilibrium lattice positions often leads to nonuniform lattice strain. The progress and collective loss in lattice periodicity can eventually lead to a disordered lattice [6]. Wildfong proposed a model to predict the ability of a material to completely transform to the amorphous state by milling. The model, predominantly adapted from inorganic material literature, is based on the estimation of critical dislocation density of a material (𝜌d ). Material-speciﬁc properties such as elastic shear modulus, magnitude of Burgers’ vector, molar volume, and heat of fusion were used in the estimation of 𝜌d . Using this model, it was possible to successfully predict the amorphization tendency of six of the seven compounds

333

334

12 Processing-Induced Phase Transformations

tested [10]. Figure 12.3 details the inﬂuence of the physical form of the starting material on the nature of the product phase obtained. As is evident from Figure 12.3, the eﬀect of milling on the physical form of the product phase is also dependent on the glass transition temperature (of the corresponding amorphous form). In general, milling anhydrous crystalline compounds well below the glass transition temperature (T g ) of the corresponding amorphous form induces direct solid-state amorphization. Examples include the formation of amorphous lactose [11], trehalose [12], griseofulvin [13], and budesonide [14] by milling the corresponding crystalline phases. The propensity of a material to amorphize upon milling is likely to result from a competition between the structural disordering of the crystalline lattice brought about by mechanical perturbation and the thermally activated recrystallization [13]. Recently, the mechanism of solid-state amorphization of α-glucose was investigated by Dujardin et al. [15] Complete loss in crystallinity could only be achieved by milling at −15 ∘ C (at temperature ≪T g of amorphous glucose; 38 ∘ C). The amorphization was attributed to two diﬀerent mechanisms: surface disorder due to mechanical shock and spontaneous amorphization as the crystallite size reached a critical value. No change in lattice structure was discerned when glucose was milled at RT. While the material tended to rapidly crystallize, there was some trace of lattice disorder. Microstructure evaluation, conducted using the Le Bail analysis of X-ray diﬀraction (XRD) patterns, suggested a competition between a mechanical fragmentation mechanism and a coherent reuniﬁcation (recrystallization) process. It was proposed that molecular mobility in the amorphous state governed recrystallization and hence the inﬂuence of milling temperature on the physical form of the product phase [15, 16]. Milling crystalline compounds above the T g of the corresponding amorphous form may induce formation of a metastable polymorph (Figure 12.3). The room temperature milling of form IV, the stable polymorph of fananserine, induced polymorphic transformation to the least stable form I, whereas milling at 0 ∘ C caused amorphization [17]. These results can be explained by the T g (∼19 ∘ C) of amorphous fananserine. In the case of mannitol (T g ∼ 10 ∘ C), milling the stable (β-) or the metastable (δ-) anhydrous forms under identical conditions (intensity, duration, and temperature) induced transformation to α-mannitol – a polymorph of intermediate stability [18]. Milling the diﬀerent polymorphs of indomethacin (the stable (γ-) or the metastable (α-)) at room temperature, i.e. close to T g (∼42 ∘ C), induced transformation to the same ﬁnal composition – ∼50% each α- and amorphous. However, milling at 4 ∘ C resulted in complete amorphization [19]. The amorphization brought about by milling a hydrate can change the state of the water in the system. The lattice water can become sorbed water, plasticize the system, and cause a pronounced lowering of the T g . Although lactose monohydrate (T g of plasticized lactose ∼40 ∘ C; milled at RT) was rendered amorphous by milling, no structural change was observed upon milling trehalose dihydrate (T g of plasticized trehalose ∼20 ∘ C; milled at RT) and glucose monohydrate (T g of plasticized glucose ∼ −20 ∘ C; milled at −15 ∘ C). Thus, in order to render the hydrate amorphous, it appears that the milling should be conducted at a temperature lower than the glass transition temperature of the plasticized phase [20].

Initial solid phase of API

Amorphous*

Stable crystalline phase Anhydrous T>Tga

Hydrate

TTgb

T20% metastable anhydrous theophylline remained [33]. At low dehydration temperatures (40 or 50 ∘ C), irrespective of the drying method, a substantial fraction of the anhydrate was the metastable form [33, 34]. The presence of PVP retarded the formation of stable anhydrous form resulting in a buildup of the metastable phase (Figure 12.5). It was postulated that PVP accumulated near the grain boundaries of the polycrystalline monohydrate and interfered with the nucleation and/or growth of the stable anhydrate during the dehydration reaction. The weight fraction of the metastable phase increased with PVP concentration [34]. The diﬀerent states of hydration of sodium naproxen were comprehensively evaluated using an automated water sorption apparatus, and the solid phases were characterized by powder X-ray diﬀractometry [35]. The authors were able to simultaneously determine the eﬀects of temperature and water vapor pressure on the hydration state of sodium naproxen. For example, anhydrous sodium naproxen when stored at a ﬁxed relative humidity of 70% and at 25, 35,

Weight fraction of metastable anhydrate

1.0 0.0% PVP 2.3% PVP 5.4% PVP 7.1% PVP

0.8

0.6

0.4

0.2

0.0 40

45

50 55 60 Temperature (°C)

65

70

Figure 12.5 Eﬀect of PVP concentration (% w/w) on the weight fraction of metastable anhydrous theophylline retained in the product phase following theophylline monohydrate dehydration. Source: Nunes et al. 2006 [34]. Copyright (2006). Redrawn (Figure 12) with permission of Springer.

339

12 Processing-Induced Phase Transformations

TH 35 30 25 Weight gain (%)

340

DH-II

20 15 DH-I 10 AH

5 MH 0 90 80 70 60 50 40 Relati ve hu 30 20 midity 10 (%)

25 30 C) e (°

50

35 40 r atu 45 per m e T

Figure 12.6 A three-dimensional empirical phase diagram based on water sorption data for sodium naproxen anhydrate–hydrate system. (The resolution of the relative humidity and temperature axis is 5% RH and 5 ∘ C, respectively). The raw data from the automated water sorption experiment was used for the construction of the empirical phase diagram. At 25 ∘ C, anhydrous sodium naproxen (AH) transforms directly to one dihydrate polymorph (DH-II). At 50 ∘ C, AH transforms stepwise to a monohydrate (MH) and then to the other dihydrate polymorph (DH-I). DH-II transforms to a tetrahydrate (TH) more readily than DH-I. Source: Raijada et al. 2012 [35]. Copyright (2012). Reproduced with permission of Springer.

and 50 ∘ C transformed, respectively, to the tetrahydrate, dihydrate (II), and dihydrate (I) (Figure 12.6). When the RH was decreased to 55%, at 25 and 50 ∘ C, the dihydrate (II) and monohydrate, respectively, were formed. The validity of the empirical phase diagram could be evaluated in sodium naproxen “wet” granules wherein the API existed as a tetrahydrate. The granules were dried in a high-shear mixer granulator either at RT or at 40 ∘ C under reduced pressure. Drying at RT yielded a mixture of dihydrate and tetrahydrate, while at 40 ∘ C, a mixture of monohydrate and tetrahydrate was obtained. The most desirable tableting characteristics were exhibited by the granules dried at RT [36]. The state of hydration of the drug (i.e. hydrate stoichiometry) can also aﬀect its dissolution behavior. Interestingly, equilibrium solubility may not reﬂect the observed dissolution performance. In the case of berberine HCl, at 37 ∘ C, the tetrahydrate had a lower equilibrium solubility than the dihydrate. However, the tetrahydrate powder exhibited the most rapid initial dissolution rate, an eﬀect attributed to superior wetting of the tetrahydrate. When anhydrous berberine HCl was wet granulated with diﬀerent excipients and dried, the dihydrate content was highly inﬂuenced by the excipient (14%, 24%, and 67% when granulated with α-lactose monohydrate, MCC, and PVP K-25, respectively) and hence

12.2 Pharmaceutical Processes Causing Unintended Phase Transformations

would have inﬂuenced the dissolution performance of the ﬁnal formulation [37]. Fluid bed drying of carbamazepine dihydrate granules at 50 ∘ C caused partial dehydration and resulted in a mixture of two anhydrous polymorphs and amorphous carbamazepine. The composition of the dried phase was dependent on the dehydration temperature and time [38]. When granules are dried, typically by heating, the crystal lattice of a hydrate can collapse, leading to the formation of an amorphous phase. The drying conditions, and speciﬁcally the dehydration kinetics, are known to inﬂuence the product phase formed. Although slow dehydration generally results in a crystalline phase, rapid removal of water can induce amorphization. In the case of trehalose dihydrate, the dehydration conditions provide exquisite control over the physical form of the product phase. Although slow dehydration (heating rate ∼1 ∘ C min−1 ) yielded the anhydrous α-polymorph, fast dehydration (heating rate 50 ∘ C min−1 ) promoted formation of an amorphous phase [39]. If drying yields an amorphous product, there can be serious stability and performance implications. Amorphous forms are known to be more chemically reactive than their crystalline counterparts. The diﬀerence in reactivity can be suﬃciently pronounced to be of concern. In addition, the amorphous form will have a tendency to crystallize. Raﬃnose pentahydrate is also known to yield an amorphous anhydrate. Bates et al. monitored its dehydration at 60 ∘ C for 72 hours in an X-ray diﬀractometer. A comprehensive examination of the X-ray data including pair distribution function analysis revealed that the pentahydrate lattice structure was retained even after removal of two molecules of water. However, the partial dehydration created defects, likely in the form of vacancies, providing the thermodynamic driving force and disorder for subsequent conversion to the completely amorphous state [40]. Another interesting study suggests excipient-induced transformation from crystalline to amorphous form during wet granulation. Dexketoprofen trometamol (polymorph “A” or “B”), when subjected to direct compression, was physically stable and the initial polymorphic form was preserved. However, when subjected to wet granulation by mixing with MCC, irrespective of the starting polymorph, transformation to an amorphous form was observed. The amorphous form was retained even after drying and compression [41]. The stabilization of the amorphous form can be attributed to the drying conditions, coupled with the excipients acting as crystallization inhibitors. Wet granulation can also induce salt formation as was observed in two weakly acidic drugs, piroxicam and lornoxicam. The presence of basic excipients, sodium bicarbonate and dicalcium phosphate, enabled this transformation. The sodium salt formation was solvent mediated – observed only in wet granulated samples and not in dry mixtures. The salt formation increased the dissolution rate of lornoxicam, which is a poorly soluble drug while it was unaﬀected for piroxicam [42] (details discussed later). The reverse transformation, i.e. conversion of salt to free base or salt disproportionation, is equally relevant. Wet granulation led to conversion of the crystalline hydrochloride salt of an investigational drug into amorphous free base. The extent of conversion was aﬀected by the water content in the granulation ﬂuid, which was an ethanol–water mixture. Granulation with 90% or 96% v/v ethanol, followed by four hours of storage, led to ∼7% and ∼4% conversion, respectively [43].

341

342

12 Processing-Induced Phase Transformations

12.2.3

Compression

Tablet compression is a complex and irreversible dynamic process and can be viewed as a number of sequential steps. The compression force ﬁrst results in rearrangement of the randomly packed particles in the die cavity to a more compact form. Further compression causes the particles to deform, which can be classiﬁed as elastic and plastic deformation and fragmentation [44]. The deformation mechanism of a speciﬁc material is aﬀected by numerous factors including the molecular and crystal structure of a material, particle size, defects in the crystal lattice, the magnitude of applied force, and the compression speed. Hard brittle materials, which have higher shear strength than tensile strength, tend to fragment more easily than soft materials, which are characterized by lower shear strength than tensile strength. Particles also have a critical diameter at which densiﬁcation mechanism changes from fragmentation to plastic deformation [45]. Methyl carboxy cellulose, sodium chloride, and stearic acid are examples of materials considered to deform mainly by plastic ﬂow. Paracetamol, sucrose, and dicalcium phosphate dihydrate are examples of fragmenting materials. Most drugs and excipients show a tendency to fracture on compression [46]. The compression pressure for tablet formation is typically in the range 40–200 MPa and applied for relatively short times (typically ≤1 s). These conditions do not induce any phase transformation in a large fraction of pharmaceuticals. However, a small but signiﬁcant number of pharmaceuticals are known to undergo transformations upon compression. Shear stress at interparticulate interfaces appears to have a key role in pressure-induced transformations [6]. In practice, although an API is likely to be compressed in the presence of excipients, numerous studies have focused on the compression behavior of pure APIs. This is typically conducted during preformulation studies to establish the baseline mechanical properties of the API. We have restricted our discussion to compression studies conducted only under pharmaceutically relevant conditions. There are investigations revealing phase transformation under extreme conditions – for example, compression under pressures as high as few gigapascal and dwell time as long as 40 min, but these may not be of practical interest. Compression-induced phase transitions can be analytically challenging to characterize and quantify. Conventionally, the tablets are gently ground and the powder is characterized using a suitable analytical technique. This sample-processing step carries with it the risk of inducing further transformations. Moreover, such an analysis gives “average” information and cannot discriminate phase composition in diﬀerent regions of tablets (speciﬁcally tablet surface vs core). Two XRD-based approaches have been used to reveal spatial heterogeneity in phase composition. In glancing angle XRD, by modulating the incident angle, it is possible to proﬁle phase transformations as a function of depth [47]. In another approach, tablets are split and two-dimensional XRD patterns are collected starting from the tablet surface and moving toward the midplane/core, in small increments. Such depth proﬁling revealed progression of phase transformations from the surface to the tablet core [48].

12.2 Pharmaceutical Processes Causing Unintended Phase Transformations

At compression pressures relevant to commercial tablet manufacture, partial amorphization was observed in tablets of theophylline, nitrofurantoin, and amlodipine besylate. The extent of amorphization, measured by grazing incidence XRD of the top and bottom tablet surfaces, increased as a function of compression pressure and was most pronounced in the surface regions [49]. Interestingly, in another study, the magnitude of tolbutamide amorphization was highest in the tablets compacted at moderate pressure (400 MPa) and lowest in the tablets compressed at 1000 MPa. It was suggested that at the higher compression pressure, recrystallization was initiated during the compression dwell time of 1 min [47]. The reverse transformation, i.e. amorphous → crystalline transition, is also extensively reported in the literature. Compression of freeze-dried amorphous sucrose, at pressures ranging from 74 to 665 MPa, facilitated the formation of critical nuclei, thereby decreasing the induction time for crystallization and lowering the crystallization temperature during thermal analysis [50]. At modest compaction pressures, ranging from 27 to 138 MPa, crystallization of amorphous celecoxib was observed. Even after the drug was formulated as a ternary solid dispersion containing PVP and meglumine, the compression-induced crystallization could be reduced but not prevented [51]. Compression of amorphous indomethacin, even at a low pressure of 44 MPa, caused a lowering of the crystallization-onset temperature attributed to the additional nucleation sites formed as a result of compression [52]. The compression-induced crystallization propensity of amorphous indomethacin was investigated at diﬀerent compression pressures [48]. Two-dimensional XRD enabled the study of spatial distribution of crystallization. At low compression pressures (10 and 25 MPa), the extent of crystallization was much higher at the radial surface, and the tablet core was substantially amorphous (Figure 12.7). However, as the compression pressure was increased, there was a pronounced reduction in the crystallization gradient. Lubricating the die with magnesium stearate (i.e. site-speciﬁc lubrication) before compression led to reduction in crystallization at radial surface, whereas crystallization in tablet core was unaﬀected. There are also several examples of compression-induced crystalline-tocrystalline (i.e. polymorphic) transformations. Caﬀeine form I, under a moderate compression pressure of 75–150 MPa, partially (25–30%) transformed to the stable form II. The extent of conversion in diﬀerent regions of tablets, mapped using low-frequency Raman spectroscopy, was found to be about the same [53]. Polymorphic transformation of ﬂuconazole form I to form VIII at about 800 MPa was evaluated using energy-dispersive XRD and high-pressure Raman spectroscopy. The forms I and VIII belonged to the same crystal system (triclinic) but had diﬀerent lattice parameters. The eﬀect of compression was attributed to reorientation of molecules in a unit cell [54]. Pressure-induced polymorphic transformations has been extensively investigated in chlorpropamide. Upon compression, the metastable form C consistently converted to stable form A. Interestingly, partial reverse transition under pharmaceutically relevant compression pressures, i.e. conversion of form A to C, has been observed only by some investigators [47, 55]. In another study, using solid-state nuclear magnetic resonance (NMR), A → C transition was

343

12 Processing-Induced Phase Transformations

70 Radial surfaces

60 50 Crystallization (% w/w)

344

Tablet core

40 30 20

D

10

C

Radial surface (unlubricated) Core (unlubricated)

0

A

Radial surface (lubricated)

B

Core (lubricated)

–10 0

20

40 60 80 Compression pressure (MPa)

100

120

Figure 12.7 Extent of indomethacin crystallization (expressed as crystalline percentage) as a function of compression pressure. Amorphous indomethacin tablets were compressed, either in an unlubricated or in a lubricated die, stored at 35 ∘ C for 24 hours, and subjected to XRD. In unlubricated systems at a compression pressure of 10 MPa, “A” is a measure of the diﬀerence in the extent of crystallization between tablet surface (red circle) and core (green circle). “B” is a measure of the same diﬀerence in lubricated systems. These proﬁles reveal the eﬀectiveness of “site-speciﬁc” lubrication in preventing surface crystallization. At a higher compression pressure of 100 MPa, the diﬀerence in the extent of crystallization between unlubricated (C) and lubricated (D) tablets is much less pronounced. Source: Thakral et al. 2015 [48]. Copyright (2015). Redrawn with permission of ACS Publishing.

not observed at compression pressure ranging from 10 to 800 MPa over a temperature range of 90–300 K [56]. Amorphous solid dispersion (ASD), a homogeneous mixture of drug and polymer, is a potentially eﬀective approach to physically stabilize amorphous drugs and enhance oral bioavailability. ASDs, if formulated as tablets, will entail a compression step, which has the propensity to cause amorphous–amorphous phase separation and drug crystallization. In naproxen–PVP ASD (30% w/w drug loading), 377 MPa was found to be the threshold compression pressure, above which amorphous–amorphous phase separation was observed. At higher pressures, the destabilization was attributed to conformational changes in PVP, which led to the weakening or distortion of hydrogen bonds between the drug and polymer [57]. However, when a naproxen solid dispersion was prepared using PVP-VA64 (vinylpyrrolidone–vinyl acetate copolymer), compression enhanced the physical stability, even at a high drug loading of 50% w/w. The compressed samples were found to be less crystalline than the uncompressed powder after storage at 75% RH (RT) for ﬁve months. This stabilizing eﬀect was attributed to enhanced drug–polymer intermolecular interactions and reduced water uptake in compressed samples [57]. Dispersions of miconazole

12.2 Pharmaceutical Processes Causing Unintended Phase Transformations

prepared with the same polymer exhibited a similar behavior. Spray-dried solid dispersions with high drug loading were characterized by two glass transition temperatures, indicative of a two-phase system. However, after compression, the dispersion displayed a single T g , an eﬀect attributed to compression-induced mixing. This was believed to be brought about by an enhancement in molecular mobility, leading to polymer “ﬂow” and a free volume reduction [58]. The eﬀect of compression on the behavior of ASD is of immense interest to formulators and warrants further mechanistic studies. 12.2.4

Freezing Aqueous Solutions

Freezing of aqueous solutions, the ﬁrst step in the manufacture of freeze-dried products, invariably results in crystallization of ice, leading to solute freeze-concentration. Several solutes, including sucrose and trehalose, tend to resist crystallization and are retained amorphous in the frozen state, whereas mannitol and glycine are examples of solutes that tend to crystallize. The physical form(s) of glycine and mannitol crystallizing from solution depend on both the formulation composition and the processing conditions. When solutions containing glycine were subjected to controlled cooling (either rapidly or slowly), the β-polymorph crystallized, whereas quench cooling completely inhibited glycine crystallization. However, upon warming the quench-cooled solution, β-glycine crystallized and during annealing converted partially to the γ-polymorph [59]. In the case of mannitol, slow cooling of aqueous solutions resulted in a mixture of α- and β-polymorphs, whereas rapidly frozen solutions primarily yielded the δ-polymorph [60]. Low mannitol concentration (100 or 200 mM) favored crystallization of the β-form, whereas a higher concentration (500 mM) led to the α-form [61]. The presence of noncrystallizing solutes can inhibit mannitol crystallization. Addition of protein increased the crystallization-onset temperature of mannitol. This eﬀect persisted even after aggressive annealing at a high temperature [62]. Sucrose as well as trehalose prevented mannitol crystallization, with the extent of inhibition dependent on the concentration ratio of mannitol to the disaccharide. When the molar ratio of mannitol to trehalose was 0.33, trehalose eﬀectively inhibited mannitol crystallization. However, when solutions with an equimolar ratio were annealed, crystallization of mannitol facilitated trehalose crystallization. When the mannitol to trehalose ratio was 3, only mannitol crystallized [63], and a mixture of δ-mannitol and mannitol hemihydrate was obtained [64]. When carboxylic and amino acid buﬀer solutions are frozen, selective crystallization of a buﬀer component can cause pronounced shifts in the pH of the freeze-concentrate with the potential to cause destabilization of API in solution. The crystallization propensity of buﬀers in frozen solutions (−25 ∘ C) were rank-ordered as succinate ≈ phosphate ≈ glycine ≈ histidine > tartrate > citrate > malate (Figure 12.8). Malate buﬀer showed no evidence of crystallization and hence negligible pH shifts. The succinate buﬀer, on the other hand, exhibited a pH swing. The pH ﬁrst increased from 4.0 to 6.1 and eventually to 8.0 and then decreased to 2.2, because of sequential crystallization of succinic acid, monosodium succinate, and disodium succinate [65]. The inﬂuence of other

345

12 Processing-Induced Phase Transformations

Crystalline Amorphous

Rank ordering most

Malate Citrate Tartarate

Preference

346

Succinate Phosphate Glycine Histidine

least 2

3

4

5

6

7

8

9

10

Initial pH (at RT)

Figure 12.8 A plot summarizing the evidence of crystallization (based on XRD) in diﬀerent frozen buﬀer systems. A propensity to crystallize over a range of pH values formed the basis of the rank ordering. Source: Sundaramurthi and Suryanarayanan 2011 [65]. Copyright (2011). Reproduced with permission of ACS Publishing.

solutes on buﬀer component crystallization has also been extensively assessed [66, 67]. Sucrose and trehalose inhibited buﬀer component crystallization, resulting in smaller pH shifts upon freezing. Similarly, glycine suppressed pH changes via inhibition of buﬀer crystallization and stabilized protein against freezing-induced aggregation [68, 69]. Additional examples of freezing-induced solute crystallization leading to protein instability are discussed later.

12.3 Pharmaceutical Processes Causing Intended Phase Transformations – Obtaining the Desired Physical Form Some pharmaceutical processes are carried out with the goal of obtaining a speciﬁc physical form of the API. In many instances, the API is desired in the amorphous state so as to exploit the solubility advantage provided by this physical form. In the following discussion, we have several examples of pharmaceutical processes carried out to obtain a desired physical form. However, as these processes may also cause unintended transformations, such representative examples have also been included. 12.3.1

Spray-drying

In this process, a concentrated solution or liquid dispersion of API can be converted to a dry free-ﬂowing powder, often with particles spherical in shape and with uniform size distribution. Spray-drying has also been used as a process for

12.3 Pharmaceutical Processes Causing Intended Phase Transformations

converting a crystalline API into an amorphous phase. The use of this technique for the preparation of ASDs has been comprehensively reviewed [70]. The physical form of API obtained after spray-drying depends on several factors including solution composition, processing conditions (feed rate, agitation and drying conditions, and pressure diﬀerence), and equipment (type of feed pump, dimensions of drying chamber, cyclone, or collector) [71]. This has been exempliﬁed in various reports of spray-drying of mannitol containing solutions. In a salmon calcitonin–mannitol formulation, mannitol remained amorphous when the mannitol content was form I, whereas the rank order for the elastic modulus values is form III > form I > form II. The ranking for the ratio of H/E is form II > form III > form I. The H/E ranking corresponds well with the ﬁnal particle size and surface energy change. This study indicates that polymorph crystal properties Table 13.3 Comparison of behavior of diﬀerent polymorphs of carbamazepine under milling.

E (GPa)

H (GPa)

H/E

𝚫𝚪50 (mJ m−2 )

D50

Form I

3.41

0.80

0.23

29.5

0.98

Form II

2.69

1.36

0.51

62.9

1.85

Form III

5.18

2.15

0.42

31.5

1.77

E, young’s modulus; H, hardness; Γ50 , surface energy changes due to micronization measured by atomic force microscopy; D50 , median size after micronization. Source: Meier et al. 2009 [75]. Adapted with the permission of Elsevier.

405

406

13 Surface and Mechanical Properties of Molecular Crystals

have a direct eﬀect on the particle size reduction due to its energetic diﬀerence during milling.

13.7 Impact of Polymorphism on Powder Compaction Properties The relationship between crystal properties and powder compaction behavior has been studied using four model compounds. A positive correlation between elastic recovery in tablets and the elastic modulus of the constituting crystals [75, 78] was found. A good correlation between the out-die Walker coeﬃcient and indentation hardness is also reported [79]. These ﬁndings demonstrate that single-crystal-level properties determine powder compaction behavior. Powder compaction properties are mainly determined by compressibility, compactibility, and tabletability. Compressibility is the ability of a powder to be reduced in volume as a result of an applied pressure and is represented by a plot of tablet porosity against pressure [80]. Compactibility is the ability of the material to produce a cohesive body with suﬃcient strength under the eﬀect of densiﬁcation and is represented by a plot of tensile strength against compact porosity [80]. Tabletability is deﬁned as the capacity of the powder material to be transformed into a tablet of speciﬁed strength under the eﬀect of compaction pressure [80]. Crystallographic features, such as dense cluster packing, slip planes [81], and defects [75], can inﬂuence powder compaction properties. Dense cluster packing oﬀers rigid structure that resists densiﬁcation under compaction pressure [82]. The presence of a slip plane in the crystal structure has been reported to allow easier interplanar slip motion under compaction pressure, thus oﬀering greater compressibility and deformation (increased plasticity) [83]. Compaction properties of any given powder material are largely a function of material plasticity, which increases the contact area and bonding between particles. The plastic deformation of crystals is expected to take place on low-index slip planes, which has higher in-plane molecular density, weak interplanar interactions, and lower nanoscale rugosity. Hence, molecular packing governs the compactibility of the materials while a slip plane system aﬀects the compressibility [81, 82, 84]. The packing and slip plane eﬀect on tableting behavior are demonstrated by a few compounds. Indomethacin polymorphs (α and γ) (Figures 13.15 and 13.16) are used to study the case where a slip plane is in an open crystal packing system. The α form has three diﬀerent molecular conformations and additional hydrogen bonds. The hydrogen bonds are between a carboxylic acid hydroxyl group and the carbonyl oxygen of an amide group. These additional hydrogen bonds and conformations aﬀord the α form closer crystal packing. The α form showed higher tabletability, lower compressibility, and higher compactibility as compared to the γ form. The γ form has a slip plane in an open crystal packing system [81]. The γ form has slip planes oﬀering greater compressibility by sliding of slip planes under compaction pressure. In addition, the γ form possesses very weak bonding strength. The hydrophobic phenyl and indole rings are prevalent

13.7 Impact of Polymorphism on Powder Compaction Properties

Carboxylic acid dimer

Carboxylic acid dimer

Additional hydrogen bond

(a)

(b)

Figure 13.15 Indomethacin crystal structure. (a) Form α. (b) Form γ. Source: From Ref. [81].

(a)

Slip plane

(b)

Figure 13.16 Slip planes in indomethacin crystals. (a) Form α. (b) Form γ. Source: From Ref. [81].

407

408

13 Surface and Mechanical Properties of Molecular Crystals

on the peripheral faces of γ-crystals and the polar mutually hydrogen-bonded carboxylic acid dimers are caged inside a hydrophobic shield. The shielding of the polar hydrogen bonded dimer may be responsible for weaker interparticulate bonding of the γ form. This oﬀsets the high bonding area provided by the sliding of slip planes. Therefore, the tablets of the γ form are softer compared to those of the α form [81]. Ranitidine hydrochloride polymorphs (form I and form II) are used to study the case where a slip plane is in a closed crystal packing [85]. Form I shows a slip plane system with closed crystal packing, whereas form II possesses a more open crystal structure (Figure 13.17). Tablets composed of form I have higher tensile strength. The closed packing of form I is due to strong intramolecular hydrogen bonding. Form I has several weak C—H· · ·O interactions across the slip plane. Although the C—H· · ·O interactions are generally considered to be weak, their presence in multiple numbers makes the planes suﬃciently strong as to hinder the slip. Hence, the slip plane in form I does not have much eﬀect on compaction properties and is sometimes termed as a “proposed” slip plane. On the other hand, form II shows greater compressibility and lower mean yield pressure, indicating its increased plasticity over form I. This may be attributed to the relatively more open crystal structure that allows multiple slips under compaction pressure. These facilitate the sliding of planes over each other under the pressure imparting higher plasticity to form II. Other examples include clopidogrel bisulfate [82] and sulfamerazine [83]. The better compactibility of clopidogrel bisulfate form I is due to its closer packing; greater tabletability of sulfamerazine form I crystals arises from the greater plasticity which their slip planes confer. This leads to more extensive plastic deformation and larger interparticulate bonding area in the tablets. Polymorphism can also aﬀect powder compaction properties through form conversion during processing. Carbamazepine granules produced by wet granulation were investigated. The mechanical strength of the tablets of the granules are in the rank of form II > form III > form IV > form I. This is so because most of form II is transformed into ﬁner particles of form III by

(a)

(b)

Figure 13.17 Crystal structure of ranitidine hydrochloride (a) form I and (b) form II. Source: From Ref. [85].

References

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of the polar and total surface energy distributions of particulates by inverse gas chromatography. Langmuir 27 (2): 521–523. Elamin, A.A., Ahlneck, C., Alderborn, G., and Nyström, C. (1994). Increased metastable solubility of milled griseofulvin, depending on the formation of a disordered surface structure. Int. J. Pharm. 111: 159–170. Feeley, J.C., York, P., Sumby, B.S., and Dicks, H. (1998). Determination of surface properties and how characteristics of salbutamol sulphate, before and after micronisation. Int. J. Pharm. 172: 89–96. Mittal, K.L. and Jaiswal, R. (2015). Particle Adhesion and Removal. Wiley. Parrot, E.L. (1986). Theory and Practice of Industrial Pharmacy, 3e (ed. L. Lachman, H.A. Lieberman and J.L. Kanig). Philadelphia: Lea & Febiger. Lutker, K.M., Quiñones, R., Xu, J. et al. (2011). Polymorphs and hydrates of acyclovir. J. Pharm. Sci. 100 (3): 949–963. Chamarthy, S.P. and Pinal, R. (2008). Plasticizer concentration and the performance of polymeric drug delivery systems. Colloids Surf. A Physicochem. Eng. Asp. 331: 25–30. Moribe, K., Wongmekiat, A., Hyakutake, Y. et al. (2005). Inﬂuence of dehydration temperature on water vapor adsorption, dissolution behavior and surface property of ampicillin. Int. J. Pharm. 288 (2): 245–252. Yamauchi, M., Lee, E.-H., Otte, A. et al. (2011). Contrasting the surface and bulk properties of anhydrate and dehydrated hydrate materials. Cryst. Growth Des. 11 (3): 692–698. Chamarthy, S. (2007). The Diﬀerent Roles of Surface and Bulk Eﬀects on the Functionality of Pharmaceutical Materials. PhD thesis. West Lafayette, IN., USA: Purdue University. Garnier, S., Petit, S., and Coquerel, G. (2002). Dehydration mechanism and crystallisation behaviour of lactose. J. Therm. Anal. Calorim. 68 (2): 489–502. Otte, A. and Carvajal, M.T. (2011). Assessment of milling-induced disorder of two pharmaceutical compounds. J. Pharm. Sci. 100: 1793–1804. Poux, M., Fayolle, P., Bertrand, P. et al. (1991). Powder mixing: some practical rules applied to agitated systems. Powder Technol. 68: 213–234. Wang, Z.L. et al. (2006). Powder formation by atmospheric spray-freeze-drying. Powder Technol. 170: 45–52. Vasilenko, A. et al. (2013). Role of consolidation state in the measurement of bulk density and cohesion. Powder Technol. 239: 366–373. Matthew Krantz, M., Zhang, H., and Zhu, J. (2009). Characterization of powder ﬂow: static and dynamic testing. Powder Technol. 194 (3): 239–245. Prescott, K.J. and Barnum, A.R. (2000). On powder ﬂowability. Pharm. Technol. 60–84. Ren, R.M., Yang, Z.G., and Shaw, L.L. (2000). Polymorphic transformation and powder characteristics of TiO2 during high energy milling. J. Mater. Sci. 35 (23): 6015–6026. Kaerger, J.S., Edge, S., and Price, R. (2004). Inﬂuence of particle size and shape on ﬂowability and compactibility of binary mixtures of paracetamol and microcrystalline cellulose. Eur. J. Pharm. Sci. 22 (2–3): 173–179.

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43 Ticehurst, M.D., Basford, P.A., Dallaman, C.I. et al. (2000). Characterisation

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and Jung Cook, H. (2015). The inﬂuence of polymorphism on the manufacturability and in vitro dissolution of sulindac-containing hard gelatin capsules. Pharm. Dev. Technol. 20 (3): 306–313. Lovette, M.A., Browning, A.R., Griﬃn, D.W. et al. (2008). Crystal shape engineering. Ind. Eng. Chem. Res. 47 (24): 9812–9833. Grzesiak, A.L., Lang, M., Kim, K., and Matzger, A.J. (2003). Comparison of the four anhydrous polymorphs of carbamazepine and the crystal structure of form I. J. Pharm. Sci. 92 (11): 2260–2271. Sypek, K., Burns, I.S., Florence, A.J., and Sefcik, J. (2012). In situ monitoring of stirring eﬀects on polymorphic transformations during cooling crystallization of carbamazepine. Cryst. Growth Des. 12 (10): 4821–4828. Javadzadeh, Y., Mohammadi, A., Khoei, N.S., and Nokhodchi, A. (2009). Improvement of physicomechanical properties of carbamazepine by recrystallization at diﬀerent pH values. Acta Pharma. 59 (2): 187–197. Chamarthy, S.P., Pinal, R., and Carvajal, M.T. (2007). Report to the Dane O. Kildsig Center for Pharmaceutical Processing Research, Purdue University. Mishra, M.K., Sanphui, P., Ramamurty, U., and Desiraju, G.R. (2014). Solubility-hardness correlation in molecular crystals: curcumin and sulfathiazole polymorphs. Cryst. Growth Des. 14 (6): 3054–3061. Feng, Y., Grant, D.J.W., and Sun, C.C. (2007). Inﬂuence of crystal structure on the tableting properties of n-alkyl 4-hydroxybenzoate esters (parabens). J. Pharm. Sci. 96 (12): 3324–3333. Roberts, R.J. and Rowe, R.C. (1996). Inﬂuence of polymorphism on the Young’s modulus and yield stress of carbmazepine, sulfathiazole and sulfanilamide. Int. J. Pharm. 129 (1–2): 79–94. Egart, M., Jankovi´c, B., Lah, N. et al. (2014). Nanomechanical properties of selected single pharmaceutical crystals as a predictor of their bulk behaviour. Pharm. Res. 32 (2): 469–481. Reddy, C.M., Rama Krishna, G., and Ghosh, S. (2010). Mechanical properties of molecular crystals – applications to crystal engineering. CrystEngComm 12 (8): 2296–2314. Reddy, C.M., Basavoju, S., and Desiraju, G.R. (2005). Sorting of polymorphs based on mechanical properties. Trimorphs of 6-chloro-2,4-dinitroaniline. Chem. Commun. (19): 2439–2441. Jankovi´c, B., Škarabot, M., Lavriˇc, Z. et al. (2013). Consolidation trend design based on Young’s modulus of clarithromycin single crystals. Int. J. Pharm. 454 (1): 324–332. Meier, M., John, E., Wieckhusen, D. et al. (2009). Inﬂuence of mechanical properties on impact fracture: prediction of the milling behaviour of pharmaceutical powders by nanoindentation. Powder Technol. 188 (3): 301–313. Zügner, S., Marquardt, K., and Zimmermann, I. (2006). Inﬂuence of nanomechanical crystal properties on the comminution process of particulate solids in spiral jet mills. Eur. J. Pharm. Biopharm. 62 (2): 194–201. Perkins, M.C., Bunker, M., James, J. et al. (2009). Towards the understanding and prediction of material changes during micronisation using atomic force microscopy. Eur. J. Pharm. Sci. 38 (1): 1–8.

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14 Analytical Tools to Characterize Solid Forms Rolf Hilﬁker, Susan M. De Paul, and Timo Rager Solvias AG, Römerpark 2, 4303 Kaiseraugst, Switzerland

Many physicochemical and physical methods are suitable to characterize solids, and excellent texts are available that describe these techniques in detail (e.g. [1, 2]). They include thermal methods such as diﬀerential scanning calorimetry (DSC), thermogravimetry (TG), thermomechanical analysis (TMA), thermally stimulated current (TSC), microcalorimetry, and thermomicroscopy; spectroscopic methods such as infrared (IR), Raman, near-infrared (NIR), terahertz (THz), and solid-state nuclear magnetic resonance (ssNMR) spectroscopies; coupled methods such as thermogravimetry coupled to Fourier transform infrared spectroscopy (TG–FTIR), thermogravimetry coupled to mass spectrometry (TG–MS), and hot-stage Raman microscopy; diﬀraction methods such as X-ray powder diﬀraction (XRPD); particle sizing methods such as Fraunhofer diﬀraction and sieving; surface methodologies such as speciﬁc surface analysis via N2-BET (Brunauer–Emmett–Teller) and inverse gas chromatography for energetics; and mechanical tests to assess hardness, ﬂow properties, etc. Of course, an invaluable method that helps to understand and characterize solids is optical microscopy; a superb description of this method can be found in [3]. This chapter will just give a brief overview on some of the frequently used techniques, grouped into methods that probe the crystal structure, the thermodynamic properties, and the stoichiometry of the solvate or hydrate.

14.1 Crystal Structure Several methods are suitable to characterize the crystal structure of a solid, such as single-crystal X-ray diﬀraction (XRD), XRPD, Raman spectroscopy, mid-infrared spectroscopy, near-infrared spectroscopy, terahertz spectroscopy, and solid-state NMR spectroscopy [2, 4–7]. Each method has its advantages and disadvantages. Although single-crystal XRD provides the ultimate characterization of the crystal structure, its practical usefulness, particularly as a method for quality control, is limited by the facts that single crystals are needed for this technique, Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development, First Edition. Edited by Rolf Hilﬁker and Markus von Raumer. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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that it only provides information on that particular single crystal, which might not be representative of the whole sample, and that it is time-consuming. All these restrictions do not apply for XRPD, which makes it one of the most widely used methods for polymorph characterization. 14.1.1

X-ray Diﬀraction (XRD)

The physical basis of both single-crystal XRD and XRPD is Bragg’s law (Eq. 14.1), which describes the relationship between the angle for constructive interference (Θ), layer spacing (d), wavelength (𝜆), and order of the interference (n): n ⋅ 𝜆 = 2 d sin(Θ)

(14.1)

In single-crystal XRD, the crystal is placed in an X-ray beam, and the spatial intensity of the diﬀracted X-ray light is recorded while the angular position of the single crystal is varied. This allows the determination of the crystal structure, i.e. the assignment of the space group and determination of the location of all (non-hydrogen) atoms in the unit cell. In XRPD, the sample exposed to the X-ray beam is a powder, and if the particles are randomly oriented, every plane in the crystal lattice will be suitably oriented with respect to the X-ray beam in at least one particle (see Figure 14.1), giving rise to constructive interference at the corresponding angle. A pattern with sharp peaks as a function of twice the angle for constructive interference as depicted in Figure 14.2 will be obtained. Diﬀerent polymorphs will have diﬀerent crystal plane spacings and will therefore lead to diﬀerent XRPD patterns (see Figure 14.2). Rare exceptions exist where the diﬀerences are so small that they might not be discernible using standard instrumentation. A common experimental problem with XRPD is so-called preferential orientation. If the particles are far from spherical (e.g. plates or needles), they might not be randomly oriented but instead will tend to lie in a speciﬁc direction (e.g. ﬂat on horizontal sample holders). In that case, some lines in the XRPD powder diﬀractogram could become greatly attenuated or even disappear. When comparing the XRPD patterns of various samples, good sample preparation is therefore

Θ

d

Θ d sinΘ

Figure 14.1 Principle of Bragg’s law: constructive interference occurs when the path diﬀerence is 𝜆 or an integer multiple of 𝜆.

14.1 Crystal Structure

Intensity (counts s–1)

6000

4000 Paracetamol Form I (offset) 2000

Paracetamol Form II 0 5

10

15

20 25 2 theta angle (°)

30

35

40

Figure 14.2 XRPD patterns of paracetamol Form I (top, oﬀset) and Form II (bottom).

essential. Orientation eﬀects can, for example, be reduced by gentle grinding of the substance. Investigating the sample by optical microscopy may also be very helpful to see if the particles are preferentially oriented. When a sample is ground, care must be taken that the solid form is not changed because of the grinding. The absence of such changes can be conﬁrmed if the positions of the lines in the XRPD diagram are not shifted by grinding when the intensity of the grinding is varied. Because of the physical principle of XRD, layer spacings in the crystal are measured, and the signal will be stronger when more layers with a constant spacing are present in the solid, i.e. the farther the spatial order extends. XRPD is therefore sensitive to long-range order. Because diﬀraction peaks are very narrow if a high-quality instrument is used and the sample has been prepared carefully, XRPD is a highly speciﬁc method and is able to detect small amounts of a polymorphic (or other crystalline) impurity. 14.1.2

Vibrational Spectroscopy (Raman, mid-IR, NIR, and THz)

Both infrared and Raman spectroscopies are vibrational spectroscopy techniques that primarily probe intramolecular vibrations in the so-called ﬁngerprint spectral region (4000 to 200 cm−1 , corresponding to a frequency range of 120 to 6 THz, and wavelengths of 2.5 to 50 μm). The two techniques are based on diﬀerent physical principles, with IR involving the absorption of radiation and Raman involving the inelastic scattering of radiation. The selection rules for IR and Raman spectroscopies are complementary: IR spectroscopy is sensitive to polar moieties that experience a change in their dipole moment during a vibration while Raman spectroscopy is sensitive to polarizability changes during a vibration and thus requires neither a permanent nor an induced dipole. Applications of one or both of these methods to pharmaceuticals have been reviewed in the literature [8–10]. In contrast to XRD techniques, conventional infrared

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and Raman spectroscopies primarily probe short-range order. Although less direct measures of polymorphism than XRD, vibrational spectroscopies have the advantages of being applicable to amorphous as well as to crystalline materials and of being less-sensitive to preferred crystal orientation and particle-size eﬀects. Measurement times are also often shorter than for XRPD. When NIR radiation (14 000 to 4000 cm−1 , corresponding to a frequency range of 420 to 120 THz and wavelengths of 714–2500 nm) is used, higher frequency overtone and combination vibrations are measured instead of the fundamental ones. NIR spectroscopy follows analogous selection rules to mid-IR (i.e. to the infrared method used in the ﬁngerprint region) in terms of dipole moments and thus primarily probes OH, NH, and CH stretching modes, but the NIR frequencies are compatible with ﬁber-optic probes, making NIR a popular choice for process analytical technology (PAT). Because of the poor resolution of NIR spectra, they cannot be easily interpreted and generally require the use of multivariate chemometric calibration methods to extract useful data. NIR is particularly sensitive to water, making the method ideal for studies of hydrates but suboptimal for studying processes in which bulk water is directly involved as the water signal can mask important structural information [8, 9]. NIR spectra, while weak, are associated with a large penetration depth into the sample [11]. Although NIR, mid-IR, and Raman spectroscopies mostly probe local, short-range order, a molecule’s vibrational frequencies are also inﬂuenced by its surrounding environment. This makes these frequencies sensitive not only to conformational polymorphism but also to the way the molecules are packed within the crystal lattice. Consequently, diﬀerent polymorphs typically have diﬀerent vibrational spectra, provided they are measured with suﬃciently high wavenumber resolution. These diﬀerences can, at ﬁrst glance, seem subtle because the overall appearance of the spectra will always be primarily determined by the chemical structure of the molecule as a comparison of the Raman spectra of three of the forms of carbamazepine as Figure 14.3a shows. However, signiﬁcant shifts in peak positions can generally be observed (e.g. between 1650 and 1550 cm−1 in Figure 14.3b), permitting identiﬁcation of the polymorphic form. In special cases, such as isomorphic solvates (i.e. solvates that are identical in structure except that diﬀerent solvent guest molecules occupy a particular lattice space in the active pharmaceutical ingredient (API) host), the speciﬁcity of IR and Raman is often superior to XRPD because the diﬀerent types of solvent molecules will exhibit diﬀerent vibrational characteristics. In addition, experiments involving the incorporation of isotopically labeled solvent vapor molecules, such as 2 H2 O, into the lattice can reveal which sites engage in isotopic exchange and thus are accessible to vapor [12]. Mid-IR spectroscopy is a well-established technique with many commercial databases of spectra, relatively inexpensive instrumentation, and wide availability. In addition, sample ﬂuorescence does not interfere with IR measurements, and hydrogen bonding can often be observed directly. Although Raman developed more slowly historically than mid-IR because of technical hurdles [10], it is actually somewhat better suited to studies of polymorphism. Two main types of instruments are currently in use for conventional

Raman intensity (a.u.) (offset)

14.1 Crystal Structure

CBZ, triclinic form (Form I) CBZ, P-monoclinic form (Form III)

CBZ, C-monoclinic form (Form IV)

1800

1400

1200 1000 800 Wavenumber (cm–1)

Raman intensity (a.u.) (offset)

(a)

1600

600

400

200

CBZ, triclinic form (Form I) CBZ, P-monoclinic form (Form III) CBZ, C-monoclinic form (Form IV)

1650 (b)

1600

1550

Wavenumber (cm–1)

Figure 14.3 Raman spectra of three anhydrous forms of carbamazepine (CBZ): Form I (top), Form III (middle), and Form IV (bottom); (a) in the ﬁngerprint range and (b) in the wavenumber range from 1650 to 1550 cm−1 . Raman intensities are scaled and oﬀset for purposes of comparison.

Raman spectroscopy: (i) Fourier transform (FT) interferometers, typically used with a near-infrared laser, and (ii) dispersive instruments involving various types of lasers and gratings. The latter instruments are often coupled to microscopes and used for Raman mapping, as will be discussed below. The main advantages of Raman spectroscopy compared to mid-IR spectroscopy in connection with solid-state characterization of pharmaceutical samples include the following: • lack of special sample preparation; transmission IR often uses KBr pellets or Nujol mulls, which can induce polymorphic transformation, but modern attenuated total reﬂectance-IR (ATR-IR) also eliminates sample preparation steps; • narrower bands, permitting easier identiﬁcation (and potentially quantiﬁcation) of multiple forms; • better spatial resolution and simpler sample preparation for Raman microscopy compared to IR-microscopy;

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• better polymorph discrimination due to Raman’s sensitivity to the carbon backbone of the molecule [11]; • accessibility of low frequencies (in the range of lattice vibrations, where the diﬀerence between polymorphs is often very pronounced) without the need for specialized equipment (see below); • ability to perform measurements through glass/quartz containers; • possibility of remote sampling (including in reactors) through the use of ﬁber-optic probes and thus amenability to use in online monitoring; • little interference from water, which is a weak Raman scatterer; and • weaker Raman scattering from (aliphatic) excipients compared to the API, permitting identiﬁcation of the solid form of the API in drug products. Raman spectroscopy is also, in principle, a quantitative method, although the intensity scale is detector dependent and not absolute, making the method diﬃcult to transfer between instruments. Furthermore, multivariate analysis is often required to deconvolve the spectral components, and calibration curves are not always linear [8]. Raman spectroscopy does have some disadvantages compared to IR spectroscopy. It cannot be performed on samples that exhibit ﬂuorescence. In addition, the laser spot sizes and penetration depth of the method are generally not particularly large (although the penetration depth is larger than that of ATR-IR), so for mixtures, tablets, or other heterogeneous samples, a Raman spectrum might not be representative of the bulk material. Consequently, sample rotation or acquisition of multiple spectra is often required. Sample rotation can also mitigate sample damage caused by the high laser powers typically needed to obtain reasonable Raman signal in a short period of time, but such equipment is not widely available [13]. Raman spectroscopy can also be used as a two-dimensional mapping technique to study the composition of tablets or other complex and heterogeneous systems. The small size of the focused Raman laser spot in a backscattering geometry permits point-by-point rastering experiments with a lateral resolution of a few microns, which is superior to that which can be obtained from other vibrational techniques [14, 15]. Alternatively, global imaging methods in which a larger area of the sample is both irradiated and detected at a single point in time can be carried out, although often at the cost of spectral resolution and with artifacts attributable to surface roughness [15]. Chemometric methods such as partial least squares (PLS) regression are frequently required for analyzing the data as the measured spectra often consist of mixtures of components due to the non-negligible penetration depth of the laser into the sample and to the diﬀerent Raman cross sections of the various components of a typical tablet [14]. Scattered Raman signals originating from out-of-focus regions of a sample have been shown to be able to pass through a confocal aperture, meaning that the measured spectra are not always surface speciﬁc [16]. The spectral responses can be nonlinear, and it is not unusual to see dramatic overrepresentation of a highly Raman-active API in a map, which means that the results cannot always be quantitatively interpreted [14] and that the analyst is forced to make subjective choices about pixel assignments [17]. Despite these drawbacks, the method has

14.1 Crystal Structure

Raman intensity (a.u.) (scaled and offset)

been widely used for characterizing formulations and detecting polymorphic or chemical impurities. Raman microscopy is particularly well suited for detecting extremely small amounts of particle impurities (hundredths of a percent of the sample by weight) that are below the limit of detection of bulk analytic techniques as the mapping approach does not average over the entire sample but rather correlates individual regions of the sample with distinct pixels on the image [15]. This sensitivity of Raman spectroscopy to the solid form has made it a desirable method for high-throughput screening (HTS) methods aimed at discovering polymorphs, co-crystals, or salts of an API. An example of a result from a co-crystal screening is presented in Figure 14.4. This experiment involved a 96-well microtiter plate with a quartz base, and the products were directly measured in the wells. The typical spatial resolution of 10 μm for the Raman microscope permitted spectra to be recorded for individual crystals, which simpliﬁes the interpretation of the data. The second spectrum from the bottom in Figure 14.4 is the Raman spectrum of a crystal found in a particular well in such a screening. This spectrum contains peaks that are characteristic of both the co-crystal former (bottom spectrum) and the API (top spectrum), conﬁrming that both reagents contribute to the chemical composition of the product. However, in a few regions of the spectrum (corresponding to the ovals in Figure 14.4), the Raman bands in the product are shifted signiﬁcantly with respect to the reagents, indicating the deﬁnite presence of a new solid structure that is potentially a co-crystal. This solid was consequently classiﬁed as a “co-crystal lead.” Repetition of this experiment on a scale of tens of milligrams provided enough material for more detailed characterization, and the Raman spectrum was successfully reproduced (second spectrum from the top in Figure 14.4). Other physicochemical characterization techniques were

Free drug

Co-crystal scale-up Co-crystal HTS

1400

1200

1000

Free co-crystal former 800

Wave number (cm–1)

Figure 14.4 Raman spectra of (from bottom to top) the co-crystal former, the co-crystal in a 96-well plate (recorded with a Raman microscope), the scaled-up co-crystal, and the API.

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able to conﬁrm that this sample was a co-crystal and to determine whether its properties were suitable for further development. The small laser spot size in Raman microscopy is also compatible with HTS miniaturization, permitting analysis of the products of a heteroseeded polymorphism screening that was carried out in 288 tiny wells (each with a volume of 0.3 μL) etched into a single microscope slide [18]. Raman spectroscopy has traditionally been performed by collecting scattered photons with either a 90∘ or, more commonly, a 180∘ (backscattering) reﬂection geometry relative to the incident laser light, but in recent years, measurements have also been carried out in the transmission mode [19, 20]. In transmission Raman spectroscopy, scattered Raman photons can come from the entire depth of the sample, and laser spot sizes are often as large as 8 mm [21]. The main advantage of transmission Raman spectroscopy is that the sampled volume is much larger and thus more likely to be representative of an entire sample rather than just a small region of its surface, making the method useful for batch analysis of whole tablets [19, 20]. Furthermore, transmission Raman is less sensitive to particle size than other vibrational spectroscopy methods [22]. The technique has been shown to be quite rapid (e.g. measurement time of 6–12 s per tablet), and it permits quantitation of polymorphic impurities in tablets down to the level of approximately 1% of the weight of the tablet [21] or even as low as 0.1% [22]. Small amounts of amorphous material in crystalline samples can also be quantiﬁed with conventional FT-Raman spectroscopy as was shown for the case of indomethacin, where a calibration curve over the entire range of 0–100% crystallinity could be established [23]. Because of the relatively small size of even a defocused laser spot, multiple measurements were required (i.e. ﬁve per sample in this study), and good results were obtained with ﬁve measurements each on three diﬀerent samples, although sample rotation was proposed as a potentially superior method. In recent years, both IR and Raman spectroscopies have been extended to lower wavenumbers (from 200 to 10 cm−1 , corresponding to a frequency range of 6 to 0.3 THz, and wavelengths of 50 μm to 1 mm). These frequencies are characteristic of lattice vibrations (also known as phonons) and are intrinsically intermolecular, although intramolecular torsional vibrations are also observed in this spectral region [24]. Such low wavenumbers (speciﬁcally those below 130 cm−1 [25]) more directly probe long-range crystal structure and thereby polymorphism in comparison to the 4000 to 200 cm−1 range, which corresponds to intramolecular vibrations that are only indirectly aﬀected by neighboring molecules. However, the resolution of such low-wavenumber spectra tends to be poorer than in the intramolecular vibration (ﬁngerprint) region [11]. Furthermore, lattice vibrations are diﬃcult to model, making detailed interpretation challenging, although some recent progress has been made with density functional theory (DFT) calculations [9, 10]. Infrared absorption spectroscopy in the 200 to 10 cm−1 (6 to 0.3 THz) far-infrared region is commonly known as terahertz (THz) spectroscopy or terahertz pulse spectroscopy (TPS) and is usually measured on dedicated instruments in a pulsed mode. Like all infrared-based spectroscopies, it is sensitive

14.1 Crystal Structure

to the presence of water, with all of the advantages and disadvantages that this implies [11]. Although the equipment needed for terahertz measurements is somewhat specialized (i.e. a femtosecond pulsed laser focused on a photoconductive switch), the intensity of the source (often 1 μW or less) is far lower than the tens to hundreds of milliwatts typically used for Raman spectroscopy, and thus, terahertz spectroscopy is less likely to lead to polymorphic transformation or sample damage [9, 24]. Terahertz spectra can also be rapidly acquired and thus used for kinetic studies [26]. The method has been shown to be capable of discriminating among polymorphs of ranitidine hydrochloride in tablets [24] and has since been applied to discrimination and quantitation studies of many other APIs as reviewed by Zeitler et al. [26]. However, it has the disadvantage of generally requiring the sample to be compressed into a pellet, often along with a polymer diluent, unless used in the attenuated total reﬂectance (ATR) mode [26]. Terahertz spectroscopy has also been used for imaging, where the radiation has the advantage of penetrating deeply into the sample and thus providing information about coating thicknesses [26]. Low-frequency Raman spectroscopy also covers the 200 to 10 cm−1 range, but this region can be more easily measured in Raman spectroscopy than in the far-IR/THz case, often merely by using a ﬁlter attachment that can be incorporated into an existing instrument [25, 27]. This permits both low-frequency and conventional Raman spectra to be recorded on the same instrument, and, as in the case of conventional Raman spectroscopy, no sample preparation is necessary. Low-frequency Raman is also less plagued by ﬂuorescence than conventional Raman [27]. In a study by Roy et al. [27], low-frequency Raman spectra were measured on polymorphs of ten diﬀerent APIs and were found to be better at diﬀerentiating among solid forms than conventional Raman or XRPD in the case of phenobarbital. Such low-frequency Raman spectra were also demonstrated to be more intense for aromatic APIs than for aliphatic excipients as demonstrated for carbamazepine, theophylline, and caﬀeine [25]. Low-frequency Raman has also been used in situ (along with multivariate analysis) to monitor polymorphic transformations of carbamazepine as a sample was heated, dissolved, and then cooled [28]. As in the case of terahertz spectroscopy, individual Raman signals from lattice vibrations are diﬃcult to assign empirically, but polymorphs that show strong similarities in the low-frequency region can be assumed to have similar molecular packing [25]. Hemi-diacid co-crystals of apixaban with fumaric acid, succinic acid, and malic acid, for instance, were shown to have nearly identical low-frequency Raman spectra, conﬁrming that they are isostructural while the ﬁngerprint region of the Raman spectra showed the expected variations due to the chemical diﬀerences among the co-crystal formers [25]. In another case, a lack of signal in the low-frequency region in the spectrum of the anhydrous beta form of caﬀeine was correlated with a known disorder in such crystals [25], and, indeed, amorphous forms by deﬁnition have no phonon peaks (although they do show a broad background intensity attributable to the Raman susceptibility) [29]. Finally, vibrational spectroscopies can often be coupled with other techniques to yield simultaneous information. Raman and NIR ﬁber-optic probes are often inserted into reactors in which the temperature, pH, and particle size distribution

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are also being simultaneously monitored, and hot stages are common accessories for vibrational spectrometers, permitting solid-form transformations to be studied as a function of temperature. Thermogravimetry has been coupled to mid-IR spectroscopy in the TG–FTIR technique to correlate mass losses with the composition of the released volatiles (see Section 14.3.1). A Raman ﬁber-optic probe has even been incorporated into a DSC instrument to permit direct correlation of observed thermal transitions with transformations into speciﬁc solid forms [30]. Similarly, a Raman spectrometer was successfully coupled with a dynamic vapor sorption (DVS) instrument to analyze a variety of humidity-dependent events including conversion of anhydrous sulfaguanidine to a hydrated form, crystallization of amorphous sucrose at 60% RH, deliquescence of ranitidine hydrochloride, and expansion of the crystal lattice of cromolyn sodium at high relative humidities [31]. A signiﬁcant time lag was often observed between the mass uptake and the corresponding change in the Raman spectrum, but this was attributed to the instrumental design since the Raman probe was located beneath the sample, whereas the moisture exposure was on the top of the sample. Consequently, the vapor molecules had to diﬀuse through the entire layer before a solid-form change could be measured by Raman spectroscopy. 14.1.3

Solid-State NMR (ssNMR) Spectroscopy

Solid-state nuclear magnetic resonance is another spectroscopic method that is useful for distinguishing among the diﬀerent solid forms of a substance. In NMR, a sample is placed in a strong magnetic ﬁeld (typically on the order of 4.7–23.5 T in modern instruments, corresponding to proton-resonant frequencies of 200 MHz to 1 GHz), and a polarization diﬀerence (magnetization) develops between nuclear spins that are aligned diﬀerently with respect to the magnetic ﬁeld. If electromagnetic energy of a frequency corresponding to the energy diﬀerence between the spin states is supplied (typically in the form of radiofrequency pulses), absorption occurs, and a spectrum can be recorded. Like mid-IR and Raman spectroscopies, solid-state NMR probes local, short-range order as the spins are sensitive not only to the strong magnetic ﬁeld provided by the superconducting magnet but also to small local magnetic ﬁelds attributable to the chemical environment in which the spins ﬁnd themselves. Although solution-state NMR is well established in synthetic organic chemistry, solid-state NMR is technically more challenging because of the need to remove the severe peak broadening attributable to the diﬀerent orientations of the crystals found in a powdered solid. (In solution-state NMR, such peak broadening is naturally averaged out by molecular motion.) In contrast to solution-state NMR, protons are particularly challenging to measure in solid-state NMR because their abundance and relatively intense polarization make their dipolar-coupling interactions diﬃcult to average out by conventional means. Standard techniques for obtaining 13 C solid-state NMR spectra include magic-angle spinning (MAS), which involves very fast rotation (up to tens of kilohertz or even over one hundred kilohertz) about a speciﬁc angle (54.7∘ ) with respect to the magnetic ﬁeld to average out some of the intermolecular interactions. The application of high-power, radio-frequency pulses that are often carefully timed with respect

14.1 Crystal Structure

to the rotation rate leads to a variety of diﬀerent experiments that can be carried out as diﬀerent interactions are selectively enhanced or suppressed. The physical principles behind MAS and solid-state NMR pulse sequences are outside the scope of this chapter but are described in detail in books on solid-state NMR spectroscopy. The most popular component of solid-state NMR pulse sequences is cross-polarization (CP), which transfers the more intense polarization of the protons to the less-sensitive and less-abundant carbon atoms. During the acquisition of such a spectrum, heteronuclear dipolar decoupling pulse sequences are usually applied to the protons to simplify the spectrum. The combination of cross-polarization and MAS (typically along with heteronuclear decoupling) is known as CP/MAS, and one-dimensional 13 C CP/MAS spectra can serve as ﬁngerprints of speciﬁc polymorphic forms of organic pharmaceuticals as shown in Figure 14.5 [32]. As in the case of vibrational spectroscopy, the overall spectral proﬁles of the two polymorphs are similar and largely attributable to the chemical composition, but the exact peak positions are sensitive to the local environment of the molecules, including crystal packing. Other routine solid-state NMR methods include spectral editing approaches (e.g. “dipolar dephasing”), which simplify the spectra and thus help the spectroscopist assign the resonances, and measurements of relaxation times, which can provide information about whether a sample is homogeneous or heterogeneous [33]. As in the case of vibrational spectroscopies, the temperature at which solid-state NMR spectra are recorded can be varied, permitting studies of solid-form transformations. Advantages of solid-state NMR spectroscopy compared to other analytical methods include the following: • high resolution of signals attributable to diﬀerent functional groups for many nuclei, with the possibility of using tailored spectral editing or two-dimensional methods to verify the assignments;

Intensity (a.u.)

Form B Form A

200

190

180 170 Chemical shift (ppm)

160

150

Figure 14.5 Comparison of 13 C CP/MAS ssNMR spectra of two diﬀerent polymorphs of the same API.

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• the ability to monitor diﬀerent nuclei with 13 C, 19 F, and 31 P and to a lesser extent 1 H and 15 N being most commonly applied to studies of pharmaceuticals but with 11 B, 14 N, 17 O, 23 Na, 35 Cl, and other more exotic nuclei increasingly being explored; highly specialized equipment is often needed in the latter cases; • nondestructive sampling; • insensitivity to particle size eﬀects; • applicability to both drug substances and drug products with the possibility of using spectral editing to suppress selected components; • applicability to both crystalline and amorphous samples and thus the ability to quantify amorphous fractions in crystalline samples (if suitable calibration experiments are carried out); • ability to provide direct proof of complexation (or alternatively, of segregation) in multicomponent systems including co-crystals, host–guest complexes, solvates, and formulations; hydrogen bonding and domain sizes can also be probed; • direct and easily observable veriﬁcation of the number of molecules in the asymmetric unit cell (Z′ ), which could theoretically provide input for solving crystal X-ray structures; • production of quantitative signals when direct detection is used; crosspolarized spectra are not necessarily quantitative, but correction factors can be used if the various relaxation rates of the system are well understood; this is time-consuming but can lead to limit of quantiﬁcation (LOQ) values as low as approximately 1%; • ability to provide dynamical information on a nanosecond to second timescale and to discriminate between dynamic disorder and static disorder. However, solid-state NMR also has several disadvantages including the following: • necessity of large sample sizes (up to ∼300 mg for insensitive nuclei) or exotic technology such as DNP (see the discussion below) for examining insensitive nuclei with low natural abundance; • time-consuming measurements with multiple days needed for some two-dimensional spectra and many measurements needed to understand the various relaxation rates within a system as a prerequisite for quantitative studies; • risk of polymorphic conversion due to high pressures from fast spinning rates and/or to temperature increases arising from both high-power radio-frequency pulses and rapid spinning; the latter eﬀect can be ameliorated to some extent by externally cooling the sample; • necessity of speciﬁc isotopic labeling in order to apply certain pulse sequences; • limited spatial resolution, making high-resolution imaging on a molecular scale impossible; and • signiﬁcant expense with the need for large, specialized, liquid-helium-cooled instrumentation and highly trained analysts. As in the case of the vibrational spectroscopies, empirical correlations can provide basic chemical information from a solid-state NMR spectrum, but a full spectral assignment often requires two-dimensional correlation experiments

14.1 Crystal Structure

or DFT calculations of chemical shielding on structures obtained from single-crystal XRD studies or from ab initio crystal-structure predictions [34]. Although relatively conventional 13 C CP/MAS experiments on natural abundance powders dominated the early applications of solid-state NMR to studying polymorphism and dehydration/rehydration, the past ﬁve years have seen a dramatic increase in the development and application of more exotic techniques. Two-dimensional homonuclear and heteronuclear correlation experiments have been increasingly applied to issues such as the hydrogen-bonding strengths and the ionization states in co-crystals [35, 36], the mechanisms of crystallization inhibition in polymer–drug complexes [37], and whether nanoscale phase separation or molecular-level complexation occurs in multicomponent systems [38, 39]. The question of phase separation can also be addressed by measurements of NMR relaxation parameters as closely connected regions will have similar relaxation times [40, 41]. Fast spinning speeds combined with special pulse sequences can permit the partial resolution of solid-state NMR proton spectra, and, in particular, two-dimensional homonuclear 1 H-1 H (double-quantum) correlation experiments can be used to probe through-space proximities of pairs of hydrogen atoms and thus provide direct information about hydrogen bonding and molecular packing in diﬀerent polymorphs of the same substance [35]. Such experiments have been applied as a form of ﬁngerprinting to identify the solid form of an API in a formulated tablet [42]. The proton dimension of solid-state NMR spectra is also increasingly being used in heteronuclear correlation experiments [35, 38], with new pulse sequences such as multiple-contact cross-polarization being employed to enhance sensitivity when material amounts are limited [43]. Even one-dimensional 1 H MAS NMR spectra at suﬃciently fast spinning rates can provide some information about hydrogen bonding based on the position of the chemical shift, although two-dimensional approaches provide more conﬁdence in the assignments [35, 42]. In addition, experiments aimed at quantifying mixtures of forms are becoming increasingly widespread with limits of quantitation down to approximately 1.0% being achievable [44], although care must be taken with calibration experiments as the relaxation times of diﬀerent polymorphs can diﬀer by several orders of magnitude as in the case of m-aminobenzoic acid, where the spin lattice relaxation time of Form II is 380 times longer than that of Form IV [45]. Although speciﬁc isotopic labels have been used in a few cases [46], including an in situ study of a solid-state co-crystallization process [47], most pharmaceutical applications focus on natural abundance spectra or on sites that can easily be labeled by exchange with a labeled solvent or vapor (such as 2 H2 O or H2 17 O) [12, 38, 48]. An interesting approach to studying the crystallization of polymorphs by solid-state NMR involves in situ experiments that take advantage of the recent development of commercial MAS rotors that can spin liquids at speeds of up to several kilohertz without leaking [46, 49]. This technology opens up the possibility of directly observing the solids that precipitate from a solution as the temperature of the sample is lowered to the point where the solution is supersaturated [46]. As the cross-polarization process is only eﬃcient for solids, application of such a pulse sequence permits the spectrum of the precipitate to

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be recorded without interference from the API that is still present in the solution. Due to the general insensitivity of NMR and due to the extensive signal averaging and large amounts of sample that are consequently needed, the nucleation and early stages of the growth process cannot usually be observed with this approach, but transient metastable states (including the amorphous form [49]) and the timescales on which they are generated can be identiﬁed. The use of isotopically labeled samples increases the sensitivity of the method, leading to better results [46], but experiments on unlabeled systems such as m-aminobenzoic acid have also been carried out at high magnetic ﬁelds [45, 49]. The method has also been applied to a series of co-crystals of α,ω-dihydroxyalkanes with isotopically labeled urea [46]. This in situ approach has recently been extended to permit studies of both the solution-state and the solid-state components of the same multiphase sample with a technique called combined liquid- and solid-state in situ crystallization (CLASSIC) NMR [45]. This method essentially consists of alternate acquisition of (i) a directly detected 13 C spectrum with a short recycle delay and no decoupling so that only the solution phase is measured and (ii) a 13 C CP/MAS spectrum, which only samples the solid phase. By interleaving the two measurements, both phases can be monitored as a function of time (albeit not simultaneously) on the same sample. Such ﬂexibility and selectivity are not generally found in other analytical techniques where either only one phase can be observed at all (e.g. XRPD) or where a mixture of the two phases is measured (e.g. conventional vibrational spectroscopies). The CLASSIC NMR technique is also applicable to host–guest complexes where mobile “guest” (solvent) molecules exhibit restricted motion on a liquid-like timescale within a more static “host” [49]. However, the relaxation times have to be within a fortuitous range to permit CLASSIC NMR to be used: in some systems, such as benzoic acid, the relaxation times in the solid state are too long to permit a spectrum to be recorded on a practical timescale. In contrast, APIs containing a methyl group have faster relaxation times due to the rapid rotation of this group and are thus amenable to the CLASSIC NMR approach [49]. Quadrupolar nuclei (i.e. nuclei with spin-quantum numbers greater than 1/2) are increasingly being studied in pharmaceutical systems. Such nuclei undergo additional interactions with local electric ﬁeld gradients in the molecule that spin- 1/2 nuclei do not experience. Although such interactions are potentially a valuable source of chemical information, more complicated experiments must be carried out to obtain well-resolved spectra, and quantum-chemical calculations (such as plane-wave DFT, which includes long-range order) are often required to interpret the results. In addition, it is sometimes necessary to carry out measurements at multiple (and rather high) magnetic ﬁelds to be able to extract all of the quadrupolar and chemical shift parameters from the lineshapes. Among the quadrupolar nuclei that have been examined in pharmaceuticals in recent years are the following: 11 B to study the molecular assembly of various forms of bortezomib [50]; 14 N to study hydrogen bonding in eight APIs, including one (ranitidine) with four nitrogen sites [51]; 17 O to study hydrogen bonding in both crystalline and amorphous forms of isotopically labeled diﬂunisal and related co-crystals and dispersions [48]; 23 Na in sodium naproxen and its formulations [52]; and 35 Cl in a variety of hydrochloride salts

14.1 Crystal Structure

[53, 54]. Although such methods can potentially provide deep insight into the molecular structure and dynamics of pharmaceuticals, the long experimental times, the necessity of carrying out multiple experiments, and the reliance on DFT computations make the methods more suitable to detailed studies of a speciﬁc system rather than to routine batch analysis. Although such work is promising and several correlations between measurable parameters and structural information have been observed, only a limited number of empirical relationships have been established for many of the more exotic nuclei, making it diﬃcult to interpret their spectra without the use of DFT simulations incorporating the GIPAW (Gauge-Including Projector-Augmented Wave) approach for calculating chemical-shielding parameters. Both simulations of molecular clusters and simulations using periodic boundary conditions have proven useful [38]. In addition to simulations, single-crystal XRD structures can be used to help interpret results from both exotic and common nuclei, but solid-state NMR data, in turn, can provide constraints for solving single-crystal structures and can give insights into molecular order in cases where the crystal structure of a speciﬁc polymorph is not yet available [34, 38]. The combination of DFT, crystal structure prediction, and 1 H solid-state NMR chemical shift data was even suﬃcient to solve the crystal structure of a polymorph of an API with a molecular weight of 422 g mol−1 for which single-crystal XRD data were not available [55]. Of course, crystal structure prediction could also have been used to solve the powder X-ray structure, but this would not have provided such direct information about the positions of the hydrogen atoms as the 1 H-NMR data. A particularly promising technique in modern NMR spectroscopy is dynamic nuclear polarization (DNP), which greatly enhances the sensitivity of NMR measurements by transferring the large intrinsic polarization from electron spins to the more weakly polarized nuclear spins. Although the phenomenon was ﬁrst discovered decades ago, it has only been possible to apply it to MAS experiments using commercial instrumentation within the past few years [56, 57]. To apply the technique, the solid sample of interest is typically doped with an organic biradical. This doping can be achieved by dissolving both components in a glass-forming solvent such as a glycerol–water mixture to distribute the radical homogeneously [56] and then freezing, spray-drying, or lyophilizing. Alternatively, and more relevantly in studies of polymorphism, a ﬁnely ground powder sample can simply be wet with a radical-containing solvent [56, 58, 59]. The resulting mixture is then placed in a cryogenic MAS probe in an NMR spectrometer that is also coupled to a gyrotron. One of the electron spins in the radical is irradiated continuously using the gyrotron microwave source to generate a polarization diﬀerence that is transferred to the nuclear spin whenever the frequency diﬀerence between the electrons matches the resonant frequency of the nucleus. Conventional solid-state NMR pulse sequences can be run using this enhanced polarization. Such DNP experiments are typically performed at temperatures of near 100 K with MAS spinning speeds of 1.5–14 kHz. The polarization transfer from electrons to protons alone leads to a theoretical maximum sensitivity enhancement factor per unit square root of time of 658, but when temperature and related relaxation eﬀects are taken into account, the sensitivities can increase by another order

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of magnitude in particularly favorable cases. Lee et al. [57] cite an example of a system for which DNP reduces the experimental time from 55 years to 1 minute, demonstrating the potential of this method for performing solid-state NMR experiments (particularly on nuclei with low natural abundance such as 17 O and 43 Ca but also on nuclei such as 15 N) that were previously considered impractical or even impossible. In practice, typical DNP enhancement factors for the proton signal, which can then be transferred to other spins, do not reach the optimal values and are in the 10–200 range [60], but even these more modest enhancements lead to a 100-fold to 40 000-fold savings in time, respectively. Several applications of DNP to studies of pharmaceuticals and, in particular, polymorphism are described in the literature. DNP enhancement was used to improve the 15 N CP/MAS signal of acebutolol and nicardipine and, in the former case, to identify a nitrogen site that could not be observed with conventional solid-state NMR experiments [51]. The 35 Cl NMR spectra of hydrochloride salts were also analyzed in a DNP experiment that alternated between MAS to improve the polarization transfer and static acquisition to accurately record the quadrupolar lineshape [54]: the resulting spectra were sensitive to hydrogen bonding in the vicinity of the chloride anion and did not contain any signal from the excipients. DNP was also used to study formulations containing amorphous cetirizine hydrochloride and to estimate the API domain sizes based on the rates at which the transferred polarization increases [59]. Such studies require careful control experiments to conﬁrm that the biradical impregnation procedure does not perturb the region of interest; dissolution of some of the API in the solvent used for impregnation is a potential risk, particularly for formulations containing amorphous API [59], so several solvents generally need to be tested [58, 60]. Sample grinding, used commonly before impregnation of samples for DNP studies, is also known to potentially lead to polymorphic transformation, although grinding at cryogenic temperatures reduces the likelihood of such transformations at the cost of introducing defects into the crystal lattice [60]. In the cetirizine hydrochloride study [59], the sample was frozen immediately after swelling of the polymeric excipient regions with the biradical solution in an attempt to prevent further changes in the structure of the formulation. Although DNP is most successful with samples, such as glucose and sulfathiazole, that have long spin–lattice relaxation times and that thus permit time-consuming 13 C–13 C correlation experiments to be performed at natural abundance, even the small enhancement factor of 5 observed for rapidly relaxing paracetamol (acetaminophen) corresponds to a reduction in measurement time by a factor of 25 and thus can also be worthwhile [58]. As higher ﬁeld magnets become more widespread and polarization transfer methodologies become more advanced, the resulting increases in sensitivity should be particularly beneﬁcial for examining low-dosage formulations. Solid-state NMR remains a powerful tool for research and development both in academic and, increasingly, in industrial settings, but despite signiﬁcant progress in recent years, it still presents challenges in terms of technical complexity and experimental duration that currently limit its use for routine purposes such as quality control.

14.2 Thermodynamic Properties

14.2 Thermodynamic Properties The most direct access to information on thermodynamic properties including the thermodynamic relationship between diﬀerent solid-state forms is provided by calorimetric measurements. These comprise the analytical techniques of isothermal microcalorimetry (IMC), solution calorimetry, and, most prominently, DSC. These methods either detect the latent heat of a transformation process directly or detect a resulting temperature diﬀerence from which the enthalpy change can be calculated with the aid of appropriate conversion factors. In addition to calorimetry, the determination of equilibrium states can also provide thermodynamic information (Chapter 4). This includes solubility measurements, which determine the concentration of a compound in solution in equilibrium with a given solid-state form at a deﬁned temperature and pressure. A variation of solubility measurements consists of competitive suspension equilibration (phase equilibration) experiments, which provide information on the less-soluble, i.e. thermodynamically more stable, solid-state form under given conditions [61]. Dynamic water vapor sorption gives access to the equilibrium water content of a solid-state form at a given temperature and relative humidity (i.e. water activity). Furthermore, despite substantial kinetic eﬀects, DVS experiments can also provide an indication of the critical water activity for the equilibrium between a hydrated and an anhydrous solid-state form or between hydrates of diﬀerent stoichiometry. 14.2.1

Diﬀerential Scanning Calorimetry (DSC)

The measuring principle behind DSC consists of comparing the heat uptake of a sample relative to an empty reference pan when the temperature is increased by the same amount [62]. The diﬀerence in heat supply is proportional to the heat requirement of the sample resulting from its heat capacity and from thermal events such as solid-state transformations, melting, recrystallization, or decomposition. Two instrumental setups exist to perform such measurements. In powercompensated DSC, a sample pan and an empty reference pan are located in two thermally separated furnaces. Heat is supplied to both furnaces separately in such a way that the temperature increase is constant and identical. An alternative instrumental concept is heat ﬂux DSC, where the sample and reference pans are located in the same furnace and exposed to the same heat ﬂow to a good approximation. The asymmetric heat requirements of the sample and the reference cause a temperature diﬀerence, from which the heat uptake of the sample can be calculated after calibration. Independent of the instrumental setup, several parameters can be varied to optimally adapt the measurement to the properties of the sample and the information to be gained. The pan type may be selected according to the chemical reactivity of the sample and the pressure to be withheld. Pressure resistance is relevant, for example, when the melting transition of a hydrate is to be determined, which generally requires a high water vapor pressure in the pan to prevent premature drying of the sample.

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Other parameters that may be varied are the sample mass and the heating rate. Both parameters may be used to ﬁnd the best compromise between sensitivity and resolution. Furthermore, high scanning rates may be used to suppress slow, thermodynamically driven processes in order to observe the properties of metastable states. Typical examples are the suppression of a solid-to-solid transformation in favor of observing the melting peak of a metastable form and the separation between adjacent melting and decomposition events. Scanning rates of up to 500 K min−1 are accessible with high-speed DSC instruments (PerkinElmer) and of up to 40 000 K s−1 with ﬂash DSC instruments (Mettler Toledo), where tiny amounts of sample are directly placed on the detector, which consists of an integrated circuit. The typical outcome of a DSC measurement for a phase-pure material undergoing a ﬁrst-order phase transition from solid to liquid (i.e. melting) is illustrated in Figure 14.6. The heat capacity of the system increases to inﬁnity at the transition temperature because of the latent heat associated with melting. In practice, the inertia of the system leads to an endothermic peak with a ﬁnite height and peak width. Depending on the calibration of the instrument, the melting temperature is deﬁned either as the onset temperature or as the temperature of the peak maximum. The melting enthalpy is given by the peak area. Both values, melting temperature and melting enthalpy, are essential parameters to describe a solid form (see, e.g. Chapter 4). More complex DSC curves may be observed in the case of metastable forms. In a system of enantiotropically related polymorphs, a DSC measurement starting with a polymorphic form that is thermodynamically unstable at its melting

Tpeak = 170.4 °C ∆fus H = 183 J g–1 Heat flow (mW)

432

Tonset = 169.1 °C

120

140

160

180

Temperature (°C)

Figure 14.6 DSC thermogram of paracetamol Form I, measured with a heating rate of 10 ∘ C min−1 . Form I is the thermodynamically stable form of paracetamol, which is monotropically related to the other known Forms II and III. The melting point is determined as 169.1 ∘ C from the peak onset. The peak area provides a melting enthalpy of 183 J g−1 (28 kJ mol−1 ).

14.2 Thermodynamic Properties

temperature may either (i) result in an endothermic solid-to-solid transformation with subsequent melting of the stable form, (ii) show an overlap of melting and recrystallization into the high-temperature-stable form, followed by melting of the latter form, or (iii) provide the melting point of the initial polymorphic form. The outcome depends on the exact properties of the sample under investigation such as particle size, crystal imperfections, small amounts of the other form, residual solvent or chemical impurities, etc. It is also aﬀected by instrumental parameters such as the scanning rate as illustrated in Figure 14.7. At fast scanning rates, only processes with little or no kinetic hindrance such as melting are observed while slower processes such as solid-to-solid transformations are more likely to become visible at slower scanning rates. In all three cases, DSC provides important information on the properties of the two forms. If melting temperatures and heats of fusion of both forms can be determined (case (iii)), the Burger–Ramberger heat of fusion rule [63, 64] can be used to deduce whether the forms are monotropically or enantiotropically related and thus if a solid-to-solid transformation can occur. The heat of transition rule provides the same answer in the other two cases: (i) and (ii). The observed temperature of a solid-to-solid transformation can vary from experiment to experiment according to the nature of the sample and will not generally correspond to the thermodynamic transition temperature for the two forms. For enantiotropic systems, it will be higher than the thermodynamic transition temperature (e.g. for

2 °C min−1

191 °C 108 J g−1

166 °C 11 J g−1

×10 Heat flow (mW)

(a) 10 °C min−1

176 °C 13 J g−1

192 °C 109 J g−1 (b)

100 °C min−1

181 °C 119 J g−1 (c)

120

140

160

180

200

Temperature (°C)

Figure 14.7 DSC thermograms for carbamazepine Form III at diﬀerent heating rates. (a) At a 2 ∘ C min−1 scanning rate, an endothermic solid-to-solid transformation is observed at 166 ∘ C, which is followed by the melting of the transformation product Form I at 191 ∘ C (case (i)). (b) At a 10 ∘ C min−1 scanning rate, a combined signal from endothermic melting and exothermic recrystallization is seen at 176 ∘ C (onset 175 ∘ C), which is again followed by the melting of Form I (case (ii)). (c) At a 100 ∘ C min−1 scanning rate, a broad signal from melting of Form III is observed with its peak maximum at 181 ∘ C (onset 174 ∘ C); the recrystallization into Form I is suppressed for kinetic reasons (case (iii)). The sum of all enthalpies is comparable in all three cases. The x-axes and the indicated temperatures are corrected for the diﬀerent heating rates.

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14 Analytical Tools to Characterize Solid Forms

the system in Figure 14.7, the thermodynamic transition temperature would be 118 ∘ C instead of 166 ∘ C), and for monotropic systems, there is no thermodynamic transition temperature at all. More complex DSC curves are also observed when measurements are performed on binary or multicomponent systems. The thermal properties of the individual components are usually no longer accessible in this case, but DSC data may provide valuable information on the phase diagram and on interactions between components. The impact of the pan type on the DSC result is illustrated in Figure 14.8 for the case of the pentahydrate of methylene blue. When the measurement is performed in a hermetically sealed, pressure-resistant pan, a single endothermic peak is observed, which corresponds to the transformation into a dihydrate at approximately constant composition of the overall system within the pan. A very diﬀerent picture is obtained in an open system, where the stepwise evaporation of water from the crystal structure is recorded. DSC is also well suited for the characterization of amorphous forms (Figure 14.9). The glass transition temperature (T g ), where the amorphous form converts from the glassy to the rubbery state, is connected with an increase in the heat capacity of the system, which manifests itself in a step in the baseline. It may also happen that the amorphous substance rapidly crystallizes as soon as it becomes rubbery and an exothermic heat of crystallization will be observed in DSC followed by the melting peak of the crystallization product. When applying DSC for the determination of the amorphous content in crystalline samples, the limit of detection typically amounts to several percent.

110 °C 212 J g–1

Pan with pinhole 86 °C 76 J g–1 Heat flow (mW)

434

85 °C 105 J g–1

Hermetic pan

0

147 °C 81 J g–1

50

100

150

Temperature (°C)

Figure 14.8 Comparison of the DSC curves of methylene blue pentahydrate in a hermetically closed, pressure-resistant pan (bottom) and in a pan with a pinhole (top) at the same heating rate of 20 ∘ C min−1 . A sharp endothermic transition is observed in the ﬁrst case, whereas multiple, broader events are observed in the second.

14.2 Thermodynamic Properties

Tpeak = 158 °C

Heat flow (mW)

∆fus H = 178 J g−1

Tg = 22 °C ∆Cp = 0.7 J (g K)−1

Tonset = 157 °C

×10 Tpeak = 76 °C ∆cryst H = –131 J g−1 0

50

100

150

200

Temperature (°C)

Figure 14.9 DSC thermogram of amorphous paracetamol, measured with a heating rate of 10 ∘ C min−1 . At 22 ∘ C, the glass transition from the glassy to the rubbery state is observable as a change in heat capacity of 0.7 J (g K)−1 . At about 76 ∘ C, the rubbery paracetamol crystallizes into the metastable Form II, which subsequently melts at 157 ∘ C. The amorphous material was prepared by melting in a ﬁrst DSC scan followed by rapid cooling.

The numerous applications of DSC also include the determination of the heat capacity of solids and liquids. One technical implementation consists of performing a baseline scan with the same pan that is subsequently ﬁlled with the test sample. A heat ﬂow calibration of the instrument is obviously necessary. Ideally, it is performed immediately before the measurement using again the same pan and a reference sample with an accurately known heat capacity (typically sapphire). Finally, DSC has been established as a tool for purity determination of crystalline solids. This application is based on the broadening of the melting peak as a result of eutectic melting point depression according to the modiﬁed van’t Hoﬀ equation TF = T0 −

R•T02 Δfus H

⋅ ximp ⋅

1 F

(14.2)

with ximp being the mole fraction of the impurity in the sample, T 0 and Δfus H the melting temperature and melting enthalpy of the pure compound, respectively, R the universal gas constant, and T F the temperature where the fraction F of the solid has melted. F is calculated from the partial peak areas of the melting peak, and ximp ⋅ 1/F gives the mole fraction of the impurity in the liquid phase at T F . A routine for the calculation of the purity based on the above equation is nowadays integrated into the instrument software. Ideally, a cumulative value for all impurities in the sample is obtained by this method. In reality, speciﬁc interactions or incompatibilities between the main component and the impurities may either overestimate certain impurities or make them invisible. Such interactions include the formation of mixed crystals between the main component and the impurity and the

435

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14 Analytical Tools to Characterize Solid Forms

insolubility of the impurity in the liquid phase. As another drawback, impurities that are small as a weight fraction of the sample may have a large impact when their molar mass is small (e.g. water) and thus the number of molecules is high. Furthermore, physical impurities in the crystalline sample such as admixtures of other polymorphic forms or crystalline imperfections can also lead to peak broadening and render the method inapplicable. The method is also not suitable in the case of an overlap of melting with decomposition. 14.2.2

Isothermal Microcalorimetry (IMC)

IMC unspeciﬁcally detects any heat released or taken up by a sample at constant temperature as a result of chemical, physical, or biological processes. The processes most relevant in the context of pharmaceutical solids are degradation and crystallization of partially amorphous samples. Such processes may be followed over hours, days, or even months. The technical implementation of an isothermal microcalorimeter consists of a thermostat with temperature stability at the sub milliKelvin level, a measuring cylinder with accommodations for sample and reference vials, and Peltier elements to detect any heat transfer among the sample, the reference, and the surrounding thermostat. Amorphous fractions are generally undesirable in pharmaceutical samples as they have a negative impact on chemical stability, change the dissolution characteristics of the product, or modify the aerodynamic properties of micronized material due to particle agglomeration. Amorphous fractions in APIs or excipients can result from suboptimal crystallization processes, which may have been carried out too fast, or from subsequent treatments such as drying or milling. Their quantiﬁcation is a precondition for process optimization. IMC is often the most sensitive analytical method to detect and quantify amorphous fractions [65, 66]. In order to obtain reproducible results within a reasonable time, the recrystallization of the amorphous fractions is usually induced with water or solvent vapor. The vapor phase is either established by introducing a small test tube with liquid into the sample vial or with a perfusion cell. Water or solvent is absorbed by the amorphous phase and decreases its glass transition temperature (T g ) to such an extent that the molecules become suﬃciently mobile at the temperature of the experiment to rearrange into a crystalline structure. The heat released during this crystallization process is recorded and the amorphous content may be calculated from it after calibration of the system (see Figures 14.10–14.12). The recrystallization process in IMC is heavily aﬀected by kinetics. For reproducible results, it is essential to choose appropriate conditions to achieve quantitative recrystallization within a reasonable amount of time, which ﬁrst of all requires that the correct solvent or water activity has been selected. The crystallization process should neither be too fast to prevent strong overlap with

14.2 Thermodynamic Properties

Vial

Crystallization

∆HC

Test tube with saturated salt solution or solvent

Mixture amorphous / crystalline

Figure 14.10 Amorphous content determination by isothermal microcalorimetry. After having identiﬁed a suitable solvent, the substance is placed in the vial together with a small test tube ﬁlled with a salt solution or solvent to provide the appropriate humidity or solvent atmosphere. Crystallization of the amorphous fraction will then occur in the isothermal microcalorimeter after a certain induction period. 70 60

Power (μW)

50 40 30 20 10 0 0

1

2

3

4 Time (h)

5

6

7

8

Figure 14.11 IMC curves for 100% crystalline (dashed line) and 99.5% crystalline (continuous line) material of an organic compound. The ﬁrst signals after 0.5 and 1 h are related to disturbances caused by sample introduction into the calorimeter. The sharp peak after 2 h is attributable to the exothermic recrystallization of the amorphous fraction; the broadening of the preceding signal is most likely caused by contributions from solvent adsorption.

the initial equilibration signals nor should it be too slow in order to detect well-integrable signals and to complete the analysis within a reasonable amount of time.

437

14 Analytical Tools to Characterize Solid Forms

4

Enthalpy (J g–1)

438

3

2

1

0

0

5

10 15 Amorphous content (%)

20

Figure 14.12 Example of the evaluation of IMC measurements for amorphous content determination. The regression line (continuous line) with 95% conﬁdence limits (dashed lines) to the measured heat ﬂow values of mixtures with varying amorphous content are shown. From the linear regression analysis, it can be calculated that the limit of detection is 0.2% and the limit of quantiﬁcation is 0.6%.

14.2.3

Solution Calorimetry (SolCal)

Solution calorimetry measures the enthalpy of solution of a test substance in a given solvent. For this purpose, the test sample is ﬁlled into a sealed glass ampule, which is ﬁxed to a stirrer unit and placed in the reaction vessel with the solvent. This whole system is located in a thermostat with extremely high temperature stability. When the system has reached a state of deﬁned heat ﬂow (exponential convergence of the temperature to the equilibrium value), the ampule is broken, which brings the test sample into contact with the solvent. The resulting change in temperature is recorded (Figure 14.13) and converted into energy based on a heat capacity determination of the system. When diﬀerent samples with identical chemical compositions (including an identical impurity proﬁle) are compared in SolCal, the diﬀerences in solution enthalpy reﬂect the diﬀerences in the energetic states of the starting materials. SolCal can be therefore used to compare the enthalpy diﬀerence between different solid-state forms at the temperature of dissolution. In combination with other data such as solubilities, melting points, and melting enthalpies or the critical activity of a component (e.g. water in a hydrate), these enthalpy data may be used to establish more accurate Gibbs free energy functions for the diﬀerent solid-state forms as a function of temperature [67]. It follows from the diﬀerences in solution enthalpy of diﬀerent solid-state forms that the solution enthalpy of a binary mixture correlates in a clearly deﬁned way with the composition. Based on this, SolCal is also used for the quantiﬁcation of amorphous content of crystalline samples and may provide a sensitivity comparable to IMC [68].

14.3 Composition Solvate/Hydrate Stoichiometry

∆T (mK)

0 –20

Amorphous

–40

Crystalline

–60

Second calibration

First calibration –80 –100 –120

Break 0

10

20

30

40

Time (min)

Figure 14.13 Example of the SolCal curves of an amorphous and a crystalline reference of the same chemical substance. The amorphous material dissolves faster and more exothermically than the crystalline one. Heating pulses with an internal heater before and after the breaking of the ampule are used for the calibration of the heat capacity of the system.

14.3 Composition Solvate/Hydrate Stoichiometry 14.3.1

Thermogravimetry (TGA, TG–FTIR, and TG–MS)

Thermogravimetry measures the variation of sample weight with temperature (Figure 14.14a). The sample is placed on a balance inside a furnace and usually heated at a constant rate from room temperature to variable end temperatures, depending on the information to be gained. Heating may either be performed in a ﬂow of inert (N2 ) or reactive (air, O2 ) gas. A typical application of TGA is the detection of volatile impurities including solvents from manufacturing and water. This information may be relevant for

100

Ethyl acetate inc. c. 0.3

Dihydrate 90

Acetone solvate

0.2

85

0.1 Temperature (K)

80 0

(a)

50

100

150 T (°C)

200

250

0.0 Wavenumber (cm–1)

(b)

Figure 14.14 TG–FTIR of three forms of carbamazepine. (a) TGA curves of the dihydrate, the acetone monosolvate, and the ethyl acetate inclusion compound are depicted. The emitted gas is identiﬁed by FTIR (the FTIR spectra of the gas phase of the acetone solvate is shown in (b)).

Intensity (a.u.)

Mass (%)

95

439

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14 Analytical Tools to Characterize Solid Forms

toxicological reasons as well as for the precise calculation of the active content (i.e. assay) of a sample as a precondition for correct dosing. Maximum temperatures of approximately 200–300 ∘ C are usually suﬃcient for this application. Alternatively, the presence of inorganic fractions (as part of the analyte itself or as impurities) may be determined by burning oﬀ all organic parts (residue on ignition). Maximum temperatures of 600 ∘ C or higher under oxidizing conditions are usually required for this. In the context of solid-state development, TGA is extremely valuable for the identiﬁcation of solvates and hydrates. In most instances, the loss of volatiles from a solvate or hydrate proceeds in a characteristic way, which is clearly diﬀerent from the evaporation from the liquid phase. The weight loss is often delayed relative to the boiling point of the solvent (although this is not mandatory) and may sometimes take place only after melting of the crystal structure. Furthermore, for solvates and hydrates with clearly deﬁned stoichiometries, the weight loss usually proceeds within a small temperature range. The height of the weight loss step provides the quantitative composition of the compound. Even more useful than simple TGA instruments are TG–FTIR (Figure 14.14b) or TG–MS instruments, where the nature of the emitted gas is determined by Fourier transform infrared spectroscopy (FTIR) or mass spectrometry (MS). Analyzing the evolved gases also permits a more reliable distinction between the loss of volatiles and thermal decomposition of the sample. 14.3.2

Dynamic Vapor Sorption (DVS)

DVS measures the variation of the sample weight at constant temperature but at variable relative humidity (RH) or solvent vapor activity. For this purpose, a sample holder is placed on a balance in a temperature-controlled chamber under a ﬂow of nitrogen, which is humidiﬁed to variable extents by mixing appropriate amounts of dry and water (or solvent)-saturated gas ﬂows. Typically, the relative humidity can be varied between 0% and 95%. In addition, sorption isotherms may be run at diﬀerent temperatures. A typical accessible temperature range is between 5 and 60 ∘ C. In order to obtain unambiguous results, it is mandatory that the substance itself or components thereof (such as the organic solvent of a solvate) do not evaporate. Sample characteristics aﬀecting diﬀusion kinetics such as particle size and height of the powder bed can also have an impact on the measurement result. DVS is a suitable method to investigate hydrate formation as well as hygroscopicity of solid samples. Humidity is either changed continuously or in a step-wise manner, and the mass of the sample is plotted as a function of time or humidity. Figure 14.15 shows the typical result of a continuous DVS scan for a hydrate-forming compound. A sharp weight decrease is observed below 30% RH when scanning from 50% RH downward. It is attributable to the conversion of a pentahydrate to a dihydrate. This conversion is reversed in the upward scan at 60% RH. The width of the hysteresis between the release and uptake of water depends on the scanning rate; the critical water activity for the equilibrium between pentahydrate and dihydrate must be located somewhere between the two transitions and is often found approximately at the middle (e.g. at about 45%

14.3 Composition Solvate/Hydrate Stoichiometry

100

80 120 60

40 110

Relative humidity (%)

Relative sample weight (%)

130

20

100

50

0

(a)

0 150

100 Time (h)

Relative sample weight (%)

130 Pentahydrate 120

Dihydrate 110

100 (b)

0

20

40 60 Relative humidity (%)

80

100

Figure 14.15 Continuous DVS scan exempliﬁed with the pentahydrate of methylene blue. The measurement was performed at 40 ∘ C with a scanning rate of 1% change in relative humidity per hour. (a) The relative sample weight is represented as a function of time with the variation of the relative humidity shown as a dashed line. (b) The relative sample weight is represented as a function of relative humidity. The dotted horizontal lines correspond to steps of one equivalent of water uptake or release. A hysteresis for the reversible conversion between the pentahydrate and a dihydrate structure is well resolved between 25% and 60% relative humidity. Transitions to states of even lower hydration are seen below 20% relative humidity.

RH in this case). Additional hystereses for transitions that involve even lower states of hydration are seen in the humidity range below 20% RH. The kinetic hindrance for hydration and dehydration may sometimes be so pronounced that the transitions are not observed at all at the given scanning rate and temperature. In some cases, observed transitions may involve metastable, structurally related states, whereas thermodynamically stable forms with a signiﬁcantly diﬀerent crystal structure are not accessible.

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14 Analytical Tools to Characterize Solid Forms

Relative sample weight (%)

80 110 60

40 105

Relative humidity (%)

100

115

20

100

0

4

(a)

8 Time (h)

0 16

12

115 Relative sample weight (%)

442

110

105

100 (b)

0

20

40 60 Relative humidity (%)

80

100

Figure 14.16 DVS curve of microcrystalline cellulose measured with a step method. The sample is equilibrated at each relative humidity level until the rate of weight change has dropped below a certain level or a maximum amount of time has passed. (a) The stepwise change in relative humidity (dashed line) and the corresponding change in sample weight (continuous line) are shown. (b) The weight change is represented as a function of relative humidity. A poorly developed hysteresis is observed, which spreads over the whole relative humidity range and is attributable to unspeciﬁc adsorption of water.

A step-wise DVS scan is shown in Figure 14.16 for the example of microcrystalline cellulose. A reduced number of data points is obtained in this case for the plot of sample weight vs relative humidity, but the sample weight at each point is expected to be closer to the equilibrium value than in the case of a continuous scan. In addition to the determination of hygroscopicity and the investigation of hydrate formation, DVS may also be used for the quantiﬁcation of amorphous content [69]. This method takes advantage of the fact that the aﬃnity of the amorphous phase for water (or for a solvent) is generally higher than that of

References

1.10

1.06

Recrystallization with release of water

Water uptake

Relative weight

1.08

1.04 Amorphous

1.02

Crystalline 1.00

0

20

40

60

80

Relative humidity (%)

Figure 14.17 Comparison of the DVS scans from 0% to 80% relative humidity for an amorphous and a crystalline sample of the same chemical substance. The amorphous sample takes up signiﬁcantly more water until the weight suddenly drops to the level of the crystalline material as a result of moisture-induced recrystallization.

a crystalline phase (Figure 14.17). The amount of water uptake of a sample at a given relative humidity therefore correlates with the amorphous content. Furthermore, suﬃcient water uptake may induce spontaneous recrystallization of the amorphous domains in analogy to the procedure used in IMC. This recrystallization is concomitant with expulsion of the absorbed water, and the amorphous content of the initial sample can be calculated from the amount of weight loss. Limits of detection of 1% and less are claimed.

14.4 Conclusion As stated in the introduction, the methods discussed are only a small selection of the methods that are required for a comprehensive characterization of a solid. The practical challenge is to select the smallest number of methods that are both necessary and suﬃcient to ensure the desired quality of the product.

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15 Industry Case Studies Ralph Diodone, Pirmin C. Hidber, Michael Kammerer, Roland Meier, Urs Schwitter, and Jürgen Thun F. Hoﬀmann-La Roche Ltd., Pharma Technical Development, Grenzacherstrasse 124, 4070 Basel, Switzerland

15.1 Introduction In the pharmaceutical industry, the selection of a suitable solid form of the drug substance is of considerable importance because changes to the solid form may aﬀect bioavailability, manufacturing, or drug stability. A thorough understanding of the solid-form landscape is crucial for selecting the solid form as well as developing a robust manufacturing process and safe drug product. As every project has its own solid-form-related pitfalls, we present several case studies to give the reader an insight into the selection process and development of a holistic solid-form control strategy as applied by F. Hoﬀmann-La Roche Ltd., Basel (Roche). Methodical aspects of solid-form screenings are not discussed in detail, as separate chapters of this book cover these topics. 15.1.1

Screening and Selection of Solid Forms

As outlined in the ICH guidelines [1], the pharmaceutical industry is obliged to develop high-quality products. The manufacturing process must deliver consistent quality of the product to ensure the safety and eﬃcacy of the drug. Selection of the most suitable solid form of the active pharmaceutical ingredient (API) is one of the crucial steps of drug development. This selection process is guided by the chemical and physical properties of the available solid forms as well as the intended use of the product. Therefore, each selection process is unique and has to be adaptive during development phases as new ﬁndings may aﬀect the current development. Roche follows a phase-appropriate approach with regard to solid-form screening, with a shift of focus during the various development phases. Early-stage (before clinical phase 1) investigations strive to identify the thermodynamically stable polymorph, hydrates, and process-relevant solvates of the selected species (parent compound, salt, or cocrystal), while during late-phase screenings (before clinical phase 3), risk mitigation is the main driver.

Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development, First Edition. Edited by Rolf Hilﬁker and Markus von Raumer. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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15 Industry Case Studies

15.1.2

Control Strategy for the Solid Form

For the solid form, a holistic control strategy needs to be established to ensure the quality of the drug product. Such a strategy should be based on thorough investigation and description of the solid-form landscape, characterization of the relevant forms, and understanding of the manufacturing process for the drug substance and drug product. A holistic control strategy (see Section 15.2) comprises four elements: (i) intrinsic control, (ii) parametric control, (iii) procedural control, and (iv) attribute control. (i) Intrinsic control: The strategy for the solid-form control is adjusted to the intrinsic properties of the selected solid form. For example, selection of the thermodynamically stable solid-form facilitates this process as the thermodynamic driving force will always direct conversions to the global minimum of the energy hypersurface. In contrast, selection of the amorphous form requires special precautions to ensure the formation of the amorphous form as well as to prevent form conversion, i.e. crystallization during drug product manufacturing and storage (see Section 15.8). (ii) Procedural control: Procedural control describes design measures and operations linked to solid-form control such as the sequence of unit operations and solvent choice (in general: process design) but also facility setup or equipment conﬁguration to prevent nucleation and growth of undesired solid forms. An example of this is the use of dry granulation to prevent hydrate formation (see Section 15.4). (iii) Parametric control: Parametric control covers all measures to control (critical) process parameters linked to the solid form, e.g. quality and quantity of seed crystals added, limiting the cooling rate in cooling crystallization, or restricting compression force during tableting. (iv) Attribute control: Attribute control comprises in-process controls (IPC), speciﬁcations, and analytical tests for intermediates, drug substance, and drug product to ensure their formation and the presence of the desired solid form. Development of a strategy for solid-form control for the drug substance is based on the ICH Q6A decision tree #4 [2, 3] and follows the quality by design (QbD) principle [4]. If experimental solid-form screening (potentially complemented with in silico calculations) has not revealed the existence of diﬀerent solid forms, no further action is required. However, if diﬀerent forms are identiﬁed, they will have diﬀerent physicochemical properties such as solubility or melting point, which may aﬀect drug eﬃcacy, processability, or stability. As it is hardly feasible to conduct safety and eﬃcacy studies for all nondesired solid forms, an attribute control for the solid form in the ﬁnal drug substance is recommended. The control strategy for the drug product is also described in decision tree #4 of the ICH Q6A guideline. This suggests that an acceptance criterion for the solid form should be determined if the eﬃcacy or safety in patients may be aﬀected [3]. However, because it is challenging to establish such speciﬁcations and to develop appropriate analytical methods, especially for drugs

15.2 Case Study #1: Holistic Control Strategy for Solid Form

with low API content, determining an acceptance criterion for solid forms is avoided if possible (see Sections 15.2 and 15.3). The rationale aims to provide comprehensive understanding of the solid-form landscape, covering all aspects of possible solid-form changes during manufacturing and storage of the drug product. Experiments must conﬁrm that the likelihood of a solid-form change is negligible (see Section 15.2).

15.2 Case Study #1: Holistic Control Strategy for Solid Form The ﬁrst case study describes a holistic solid-form control strategy developed for a drug substance and drug product. Because the drug product contained a low drug load, a scientiﬁc rationale was built to support the strategy that no polymorph acceptance criterion was required for the drug product speciﬁcations according to ICH Q6A [3]. 15.2.1

Solid-Form Control for Drug Substance

Studies of polymorphism of this drug substance revealed three polymorphs (form A, form B, and form C) in addition to its amorphous form. No hydrate or solvate forms were identiﬁed. The thermodynamically stable polymorph, form B, was selected for development (intrinsic control, see Table 15.1). Form B has a melting point of 163 ∘ C, is not hygroscopic, and exhibits good chemical stability in the solid state. Form A is a nonhygroscopic, metastable polymorph that transforms into form B upon melting. Form C and the amorphous form transform into form A at ambient conditions. Based on the low dosage anticipated in the clinical setting and high in vitro cell permeability,1 the drug substance in form B can be classiﬁed as a class I compound in the Biopharmaceutics Classiﬁcation System (BCS) despite the poor solubility in water. Seeded cooling crystallization was developed to ensure crystallization of form B (procedural/parametric control). With respect to polymorphic control, the process proved to be highly robust. Even seeding with form A resulted in the formation of form B, indicating a strong thermodynamic driving force. Table 15.1 Physicochemical properties of form A and form B. Crystal form

Melting point (∘ C)

Solubility in water at 37 ∘ Ca)(mg ml−1 )

Intrinsic dissolution rate at 37 ∘ C/pH 6.8 (𝛍g (cm2 min)−1 )

Form A

153

∼0.05

8.6

Form B

163

∼0.05

4.4

a) Equal solubility data (within the error limits) were obtained in 0.1 N HCl, acetate buﬀer pH 4.5, and phosphate buﬀer 6.8. 1 Caco-2 cell system: 32.7 × 10−6 cm s−1 , AP-BL 0.2 mM at pH 6.5 on apical side and at pH 7.4 on basolateral side.

449

450

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Air-jet milling was applied to achieve the desired particle size distribution. It is well known that milling might result in partial amorphization [5]. However, diﬀerential scanning calorimetry (DSC) and X-ray powder diﬀraction (XRPD) examination of freshly milled samples did not show any amorphization or solid-form conversion. Therefore, speciﬁcation of the amorphous content was not considered necessary. Finally, as an attribute control element, an identity test by XRPD was implemented for drug substance release to conﬁrm the desired polymorphic form. Spiking tests revealed that the limit of detection of form A in form B by XRPD is approximately 3%. 15.2.2

Solid-Form Control for Drug Product

For the commercial formulation, ﬁlm-coated, immediate-release tablets of 1 and 5 mg dose strengths for oral administration were developed. The API is suspended in the granulation liquid (aqueous binder solution) for even distribution in the powder bed during the ﬂuid bed granulation process. After drying and sieving, the granules are blended with additional excipients followed by tablet compression and ﬁlm coating of the kernels. Solubility of the drug substance in the binder solution was assumed potentially critical with respect to the solid-form control. The fraction of drug substance that is temporarily dissolved in the wet granulation process could resolidify into another crystal form during the subsequent evaporation/drying step. Solubility of form B in the aqueous binder solution at the highest process temperature expected (35 ∘ C) is approximately 0.1 mg ml−1 . Hence, the dissolved fraction of form B is approximately 0.6% of total drug substance suspended for the formulation process.2 Accordingly, more than 99% of the solid form remains unaﬀected, and the associated risk of uncontrolled spontaneous crystallization of the dissolved portion is very low. Furthermore, transformation into a hydrate could be excluded as no hydrated form had been discovered during the polymorph-screening activities. To estimate the potential of solid-form conversion during tableting, the behavior under pressure was tested. No signs of solid-form conversion were observed for this compound at 300 MPa, which is well above the applied compression force (parametric control) during tableting. In the wet coating process, the tablet kernels are again exposed to water at elevated temperatures. Considerations similar to those applied to the wet granulation process (see above) led to the conclusion that even the ﬁnal step of wet coating should not induce any solid-form conversion. This case shows that the favorable physicochemical properties of the selected polymorph, form B (intrinsic control), in conjunction with appropriate process design (procedural and parametric control) and a solid-form identity test as part of drug substance release testing (attribute control) allowed to build a consistent argument to omit the ﬁnal attribute control in the drug product. 2 In the most diluted suspension, 1.6%-m/m drug substance, form B, is suspended in the granulation liquid for tablets containing 1 mg of API.

15.3 Case Study #2: Solid-Form Control of API for Low-Dose Drug

The proposed solid-form control strategy received positive feedback from the health authorities.

15.3 Case Study #2: Solid-Form Control of API for Low-Dose Drug This section covers practical aspects of developing a strategy for solid-form control of a low-dose drug whose active ingredient undergoes solid-form transformation during manufacture of the drug product. Polymorph screening of the highly active free carbonic acid (pK a = 3.4) drug substance discussed in this section revealed three polymorphs, a labile hydrate, and several solvates not relevant for the chemical manufacturing process. The stable polymorph at ambient conditions fulﬁlled all requirements (stability, bioavailability, manufacturability, etc.). For content uniformity of this low-dose drug (0.1% m/m drug load), the API had to be completely dissolved in the ﬁrst step of the drug product manufacturing process. Because of poor aqueous solubility, the carbonic acid compound was dissolved in a sodium phosphate-buﬀered medium (pH = 7). This solution was then sprayed onto solid carrier granules in a ﬂuidized-bed granulation process. Generally, such a process of complete dissolution and precipitation leads to a change of the solid form of the API. In this case, a sodium salt of the drug moiety was formed. The resulting solid form could not be identiﬁed because the content in the formulation was too low. The ICH Q6A [2] guideline stipulates that the solid form of the drug substance should be speciﬁed if diﬀerent solid forms of the drug substance were shown to aﬀect drug product performance, bioavailability, or stability. Because the sodium salt of the compound is highly soluble in neutral aqueous media (>50% m/m), other crystallized forms, e.g. a hydrated crystal form, were not expected to be signiﬁcantly less soluble as even the free acid of the compound is soluble to a reasonable extent. However, other properties, such as chemical stability, may be jeopardized by a change of solid form, i.e. by formation of an amorphous phase. As a ﬁrst step to mitigate the risks, the solid forms of the sodium salt that may be produced during the drug product manufacturing process had to be identiﬁed. Moreover, the inﬂuence of excipients on crystallization of the sodium salt was studied. In addition to irrelevant solvated forms, an amorphous phase (Amorphous), a stable polymorph (Polymorph 1), a liquid crystalline phase (Polymorph 3), a water-sensitive polymorph (Polymorph 2), a kinetically stable dihydrate (Dihydrate), and a humidity-sensitive higher hydrate (Hydrate) were identiﬁed (see Figure 15.1). Polymorph 3 was not expected to arise under the process conditions as it only occurred in experiments involving temperatures >100 ∘ C. The higher hydrate (Hydrate) may appear as an intermediate form but will rapidly convert to the dihydrate (Dihydrate) at the ﬁnal conditions in the drug product. Similar considerations led to the exclusion of the labile polymorph (Polymorph 2) that only formed if the dihydrate was dehydrated at 275 °C

>110 °C Crystallization from solvent/water mixture

Polymorph 1

Slurry in water

Hydrate

205 °C

Polymorph 3

>80% RH

Ambient conditions

>100 °C

>50% RH

5% RH

>35% RH

>65 °C

Figure 15.1 Transformation scheme of the main solid forms of the drug substance as sodium salt. The solid forms framed with dotted lines were considered irrelevant for the drug product.

15.4 Case Study #3: Development of Crystallization Process

The solid forms of the sodium salt suspected to be present in the drug product were synthesized in multigram quantities. Chemical stability data and in vitro dissolution data of the amorphous state, Polymorph 1, and the Dihydrate of the sodium salt were compiled to conﬁrm that the safety and eﬃcacy of the drug product would not be aﬀected by any of the possible solid forms present in the ﬁnal drug formulation. This case shows that the ICH Q6A decision tree #4(2) [3] (Investigating the Need to Set Acceptance Criteria for Polymorphism in Drug Substances and Drug Products) may lead to the conclusion that no further test or acceptance criteria for the polymorph content in the drug product are required.

15.4 Case Study #3: Development of Crystallization Process and Unexpected Inﬂuence of Impurity Bitopertin 1 is a small-molecular drug candidate intended for oral administration. The polymorphic landscape was thoroughly investigated revealing three unsolvated, nonhygroscopic crystalline forms, designated as form A, form B, and form C (see Table 15.2) [6]. The energy–temperature diagram in Figure 15.2 shows the relationships between the three polymorphs of 1 as derived from their thermoanalytical data [7]. According to Gibbs free energy considerations, form A is enantiotropically related to form B, with form A being the thermodynamically stable polymorph below the calculated transition temperature TT(A/B) (∼83 ∘ C) [8]. Form A and form C are also an enantiotropic pair with form A being the thermodynamically stable form below the calculated transition temperature TT(A/C) (∼70 ∘ C). Form B and form C are monotropically related, whereas form C is more stable over the entire solid range (from 0 K to the respective melting temperatures). Although calculations of transition temperatures may be inaccurate, the predictions for Table 15.2 Chemical structure of bitopertin and thermoanalytical data of the relevant solid forms.

O

O

F F

Crystal form

Melting temperature (T fusion ) (∘ C)

Enthalpy of fusion (𝚫Hfusion ) (J g−1 )

Form A Form B Form C

140 153 155

59.0 51.4 52.5

F F

N N

F

N O=S=O

F F

1

453

ΔHf,A

ΔHf,B ΔHf,C

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Energy

454

HL HB HC HA

Liquid Form B Form C Form A

GL –273

0

TT(A/C) TT(A/B) 100

Tf,A Tf,B Tf,C

GA GB GC

180

Temperature (°C)

Figure 15.2 Schematic energy–temperature diagram for the identiﬁed polymorphs of bitopertin (form A, form B, and form C) constructed using the melting temperatures (T f = T onset , DSC) and melting enthalpies (ΔHf , DSC). T T , calculated transition temperatures; G, Gibbs free energy; H, enthalpy; L, liquid.

the thermodynamic ranking of the three polymorphs in the present case were conﬁrmed in slurry equilibration experiments at diﬀerent temperatures. Form A, i.e. the thermodynamically stable polymorph at the relevant conditions, was chosen for further development. Because form A is poorly water soluble, the compound had to be micronized to achieve the targeted bioavailability. Due to the low glass transition temperature (∼64 ∘ C for dried material) and associated tendency to crystallize, the amorphous phase was not considered as an option for the development of 1. Solid-form screening and early-stage development had shown that compound 1 may crystallize in the undesired, metastable, but kinetically favored form B if no adequate procedural control is applied. Hence, the crystallization procedure was re-evaluated during technical scale-up to ensure that the desired form A is produced. Ethanol was chosen as the solvent because the solubility of form A in ethanol exhibits pronounced temperature dependence (see Figure 15.3), with an increase from 80% m/m at the boiling point. This opens a large window for an eﬃcient cooling crystallization process. For seeded cooling crystallization to succeed, a wide metastable zone is desired. The metastable zone width (MSZW) was determined by measuring the cloud point at diﬀerent concentrations and cooling rates (Figure 15.3). Spontaneous nucleation occurred rather reliably at temperatures ≥20 ∘ C below the respective clear point temperature at a given concentration. As expected, increasing cooling rates tended to lead to higher supersaturation until the occurrence of spontaneous nucleation.

15.4 Case Study #3: Development of Crystallization Process

35 Solubility in ethanol

30

Concentration (%-m/m)

Target point seeding

25

Proven seeding range Cloud points at 5.0 K h–1

20 Cloud points at 7.5 K h–1 Cloud points at 10.0 K h–1

15

Cloud points at 12.5 K h–1

10

Cloud points at 15.0 K h–1 Cloud points at 17.5 K h–1

5 0 –20

–10

0

10

20 30 40 Temperature (°C)

50

60

70

Figure 15.3 Solubility of bitopertin in ethanol, target point for seeding of the crystallization, and proven temperature and concentration range for seeding. The cloud points were measured at cooling rates between −5 and − 17.5 K h−1 . The ﬁlled area is an approximation of the metastable zone; the black square indicates the acceptable space for seeding.

Based on the gathered data (polymorphic landscape, solubility behavior, and MSZW), a protocol for a robust standard seeded cooling crystallization from ethanol was established covering aspects such as a favorable volume factor, reasonable temperatures for polishing ﬁltration, seeding, isolation of the product, and acceptable yield. Unexpected issues arose during use testing of raw materials from diﬀerent suppliers for the chemical synthesis of compound 1. A known dimer impurity 2 depicted in Figure 15.4 appeared in slightly increased amounts in the ﬁnal step of the synthesis. Levels above 0.2% m/m of 2 in the crude API caused the formation of variable amounts of the undesired polymorph, form B, despite seeding with form A. Monitoring the concentration of 1 during crystallization showed that compound 2 strongly inhibited the growth of form A seed crystals. This “poisoning” of the surface of form A seed crystals led to undesirably high supersaturation in the course of the cooling ramp. The high supersaturation induced spontaneous nucleation of the kinetically preferred metastable polymorph, form B. Tighter speciﬁcations of the starting materials were required as an additional step in the control strategy to ensure “nonpoisoning” amounts of compound 2 in the crude API. This case study illustrates that development of the ﬁnishing steps – especially the ﬁnal crystallization process – must be addressed in the context of the entire chemical manufacturing sequence rather than as an isolated step. Subtle changes in the impurity proﬁle may dramatically aﬀect the crystallization behavior of a compound.

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F F F

F N

N

N O

O O

N N F F

N

F

O

S

O

F

2 Figure 15.4 Chemical structure of dimer impurity 2.

15.5 Case Study #4: Hydrate/Anhydrate Dilemma Preclinical formulations typically strive for aqueous solutions or suspensions. The unintended formation of a hydrate of the drug substance during preparation or storage of aqueous formulations may lead to undesired particle growth and insuﬃcient aqueous solubility, jeopardizing processability and bioavailability. The search for hydrates is therefore a focus area of early-phase polymorph screening (Chapters 6 and 8). Typically, a solid oral dosage form for the commercial product is envisaged for convenience of logistics and administration. The stable polymorph of the drug substance is typically preferred if the stability window with regard to hydrate formation in aqueous environment and upon humidity exposure is large enough for secure manufacturing and storage of the drug product. For a recent development compound, a hydrate/anhydrate system was identiﬁed, leading to a challenging solid-form selection. Figure 15.5 shows the polymorph landscape and transformation scheme of the relevant polymorphs and a hydrate. Although the hygroscopic amorphous material (glass transition temperature approximately 73 ∘ C) and high-temperature Polymorph 2 were not considered as candidates, the choice between Polymorph 1 (thermodynamically stable at ambient temperature) and the Monohydrate was diﬃcult. As orally administered Polymorph 1 rapidly (within 175 °C

Slurry in org. solvents at >60 °C

Slurry in org. solvents at ≤60 °C

Polymorph 2

50 °C/5 mbar

Ambient conditions

Monohydrate

>50 %-RH

Amorphous

>85°C

70 °C (long-term storage)

Figure 15.5 Transformation scheme of the relevant solid forms. The dotted line indicates incomplete transformation.

Flash-cooling of melt

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problems during drying (e.g. ﬁnding the proper endpoint and micronization). Indeed, partial dehydration of the Monohydrate and transformation (∼10%) into Polymorph 1 were observed after standard jet milling. Fortunately, exposure to ambient conditions triggered complete retransformation into the monohydrate form. There are technical solutions to isolate and micronize labile hydrates without transformation into an anhydrate form by proper humidity control. Alternatively, a diﬀerent solid form, i.e. a salt or cocrystal of the drug moiety, may be identiﬁed to escape the described dilemma. Multiple crystalline species with commonly used salt/cocrystal formers were identiﬁed, but all of them exhibited similar physical instability (i.e. formation of labile hydrates) or even rapid disintegration into the free form and salt/cocrystal former. Time constraints, lack of an alternative candidate, and existing toxicological studies encouraged the development team to accept the technical risk and to select the monohydrate as the solid form for further development, at least for good laboratory practice (GLP) toxicity and clinical phase 1 studies. This case illustrates the necessity to investigate the critical water activity needed to form and preserve the desired hydrated crystal form throughout its life cycle. The conditions required to preserve the hydrated form need to be identiﬁed for the various consecutive formulation process steps (i.e. blending with excipients, granulation, tableting, coating, storage, and packaging), particularly when developing the commercial formulation.

15.6 Case Study #5: Quality by Design by Selecting a Cocrystal It is rare that all relevant solid forms are known when a (preliminary) solid form is selected for a speciﬁc purpose, e.g. for manufacturing of the drug supply for a preclinical study. Because of the high attrition rate in drug development, resources to fully explore the solid-form landscape of every compound in early stages are usually limited. Thus, “ﬁt for purpose” solid-form selections are common. When the development candidate discussed in this section entered early development, the amorphous free base was used for lack of alternatives, and an oral solid dosage form with immediate release was foreseen for the drug product. Despite the high dose anticipated for human use (800–1600 mg), the compound still fulﬁlled BCS class I criteria because of its suﬃciently high solubility in water (∼16 mg ml−1 over a pH range of 1.0–7.5) and good permeability. Despite extensive crystallization screenings, no conditions were found to isolate crystalline material of the neat compound, not even in a hydrated or solvated structure. Hence, the free base could only be isolated as hygroscopic amorphous material, exhibiting low purity, a high level of residual solvents, and low chemical stability during storage. To overcome these issues, we decided to convert the free base into a salt. Because of the low pK a value of the protonated corresponding acid (pK a ∼ 3.1), only strong acids were considered in the ﬁrst salt-screening eﬀorts. Crystalline

15.6 Case Study #5: Quality by Design by Selecting a Cocrystal

salts of the compound with promising physicochemical properties were only obtained with sulfonic acids (p-toluenesulfonic acid, benzenesulfonic acid, and methanesulfonic acid). In contrast, the strong inorganic acids (e.g. hydrochloric acid and sulfuric acid) were not suitable to obtain crystalline salts. Based on the improved solid-state properties (crystallinity, melting temperature, hygroscopicity, ease of manufacturing, and no hydrate formation), the tosylate salt was preferred to the other sulfonic acid salts and amorphous free base. Polymorph screening did not reveal any additional crystal forms of the tosylate. Solubility, intrinsic dissolution rate, and stability of the tosylate salt were equal or even superior to those of the amorphous parent compound. Consequently, the tosylate salt was selected as the solid form for the early clinical phase 1 program. In compliance with the requirements for clinical drug candidates, the potential to form genotoxic impurities was assessed. From these studies, several alerts for the sulfonic acid salt were identiﬁed. Despite the progress in understanding and handling of sulfonic acid-related impurities [9, 10], the issue could not be resolved easily. To follow the principle of QbD, we decided not to limit the levels of genotoxic impurities of this high-dose drug candidate by procedural, parametric, or attribute controls. Instead, we attempted to identify a new solid form intrinsically devoid of genotoxic issues – also excluding the already identiﬁed crystalline salts with other sulfonic acids. Additionally, the new solid form had to display equal or better physicochemical properties (e.g. solubility and stability) compared to those of the tosylate, and the molecular weight of the high-dose drug was hoped to be reduced (53% increase from the free base to the 1 : 1 tosylate salt). As no crystalline form of the parent compound was identiﬁed and the potential for salt formation had already been investigated exhaustively, the screen was extended to the search of suitable cocrystals. Approximately 30 cocrystal formers were selected according to structural considerations (e.g. potential to form strong hydrogen bonds between drug substance and cocrystal former). Not all experiments leading to a crystalline “hit” during the screening phase could be reproduced successfully on a larger scale. From scale-up experiments, the four most promising compounds with respect to their properties (e.g. crystallinity, low hygroscopicity, high melting/decomposition temperature, and ease of preparation) were selected for further proﬁling studies. Interestingly, all of them contained dicarboxylic acids (adipic acid, fumaric acid, glutaric acid, or malonic acid). Furthermore, the 2 : 1 cocrystals (2 API molecules, 1 cocrystal former molecule) showed superior physicochemical properties than the 1 : 1 complexes, as shown for the fumaric acid example for which both stoichiometric forms (2 : 1 and 1 : 1) were identiﬁed. The melting/decomposition temperature of the 2 : 1 cocrystal was approximately 157 ∘ C, whereas the equimolecular cocrystal melted/decomposed already at approximately 112 ∘ C. The other 1 : 1 cocrystals identiﬁed (with anthranilic acid and α-ketoglutaric acid) were more hygroscopic than the 2 : 1 cocrystals. Consequently, the physicochemical and biopharmaceutical properties of the 1 : 1 cocrystals were not assessed. In addition, the cocrystal with the class 2 salt former malonic acid was not characterized further because the anticipated dose for human use was high and there were viable alternatives [11].

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The fumaric acid cocrystal was deprioritized because of its potential to yield new forms (including forms with diﬀerent stoichiometric ratios). The glutaric acid cocrystal exhibited superior stability, compatibility, and ease of manufacturing. In addition, the powder properties suggested best handling characteristics for drug product manufacturing. The adipic acid cocrystal, for which fewer data were available at the time point of the decision, was kept as a backup option. Until recently, the health authorities had diverging views on how cocrystals should be treated. The European Medicines Agency (EMA) classiﬁed cocrystals as drug substance [12], whereas the American Food and Drug Administration (FDA) regarded cocrystals as drug product intermediates [13]. This unequal treatment was lively discussed as an exact boundary between salt and cocrystal is diﬃcult to deﬁne [14]. Recently, the FDA has revised its standpoint and proposes now to treat cocrystals from a regulatory perspective in the same manner as polymorphs of the drug substance [15]. This reclassiﬁcation may encourage the pharmaceutical industry to search for cocrystals to optimize the solid state and biopharmaceutical properties of their APIs. In our case, solid-state nuclear magnetic resonance (ssNMR) investigations as well as the characterization of the crystal structure by single-crystal X-ray analysis were conclusive and did not show any signs of protonation of the active moiety. From a quality target product proﬁle (QTPP) [4] point of view, the glutaric acid cocrystal fulﬁlled all functional attributes desired (chemical and physical stability, dissolution behavior, powder properties, manufacturability, etc.). Thus, the glutaric acid cocrystal was ﬁnally selected as the solid form for the development of the compound. This case study shows that from a scientiﬁc point of view, a cocrystal can be the most suitable solid form of a given API by showing superior properties to those of salts or the parent compound.

15.7 Case Study #6: Dealing with the Consecutive Appearance of New Polymorphs The high attrition rate of pharmaceutical development projects requires risk-based balancing of the available resources for the various activities. Solid-form screening is one of the tasks that might be underestimated if the need for screening is not obvious. In this particular case, the early-phase project team concluded that the available crystal form of the parent compound, Polymorph 1, met the quality criteria in terms of aqueous solubility, chemical stability, bulk powder properties, etc. Initial polymorph assessment quickly revealed that the selected polymorph was obtained by drying of a labile trihydrate that was formed in the crystallization process using a mixture of an organic solvent and water. In addition, a new polymorph (Polymorph 2) was discovered. A set of competing slurry equilibration experiments between Polymorph 1 and Polymorph 2 under water-free conditions led to the conclusion that Polymorph 2

15.7 Case Study #6: Dealing with the Consecutive Appearance of New Polymorphs

Table 15.3 Thermoanalytical data of the identiﬁed polymorphs.

Polymorph

Melting temperature (T fusion ) (∘ C)

Enthalpy of fusion (𝚫Hfusion ) (J g−1 )

Polymorph 1

164.5

79

Polymorph 2

164.7

85

Polymorph 3

179.4

85

Polymorph 4

173.9

90

was the thermodynamically stable polymorph. This thermodynamic ranking was also supported by the comparison of thermoanalytical (DSC) data. Polymorph 2 showed a similar melting temperature but higher enthalpy of fusion compared to Polymorph 1, which indicated a monotropic relationship between the two polymorphs (see Table 15.3) [7]. However, a switch of the selected solid form was not deemed necessary in the preclinical phase. It was acknowledged though that the polymorphic investigations should be continued and intensiﬁed. The subsequent polymorph-screening activities revealed a couple of solvated forms, some of them with isomorphous structures (also to Polymorph 2). One of the solvates (p-xylene hemi-solvate) transformed into a new polymorph, Polymorph 3, by heat-induced desolvation (at 130 ∘ C). Polymorph 3 was occasionally obtained also by evaporative crystallization from other solvents. It showed a considerably higher melting point and similar enthalpy of fusion compared to Polymorph 2. Accordingly, Polymorph 3 would be expected to be thermodynamically favored compared to Polymorph 2, at least in the relevant temperature range. With the aim to conﬁrm this ﬁnding, other competing slurry equilibration experiments in a variety of nonsolvate-forming organic solvents were conducted at 20 ∘ C and 60 ∘ C. Unexpectedly, none of these experiments led to any of the forms already known, but all of them led to the same new Polymorph 4. Compared to Polymorph 3, Polymorph 4 exhibited a lower melting point but by far the highest enthalpy of fusion of all polymorphs (see Table 15.3). Subtle diﬀerences in the impurity proﬁle of the materials may have played a role, but no clear reason could be identiﬁed for this unexpected ﬁnding. However, Polymorph 4 proved to be the thermodynamically most stable of all discovered polymorphs, at least in the temperature range (20–60 ∘ C) investigated. Based on the thermoanalytical data, the energy–temperature diagram shown in Figure 15.6 was established. Accordingly, Polymorph 4 proved to be the thermodynamically stable polymorph below approximately 110 ∘ C (calculated transition temperature T T(3/4) between Polymorph 3 and Polymorph 4). Above this calculated transition temperature and up to its melting temperature (∼179 ∘ C), the enantiotropically related Polymorph 3 has a lower relative Gibbs free energy. Polymorph 1 and Polymorph 2 are monotropically related to Polymorph 4, meaning that they are thermodynamically less stable compared to Polymorph 4 over the entire temperature range.

461

ΔHf,1 ΔHf,2 ΔHf,4 ΔHf,3

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Energy

462

HL

H1 H3 H2 H4

Liquid Poly. 1 Poly. 3 Poly. 2 Poly. 4

G2 G1 G4 G3 GL –273

100 TT(3/4)

0 Temperature (°C)

150 Tf,1 Tf,4 Tf,3 200 Tf,2

Figure 15.6 Schematic energy–temperature diagram for the identiﬁed polymorphs (Polymorph 1, Polymorph 2, Polymorph 3, and Polymorph 4) constructed using the melting temperatures (T f = T onset , DSC) and melting enthalpies (ΔHf , DSC). T T , calculated transition temperatures; G, Gibbs free energy; H, enthalpy; L, liquid.

Investigations using additional methods and parameters did not reveal any further polymorphs of the compound. Figure 15.7 provides the polymorph landscape and transformation scheme of the crystal forms identiﬁed. The project team responsible for the early phase (≤ clinical phase 2a) decided to switch to the most stable polymorph, Polymorph 4, thus reducing the risk of phase transformation during processing and storage. Aqueous solubility data of all known polymorphs were comparable because of the rapid conversion into the trihydrate, and the BCS class I classiﬁcation was therefore not at risk. The project team in charge of the late phase of development (≥ clinical phase 2b) was concerned that yet another polymorph with undesirable aqueous solubility might appear unexpectedly. More importantly, the intrinsic danger of polymorphs to transform into the trihydrate during further processing and storage was now regarded as critical for the life cycle of the product. Motivated by these concerns, the search for alternative solid forms with diﬀerent chemical composition was initiated. With a pK a value of 10.5, the API can form salts with a variety of the commonly used salt formers. Indeed, the salt-screening eﬀorts resulted in a solid form containing succinic acid with excellent intrinsic properties (e.g. high melting point, nonhygroscopic, favorable crystal habit, ease of preparation, and physical stability). In addition, the compound showed no signs of polymorphism, which was of particular value in the present case.

Crystallization from solvent/water mixture Slurry in solvent/water mixtures Trihydrate

60% RH 50 °C/ 5 mbar

Slurry in solvent/ water mixtures

Polymorph 1

Slurry in org. solvents at 20 or 60 °C

Multiple proccesses with org. solvents

Evaporative crystallization from p-xylene

Competing slurry equilibration in org. solvents at 20 or 60 °C

Polymorph 2

50 °C/5 mbar Solvates

p-Xylene hemi-solvate

Figure 15.7 Transformation scheme of the known solid forms after completion of polymorph-screening activities.

Polymorph 3

130 °C

Evaporative crystallization from water sat. butanol

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However, single-crystal X-ray analysis revealed an unexpected structural detail. The species with succinic acid in the crystal lattice was a cocrystal (see Section 15.6) rather than the expected salt form. Proﬁling studies did not reveal any improved stability or biopharmaceutical advantages of the succinic acid cocrystal over Polymorph 4. The ﬁnal team decision was to continue the development with Polymorph 4 of the parent compound and to accept the intrinsic risk of a new crystal form to appear, regardless of the eﬀort spent on polymorph-screening activities [16]. The undesired transformation into the hydrated form in humid environment needs to be prevented in the formulation process and during storage of drug substance as well as drug product by applying appropriate procedural and parametric measures. In an ideal situation, all solid-form-screening activities – including studies of the fate of the solid form of the API during drug product manufacturing and storage – are completed before selecting the ﬁnal solid form of the drug substance. At the latest, all relevant solid forms of the drug substance should have been identiﬁed before development activities for the commercial formulation are started. This case study illustrates that, in the context of a holistic solid-form control strategy, solid-form-screening activities should be coordinated with other key activities during the entire development process. Only in this way, selection of the most appropriate solid form as a key element in a QbD approach is possible.

15.8 Case Study #7: Amorphous API: Issues to be Considered in Drug Development Vemurafenib (see Figure 15.8) is a potent and selective B-Raf kinase inhibitor that blocks the constitutive activation of the ERK3 pathway in mutant B-Raf-containing tumors [17]. It is branded Zelboraf for the treatment of malignant melanoma [18]. Vemurafenib shows complex polymorphism. Besides amorphous material, 6 polymorphs and 12 solvates were identiﬁed and characterized [19]. Figure 15.9 shows the transformation scheme of the relevant solid forms of vemurafenib. All known polymorphs and the amorphous phase convert into the thermodynamic stable form II upon slurry equilibration or temperature incubation. Cl

O

F

H N

S

N N H

O F

O

Figure 15.8 Chemical structure of vemurafenib. 3 Extracellular signal-regulated kinases.

15.8 Case Study #7: Amorphous API: Issues to be Considered in Drug Development

Form I

>70 °C

Specific Solvates

Slurry in, e.g. MeOH or H2O at 20 – 60 °C

Slurry in specific organic solvents

Amorphous

Slurry in, e.g. MeOH or H2O at 20 – 60 °C

Form II >145 °C

Flash cooling of melt or spray drying

Figure 15.9 Transformation scheme of the relevant solid forms of vemurafenib.

Crystalline vemurafenib, form I, was used in clinical phase 1 studies. Form I is suﬃciently soluble to ensure the intended bioavailability. During development of the synthesis route, a new, more stable polymorph (form II) with inferior solubility characteristics appeared. Because of diﬃculties in converting the new form II into pure form I, alternative approaches to develop an API with suﬃcient solubility to achieve good bioavailability in humans had to be found before clinical studies could be continued. As there are no generic means to stabilize a metastable polymorph, an amorphous formulation seemed to be a more practical option. Manufacturing of pure amorphous API (glass transition temperature approximately 102–107 ∘ C) turned out to be diﬃcult because of the marked tendency of the API to crystallize. Therefore, the amorphous form of vemurafenib had to be stabilized, e.g. by embedding into a polymer matrix. The excipient hydroxypropyl methylcellulose acetate succinate (HPMC-AS) was identiﬁed as an excellent polymer to stabilize the amorphous state [20]. The API was combined with HPMC-AS to yield a single-phase solid dispersion called microprecipitated bulk powder (MBP). The MBP provided a higher rate and extent of dissolution than the crystalline drug (form II), reaching an apparent drug concentration of 28–35 μg ml−1 , which is approximately 30-fold higher than the solubility of crystalline drug (1 μg ml−1 ) [21]. For the manufacturing of MBP, an innovative production process was established [22]. The MBP is manufactured by a solvent/antisolvent precipitation process utilizing a high-shear mixer. MBP was chosen for further development to replace the clinical phase 1 formulation containing crystalline API (form I). The dissolution proﬁle [23] of MBP shows superior release properties compared to crystalline API (with and without HPMC-AS) or amorphous API, as shown in Figure 15.10. In the physical mixture of HPMC-AS and amorphous API, supersaturation is also possible, albeit to a lesser extent than in MBP. In the case of MBP and the physical mixture of amorphous API and HPMC-AS, the polymer enables higher dissolution rates than the pure amorphous API by preventing precipitation and/or crystallization (spring and parachute) [24]. To establish the MBP process for further development and subsequent commercial production, stability of the amorphous system was tested for each processing parameter. These tests were performed under nonambient conditions

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15 Industry Case Studies

100

80 Dissolved API (%)

466

60

40

20

0 0

20

40

60

80

100

120

140

160

180

Time (minutes) MBP Physical mixture of HPMC-AS and amorphous API Physical mixture of HPMC-AS and crystalline API (form II) Amorphous API Crystalline API (form II)

Figure 15.10 USP4 dissolution proﬁles of several vemurafenib preparations. MBP and mixtures of API and HPMC-AS were in the ratio of 30/70 (m/m).

(e.g. 30 ∘ C/75% RH) to accelerate potential crystallization. Premature crystallization of vemurafenib in the corresponding samples indicated that the value of the processing parameter investigated was critical (CPP) and required to be monitored in production. For the detection of crystalline vemurafenib, a validated XRPD method was elaborated to be used as attribute control of drug substance and drug product to guarantee the amorphous state of the API. This case study shows that disappearance of a polymorph [25] (or appearance of a more stable/less soluble polymorph) can be overcome by using an amorphous formulation. In this case, the amorphous state of the API was stabilized in a solid dispersion with a polymer.

15.9 Case Study #8: Computational Prediction of Unknown Polymorphs and Experimental Conﬁrmation

O S

NH

O

Figure 15.11 Chemical structure of dalcetrapib.

Dalcetrapib, a cholesteryl ester transfer protein (CETP) inhibitor (Figure 15.11), is a small-molecular drug candidate with an oral solid dosage form. When entering the late stage of development, extensive experimental screening had identiﬁed only two polymorphs. Apart from a low-temperature polymorph stable only below approximately −87 ∘ C (form B), no crystalline form other than the already known polymorph form A was found.

References

Was a (more stable) polymorph missed because of a high nucleation barrier? As even extensive experimental screening eﬀorts can never guarantee that all (relevant) polymorphs are found, alternative strategies are needed. Mapping the crystal energy landscape by computational techniques followed by targeted crystallization experiments to bring the predicted, potentially relevant forms into existence may be such an alternative. Clearly, a predicted more stable crystal structure would be very worrisome if it could not be conﬁrmed in real experiments. Dalcetrapib is a rather ﬂexible molecule with 10 rotatable bonds. Comprehensive in silico prediction of the crystal structure was performed, suggesting two candidates for thermodynamically more stable polymorphs [26]. Pressure-dependent lattice energy calculations indicated that these high-density polymorphs should be more stable at high pressure, suggesting a method to access them experimentally. One of the predicted high-pressure polymorphs, designated form C, could indeed be prepared by crystallization between 20 and 500 MPa. As expected based on the prediction, the crystal form C turned out to be metastable at ambient pressure. It transforms into form A within hours, even in the solid state. This case proves that computational prediction of crystal structure has already established its place in the portfolio of solid-form-screening methods and is expected to gain more importance in the future.

References 1 http://www.ich.org/home.html (accessed 26 February 2016). 2 http://www.ema.europa.eu/docs/en_GB/document_library/Scientiﬁc_guideline/

2009/09/WC500002823.pdf (accessed 26 February 2016). 3 http://www.ich.org/ﬁleadmin/Public_Web_Site/ICH_Products/Guidelines/

Quality/Q6A/Step4/Decision_Trees.pdf (accessed 26 February 2016). 4 http://www.ema.europa.eu/docs/en_GB/document_library/Scientiﬁc_guideline/

2009/09/WC500002872.pdf (accessed 26 February 2016). 5 Willart, J.F. and Descamps, M. (2008). Mol. Pharm. 5 (6): 905. 6 Bubendorf, A., Deynet-Vucenovic, R., Diodone, R. et al. (2008). Crystalline 7 8 9 10 11

12 13 14

forms GLYT1. Patent WO2008080821 A1. Burger, A. and Ramberger, R. (1979). Microchim. Acta 2: 259–271. Yu, L. (1995). J. Pharm. Sci. 84: 966–974. Elder, D.P. and Snodin, D.J. (2009). J. Pharm. Pharmacol. 61: 269–278. Elder, D.P., Delanay, E., Teasdale, A. et al. (2010). J. Pharm. Sci. 99 (7): 2948–2961. Stahl, P.H. and Wermuth, C.G. (2011). Handbook of Pharmaceutical Salts: Properties, Selection, and Use, 2e, 404. ISBN: 978-3-906390-51-2. Verlag Helvetica Chimica Acta VCA, Zürich (Switzerland). Guidance for Industry, Regulatory Classiﬁcation of Pharmaceutical Co-Crystals; FDA, April 2013. http://www.fda.gov/downloads/Drugs/.../Guidances/UCM281764.pdf (accessed 26 February 2016). Childs, S.L., Stahly, G.P., and Park, A. (2007). Mol. Pharm. 4 (3): 323–338.

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15 http://www.fda.gov/ucm/groups/fdagov-public/@fdagov-drugs-gen/

documents/document/ucm516813.pdf (accessed 25 August 2016). 16 McCrone, W.C. (1965). Physics and Chemistry of the Organic Solid State,

vol. 2, 725–767. New York: Wiley Interscience. 17 Nazarian, R., Shi, H., Wang, Q. et al. (2010). Nature 468: 973–977. 18 http://de.wikipedia.org/wiki/Vemurafenib (accessed 15 May 2016). 19 Diodone, R., Fahnrich, K., Ibrahim, P.N. et al. (2012). Solid forms of a phar-

maceutical active substance. Patent WO2012161776 A1. 20 Hu, Q., Soon Choi, D., Chokshi, H. et al. (2013). Int. J. Pharm. 450: 53–62. 21 Shah, N., Mair, H., Choi, D. et al. (2013). J. Pharm. Sci. 102: 967–981. 22 Diodone, R., Lauper, S., Mair, H. et al. (2011). Novel process for the manufac-

ture of pharmaceutical preparations. Patent US20110112136 A1. 23 https://www.usp.org/sites/default/ﬁles/usp/document/harmonization/gen-

method/stage_6_monograph_25_feb_2011.pdf (accessed 8 August 2018). 24 Brouwers, J., Brewster, M.E., and Augustijns, P. (2009). J. Pharm. Sci. 98:

2549–2572. 25 Bucar, D.-K.L., Robert, W., and Bernstein, J. (2015). Angew. Chem. Int. Ed. 54:

6972. 26 Neumann, M.A., van de Streek, J., Fabbiani, F.P.A. et al. (2015). Nat. Com-

mun. 6.

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16 Pharmaceutical Crystal Forms and Crystal-Form Patents: Novelty and Obviousness1 Joel Bernstein1,2,3 and Jill MacAlpine4 1 Ben-Gurion University of the Negev, Department of Chemistry (Emeritus), Beer Sheva 84120, Israel 2

New York University Abu Dhabi, Department of Science, P.O. Box 129188, Abu Dhabi, United Arab Emirates New York University Shanghai, Department of Science, 1555 Century Avenue, Pudong New Area, Shanghai 200122, China 4 Finnegan, Henderson, Farabow, Garrett & Dunner, LLP, 901 New York Avenue, NW, Washington, DC 2000-4413, USA 3

The invention all admired. And each to be the inventor missed. How easy it seemed when done. Yet undone all would have said impossible. Paradise Lost – John Milton

16.1 Introduction It is no accident that societies that have well-developed and regulated patent systems have been the leaders of the industrial and technological revolutions of the last three centuries. The patent system, an engine for innovative progress, is a social contract: society, in the form of some sovereign entity, provides an inventor with the incentive to publish their invention in return for granting a limited period with the right to exclude others from making, using, oﬀering for sale, selling, or importing that invention. In the United States, the patent system 1

As the chapter on other aspects of pharmaceutical patents in the ﬁrst edition of this title [1], this chapter seeks to describe some aspects and raise some issues for academic discussion in an area that is the meeting ground between science and the law. In the context of the general subject matter of this book, it is an area that has generated a remarkable increase in interest and activity in the last 40 years – due, to a great extent, to some of the litigations described herein, and the underlying scientiﬁc, legal, and economic issues involved. No attempt has been made to be comprehensive, nor does the chapter purport to provide legal advice or make any deﬁnitive statements on the current status of the law on the issues raised. The intent is to demonstrate how the chemical and crystallographic issues are argued and interpreted in the speciﬁc framework of patent law, with particular emphasis in this instance on obviousness and novelty of crystal form patents. Where legal opinions are presented, for the most part, they are in the context of direct quotations from publicly available decisions of the courts or transcripts of trials, and they do not necessarily represent the opinion of the authors.

Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development, First Edition. Edited by Rolf Hilﬁker and Markus von Raumer. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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16 Pharmaceutical Crystal Forms and Crystal-Form Patents: Novelty and Obviousness

is enshrined in the US Constitution of 1789. In the United States, inventors are regarded almost as folk heroes: witness Thomas Edison, Samuel F.B. Morse, Eli Whitney, Edwin Land, and Steve Jobs. The patent system has played a particularly crucial role in the development of the pharmaceutical industry since the end of WWII. At that time, the number of available drugs was extremely limited, with many maladies and serious illnesses lacking an eﬀective pharmaceutical treatment. For example, although penicillin was discovered in the 1930s and initially developed for use in military situations, it was not available to the public until well after the war. In the late 1940s and early 1950s, family doctors commonly prescribed two medicines, aspirin and penicillin. A classic example of an aﬄiction for which there was no eﬀective drug treatment, and how that situation has changed, is stomach ulcers. When antacids or drinking milk before eating failed to cure the problem, a common treatment was surgery to remove the ulcers from the stomach wall. When these procedures did not succeed, patients often bled to death. The revolution came with James Black’s recognition of H2 antagonists that limited acid secretion [2] and led to SmithKline’s development of cimetidine, marketed in the 1970s as Tagamet, the ﬁrst billion-dollar drug. The family of H2 antagonists and the subsequent proton pump inhibitors [3] have virtually eliminated ulcers as a major medical problem, and the surgical procedure is no longer part of the medical school curriculum [4]. In addition to the need to solve a widespread medical problem, a crucial component of the engine that drove that development was the patent system. The exclusivity obtained for those new drugs led to the revenues for the pharmaceutical companies that facilitated signiﬁcant expansion of their research capabilities and eﬀorts and the subsequent development of an impressive array of pharmaceuticals for treating an ever-expanding number of diseases and disorders. In accord with the social contract, virtually the entire family of ulcer drugs is now commonly available from generic manufacturers as well as from the original developers. Because the patent system provides the legal framework for protecting technological developments, it is a meeting ground for issues of science and the law. As Peter Huber has pointed out, these are not always complementary or even compatible [5]. Words common to both disciplines are often understood and interpreted diﬀerently by scientists and lawyers. The mode of thinking or attacking and solving problems is diﬀerent, and often in conﬂict.

16.2 Novelty and Obviousness In general, two of the most important requirements for obtaining a patent are that the claimed invention must be (i) novel, i.e. not inherently present or disclosed in the available prior art at the time that the invention was made or, under ﬁrst to ﬁle systems, the time that the ﬁrst patent application was ﬁled, and (ii) nonobvious to a hypothetical person of ordinary skill in the art in the relevant ﬁeld. Accordingly, in challenging a patent or in defending against a claim of infringement, it is often

16.3 The Scientiﬁc Perspective

argued that the patent in question is not valid as the invention was not novel or would have been obvious to a person of ordinary skill in the art. These two issues are particularly common in the realm of prosecution and litigation of patents covering pharmaceutical solid forms. The issue of novelty is perhaps more straightforward than that of obviousness, although by no means is it always clear-cut. In the simplest sense, novel and new have the same etymology.2 Therefore, a new crystal form is, by deﬁnition, novel: it has never previously been prepared. Although that would seem to settle the issue, the chemistry may be such that the prior art (including literature, conference proceedings, poster sessions, etc.) intentionally or unintentionally contained information suﬃcient to establish the inherent existence of the previously unknown novel crystal form. Considerable controversy and debate can surround such a situation. An obviousness inquiry can be even more subject to controversy and debate. As noted above, in the ﬁrst instance, the inquiry requires deﬁnition of a person of ordinary skill in the art before determination of whether or not the invention would have been obvious to that person. Then, to determine whether an invention is considered obvious, courts assess a variety of factual inquiries, including whether there was motivation to make the previously unknown crystalline form, whether there would have been a reasonable expectation of success in doing so, whether the selection and preparation of the crystalline form was the result of examining a ﬁnite number of identiﬁed, predictable solutions, and whether formation of the new crystalline form was unexpected or possessed properties that could not be predicted in advance of its creation. Each one of these issues requires determination of all of the facts at the relevant time, an understanding of the methodology of the discipline, and considerable judgment on any expectation of success. In this chapter, we will deal primarily with the issue of obviousness of patents covering solid state(s) of pharmaceuticals, including the science, the current legal standards, and the case law as of this writing.

16.3 The Scientiﬁc Perspective 16.3.1

Novelty from a Scientiﬁc Perspective

The course of research and development of a drug starting from the identiﬁcation of a lead compound to a ﬁnal marketed product is currently estimated to cost about $1.4 billion (http://csdd.tufts.edu/news/complete_story/pr_tufts_csdd_ 2014_cost_study) and to take an average of 7.5 years [6]. As the vast majority of drugs are marketed as tablets or pills containing a solid form of the active pharmaceutical ingredient (API), that course of drug research and development may involve an investigation – often a continuing investigation – of the crystal-form landscape of the API. In the course of that investigation, and not infrequently even serendipitously, new crystal forms (i.e. polymorphs, solvates, and hydrates) 2 According to the Merriam-Webster on line dictionary (http://www.merriam-webster.com/ dictionary): Novel = new and diﬀerent from what has been known before.

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16 Pharmaceutical Crystal Forms and Crystal-Form Patents: Novelty and Obviousness

may be discovered. For a new chemical entity, by deﬁnition, such crystal forms are novel. Even for a chemical entity known for many years, a new crystal form is novel. The common question that arises in assessing the novelty of a crystal form is whether that particular crystal form, with all of its identifying characteristics, previously existed even if it was not recognized. 16.3.2

Obviousness from a Scientiﬁc Perspective

From a scientiﬁc point of view, obvious is synonymous with predictable. Webster’s Dictionary deﬁnes “predict” as “to be made known beforehand”.3 Therefore, predictable means “can be known beforehand.” In terms of current knowledge and understanding, no crystal form is predictable. To put that statement into more concrete terms, in spite of the fact that the community of chemists that deal with molecular crystals has made notable progress in understanding and working with those materials [7], it is still not possible to predict from a molecular formula the crystal-form landscape, including the number of polymorphs, hydrates, and solvates that might be possible (if any), how one might make the as-yet unknown crystal forms, or what their properties might be [8]. On that basis, no matter how one deﬁnes the person of ordinary skill in the art, a new crystal form can never be obvious. As such, it seems that legally the result should be the same, as one cannot “predict” or “expect” the existence of a new crystalline form, including what its properties will be. Indeed, in spite of considerable eﬀort by quite a few very talented chemists, no one can look at the two-dimensional molecular diagram of a compound and predict with even a minimal modicum of conﬁdence the crystal-form landscape of that molecule. The exploration of that landscape requires experimentation. In addition, there is no textbook recipe for carrying out that experimentation. A plethora of techniques and options exist for chemists to pick and choose from in a search for new crystal forms. Furthermore, each compound presents a new situation with its own unique challenges. Lessons learned from one compound do not necessarily apply to even a structurally related compound or one with the same therapeutic activity. Some compounds exhibit a seemingly endless number of crystal forms. Others, in spite of being common, and widely studied, have exhibited no tendency whatsoever for multiple crystal forms [9]. In the pharmaceutical ﬁeld, the object of an investigation into crystal forms is to be able to consistently and robustly produce a solid form of the API suited for the ﬁnal pharmaceutical formulation. This requires identifying, characterizing, and evaluating various crystal forms that can be obtained. By thermodynamic principles, only one of the known crystal forms obtained is the thermodynamically “most stable” form at a speciﬁc temperature and pressure, for example, ambient temperature and pressure. Other forms per force must be thermodynamically less stable under those conditions and are often referred to as “metastable forms,” and additional, more stable forms may subsequently be discovered [10]. Metastable does not necessarily mean unstable. Metastable forms can exist indeﬁnitely in spite of their thermodynamic metastability under certain conditions; they do not 3 See web site cited in footnote 2.

16.3 The Scientiﬁc Perspective

spontaneously convert to a more stable form for kinetic reasons. Diamond is perhaps the classic example; it is metastable with respect to graphite, the more common form of carbon. Yet, as de Beers commonly advertises, “Diamonds are forever” [11]. This kinetic stability, as opposed to thermodynamic stability, also cannot be predicted. Indeed, none of the properties of as-yet unprepared crystal forms can be predicted. Nor can anyone prescribe in advance how to make an as-yet unknown crystal form. Hence, nothing at all is obvious about unknown crystal forms: the existence, the nature and properties, and the method of making a new crystal form are simply unknowable. One of the enigmatic problems in addressing the question of obviousness on the basis of what appears in a granted patent is often the superﬁcial simplicity with which the invention is described in the speciﬁcation, and even more so in the claims. There is no need, indeed no requirement, to describe all of the steps, successes, and/or failures that occurred en route to the invention. A patent need only describes the invention in a manner that would allow a reader having ordinary skill in the art to identify, make, and use the invention. Thomas Edison’s invention of the incandescent bulb involved the unsuccessful testing of over 1600 materials [12]. Yet, the patent covering that invention is only three pages long (including ﬁgures) and describes only the ﬁnal invention [13].4 Hence, it is virtually impossible to extract from the patent any information about the time, eﬀort, creativity, serendipity, unpredictability, and/or expense that lead to the claimed invention. The same is very often true for patents covering new crystal forms. As Milton pointed out approximately 350 years ago, “How easy it seemed when done.” Further, and equally as important, whether the new crystalline form appears as the result of years of toil or completely due to random chance is irrelevant in terms of obtaining a patent. Indeed, the patent statute itself recognizes this very point, by stating that “[p]atentability shall not be negated by the manner in which the invention was made.” 35 U.S.C. § 103. Nevertheless, opponents challenging patents covering novel crystalline forms often argue that it would have been obvious to obtain the form based on the alleged “routine” practice of screening for polymorphic forms.5 Such arguments are exempliﬁed by a recent patent opposition. There, the opponents challenged the patent covering the patented crystalline form of the salt, asserting that it would have been obvious in view of the prior patent disclosing the free base compound. They argued that, at the relevant time, preparation and characterization of salt forms involved merely routine chemistry that could have been performed by any chemist or technician with ordinary skill in a short amount of time.6 They also argued that at the relevant time, the search for polymorphs was so routine that there “isn’t even a spark of invention” in ﬁnding three polymorphs of the claimed salt. 4 The late R.B. Woodward’s 1965 Nobel Prize citation reads: “The Nobel Prize in Chemistry 1965 was awarded to Robert B. Woodward for his outstanding achievements in the art of organic synthesis” http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1965/. 5 Similar arguments are made to allege obviousness of new salt forms. See, e.g. Pﬁzer, Inc. v. Apotex, Inc., 480 F.3d 1348 (Fed. Cir. 2007). 6 See similar arguments at id., 480 F.3d at 1367–68.

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Notwithstanding that the patent statute and controlling precedent of the Federal Circuit speciﬁcally mandate that the “spark of invention” standard is the wrong inquiry for determining obviousness,7 such challenges grossly understate the time and eﬀort often expended in inventing a new crystalline form. For example, the patent at issue in the opposition contained an independent claim drawn to a solid API intended for use in an inhalator for treating bronchial congestion and read: A [n anion] acid salt of [name of compound] or a solvate thereof which is the Form 1 crystalline solid state form wherein the salt is characterized by an x-ray powder diﬀraction pattern having diﬀraction peaks at 2θ values of [Table with ∼20 2θ ± 0.3∘ values] What were the science and the work behind this deceptively simple claim? For inhalable pharmaceutical compositions containing a solid API, the solid material must possess a number of physical characteristics. For example, it is commonly desirable to use a crystalline form of the API that is neither hygroscopic or deliquescent, has a relatively high melting point (i.e. ≥150 ∘ C), and/or can be micronized to a fairly narrow and controllable particle size distribution without signiﬁcant decomposition or loss of crystallinity. In the patent at issue in the opposition proceeding, the prior art being asserted was a prior patent that described the preparation of over 150 neutral, free base compounds with potential therapeutic eﬃcacy. From such a starting point, a single compound had to be chosen for further development. That compound was ultimately determined to not have been suitable for processing (scale-up, puriﬁcation, milling, formulation, etc.). A decision to continue working with that compound was made as was a decision to investigate the properties of its salts. Approximately 35 anions were included in the salt screen. In addition, the anion of the claimed salt comprises

Polymorphism in the Pharmaceutical Industry: Solid Form and Drug Development

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