Modeling Electrochemical Energy Storage at the Atomic Scale

Topics in Current Chemistry Collections

Martin Korth Editor

Modeling Electrochemical Energy Storage at the Atomic Scale

Topics in Current Chemistry Collections

Journal Editors Massimo Olivucci, Siena, Italy and Bowling Green, USA Wai-Yeung Wong, Hong Kong Series Editors Hagan Bayley, Oxford, UK Greg Hughes, Codexis Inc, USA Christopher A. Hunter, Cambridge, UK Seong-Ju Hwang, Seoul, South Korea Kazuaki Ishihara, Nagoya, Japan Barbara Kirchner, Bonn, Germany Michael J. Krische, Austin, USA Delmar Larsen, Davis, USA Jean-Marie Lehn, Strasbourg, France Rafael Luque, Córdoba, Spain Jay S. Siegel, Tianjin, China Joachim Thiem, Hamburg, Germany Margherita Venturi, Bologna, Italy Chi-Huey Wong, Taipei, Taiwan Henry N.C. Wong, Hong Kong Vivian Wing-Wah Yam, Hong Kong Chunhua Yan, Beijing, China Shu-Li You, Shanghai, China

Aims and Scope The series Topics in Current Chemistry Collections presents critical reviews from the journal Topics in Current Chemistry organized in topical volumes. The scope of coverage is all areas of chemical science including the interfaces with related disciplines such as biology, medicine and materials science. The goal of each thematic volume is to give the non-specialist reader, whether in academia or industry, a comprehensive insight into an area where new research is emerging which is of interest to a larger scientific audience. Each review within the volume critically surveys one aspect of that topic and places it within the context of the volume as a whole. The most significant developments of the last 5 to 10 years are presented using selected examples to illustrate the principles discussed. The coverage is not intended to be an exhaustive summary of the field or include large quantities of data, but should rather be conceptual, concentrating on the methodological thinking that will allow the non-specialist reader to understand the information presented. Contributions also offer an outlook on potential future developments in the field. More information about this series at http://www.springer.com/series/14181

Martin Korth Editor

Modeling Electrochemical Energy Storage at the Atomic Scale With contributions from Isidora Cekic-Laskovic • Mangesh I. Chaudhari • Axel Groß Johannes Kasnatscheew • Abhishek Khetan • Dilip Krishnamurthy Ajay Muralidharan • Kristin A. Persson • Lawrence R. Pratt Xiaohui Qu • Nav Nidhi Rajput • Susan B. Rempe • Trevor J. Seguin Venkatasubramanian Viswanathan • Ralf Wagner • Martin Winter Brandon M. Wood

Editor Martin Korth Molecular Projects UG Münster, Germany

Partly previously published in Top Curr Chem (Z) Volume 376 (2018) ISSN 2367-4067 Topics in Current Chemistry Collections ISBN 978-3-030-00592-4 Library of Congress Control Number: 2018957348 © Springer Nature Switzerland AG 2018 The chapters “Assessment of Simple Models for Molecular Simulation of Ethylene Carbonate and Propylene Carbonate as Solvents for Electrolyte Solutions” and “Elucidating Solvation Structures for Rational Design of Multivalent Electrolytes—A Review” are licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). For further details see license information in the chapters. This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Contents

Preface ................................................................................................................... vii Fundamental Challenges for Modeling Electrochemical Energy Storage Systems at the Atomic Scale ................................................................. Axel Groß: Top Curr Chem (Z) 2018, 2018:17 (23, April 2018) https://doi.org/10.1007/s41061-018-0194-3

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Interfaces and Materials in Lithium Ion Batteries: Challenges for Theoretical Electrochemistry ....................................................................... 23 Johannes Kasnatscheew, Ralf Wagner, Martin Winter and Isidora Cekic-Laskovic: Top Curr Chem (Z) 2018, 2018:16 (18, April 2018) https://doi.org/10.1007/s41061-018-0196-1 Assessment of Simple Models for Molecular Simulation of Ethylene Carbonate and Propylene Carbonate as Solvents for Electrolyte Solutions ...................................................................................... 5 3 Mangesh I. Chaudhari, Ajay Muralidharan, Lawrence R. Pratt and Susan B. Rempe: Top Curr Chem (Z) 2018, 2018:7 (12, February 2018) https://doi.org/10.1007/s41061-018-0187-2 Elucidating Solvation Structures for Rational Design of Multivalent Electrolytes—A Review ............................................................. 79 Nav Nidhi Rajput, Trevor J. Seguin, Brandon M. Wood, Xiaohui Qu and Kristin A. Persson: Top Curr Chem (Z) 2018, 2018:19 (26, April 2018) https://doi.org/10.1007/s41061-018-0195-2 Towards Synergistic Electrode–Electrolyte Design Principles for Nonaqueous Li–O2 batteries . ........................................................................ 125 Abhishek Khetan, Dilip Krishnamurthy and Venkatasubramanian Viswanathan: Top Curr Chem (Z) 2018, 2018:11 (20, March 2018) https://doi.org/10.1007/s41061-018-0188-1

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It has become apparent that electrochemical energy storage is going to play a central role for our energy future. Current storage devices are unfortunately not yet as safe, cheap and efficient as we would need them to be for a quick exit from fossil fuels. Fortunately, tremendous efforts are made both experimentally and more recently also theoretically to understand the above mentioned problems in detail and to work on economically viable solutions or alternatives. The challenges cannot be overlooked, especially on the theoretical side. While more and more substances are coming into consideration as possible electrode or electrolyte materials, knowledge about the basic storage processes is still very limited. The complexity of real materials is causing great problems here, but also the fact that there is no generally applicable, black-box computational model available to treat physical systems at the atomic scale under electrochemical conditions, i.e., including the effect of electrolytes and electrode potentials. It has nevertheless become clear that such methods and the knowledge we could gain from them are key for innovating electrochemical energy storage, as any rational design of essentially redox-based devices will require a quantum-mechanical understanding of atomic-scale structures and reactivity. With this publication, we present studies from five research teams who dare to venture into the unknown of electrochemical energy storage at the atomic scale. We start with Groß, who discusses the technical obstacles we face when applying computational methods and especially those from quantum chemistry to electrochemical energy storage systems. The second contribution gives the complementary view from a leading experimental group with a focus on current battery technology and a discussion of where help from modeling and simulation would be most welcome. Rempe and co-workers then give us a classical mechanics view of electrolytes, before Rajput et al. Persson review the current state of investigations into complex (here multivalent) electrolytes, where theory can at least help to understand and organize contradictory experimental results.

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We finish with Viswanathan and co-workers, who show us how to build a bridge from theory to experiment with the development of design principles for new device types (here Lithium-Oxygen batteries), keeping both electrodes and electrolyte features in mind. We hope that the presented contributions inspire more theoreticians to turn at least part-time to theoretical electrochemistry, not only because of the great importance it has for societies around the globe, but also for the intellectual challenges it poses and last but not least for the fun of it. We also hope to have convinced one or the other experimentalist of the value of atomic-scale theoretical investigations into electrochemical experiments. For having made this a possibility, we would like to thank all authors for their valuable contributions.

Dr. Martin Korth Molecular Projects UG, Münster, Germany

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Top Curr Chem (Z) (2018) 376:17 https://doi.org/10.1007/s41061-018-0194-3 REVIEW

Fundamental Challenges for Modeling Electrochemical Energy Storage Systems at the Atomic Scale Axel Groß1,2

Received: 26 April 2017 / Accepted: 23 March 2018 / Published online: 23 April 2018 © Springer International Publishing AG, part of Springer Nature 2018

Abstract There is a strong need to improve the efficiency of electrochemical energy storage, but progress is hampered by significant technological and scientific challenges. This review describes the potential contribution of atomic-scale modeling to the development of more efficient batteries, with a particular focus on firstprinciples electronic structure calculations. Numerical and theoretical obstacles are discussed, along with ways to overcome them, and some recent examples are presented illustrating the insights into electrochemical energy storage that can be gained from quantum chemical studies. Keywords Computer simulations · Density functional theory calculations · Electrochemical energy storage · Batteries · Electrode–electrolyte interfaces

1 Introduction There is in principle no need to emphasize the important role of energy storage in the context of the energy transition towards renewable energy based on, e.g., solar or wind power. As these resources are volatile and not necessarily available when they are needed, they must be efficiently stored. Furthermore, there is also Chapter 1 was originally published as Groß, A. Top Curr Chem (Z) (2018) 376: 17. https://doi.org/10.1007/ s41061-018-0194-3. * Axel Groß [email protected] 1

Helmholtz Institute Ulm (HIU) Electrochemical Energy Storage, Helmholtzstrasse 11, 89069 Ulm, Germany

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Institute of Theoretical Chemistry, Ulm University, Albert-Einstein-Allee 11, 89069 Ulm, Germany

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a tremendous demand for energy storage in mobile devices and applications. One of the most efficient energy carriers is the chemical bond  [1]. Chemical energy can be stored either in fuels or in batteries. Here we focus on the electrochemical energy storage in rechargeable batteries. There has been enormous technological progress in improving the efficiency and storage capacity of batteries. The widespread use of mobile devices such as cellular phones or laptops would not have been possible without this progress, which is mainly due to advances in Li–ion battery technology [2, 3]. Still, the specific energy of today’s batteries is not sufficient to enable car driving distances comparable to those of combustion energy-driven vehicles [4]. In addition, the incidents related to short circuit induced thermal runaway failures in Li–ion batteries  [5] raises concerns about safety issues. Furthermore, global lithium resources are limited [6], which might be addressed by developing battery chemistries based on other charge carriers. Hence there is certainly a strong need for further improvements in battery technology, even in a disruptive sense. In spite of these technological challenges, our knowledge about the atomistic structures and processes in devices for electrochemical energy storage is still rather limited  [2]. This is because it is difficult to atomically observe and resolve these structures and processes in  situ under operating conditions. Here, a close collaboration between experiment and theory could help. However, the theoretical description of batteries also faces severe problems, as structures and processes from the atomistic level up to the macroscopic level need to be understood, which calls for a multiscale approach. In particular, the interfaces between the electrodes and the electrolytes are often very poorly characterized, because experimental tools with atomic resolution often do not work at these interfaces. Any theoretical structure determination is nearly impossible without experimental information as input  [7, 8]. In addition, the microscopic description of liquid electrolytes in principle requires performing statistically demanding averages over many possible structures [9–11]. All these obstacles to an appropriate and realistic theoretical description of electrochemical energy storage systems are very discouraging. Yet, there are rewarding incentives to start such an effort. This field is of the highest technological and societal relevance, but there are also interesting scientific questions that need to be addressed. And indeed, significant progress has already been made with respect to the atomistic description of processes and structures in batteries [12]. In this  review, I will address the fundamental challenges associated with modeling electrochemical energy storage systems at the atomic scale. Rather than giving a comprehensive overview of existing work in this field, I will instead focus on particular problems that characterize the challenges, but also the possibilities, in the theoretical description of batteries. First I will briefly reiterate the basic principles of battery operation which sets the stage for any theoretical and numerical modeling. I will then describe the appropriate theoretical methods that are needed for a reliable description of structures and processes in batteries. In the main part of this  review, I will illustrate the issues in batteries that can and cannot be addressed at the moment with state-of-the-art theoretical methods.

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2 Basic Principles of Battery Operation Figure  1 illustrates the principle of operation of a rechargeable battery, using a Li–ion battery as an example  [13]. Basically, the operation of a battery is rather simple. A battery consists of two electrodes, the anode and the cathode, that are separated by an electrolyte, which can be either liquid or solid. The electrolyte is an ion conductor, but an insulator with respect to electron transport. Thus, it forces the electrons to propagate through an external circuit where they can do work. Upon discharge, ions propagate spontaneously through the electrolyte from the anode to the cathode, where they recombine with the electrons that have passed through the external circuit and have provided useful power. The driving force for the discharge process in the Li–ion battery is the gain in free energy ΔG upon the chemical reaction

xLi (anode) + Liy (cathode) → Lix+y (cathode).

(1)

Note that this chemical reaction is expressed for the neutral species of the charge carrier (here Li). When the external circuit is not open, there is no driving force for this chemical reaction. The maximal voltage V of a battery is given by the open circuit voltage

VOC =

−ΔG , xF

(2)

where F is the Faraday constant and x corresponds to the charge being transferred upon the chemical reaction. In order to determine ΔG , the particular chemical reactions occurring at the anode and cathode must be taken into account. This can be a de-insertion reaction at the anode and an insertion reaction at the cathode in an insertion battery, but conversion reactions involving phase transitions can also occur in conversion batteries. Equivalently, the open circuit can also be defined as the Fig. 1 Schematic presentation of the operation of a battery using a Li–ion battery as an example

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difference between the electrochemical potentials 𝜇A and 𝜇C of the anode and the cathode [3]:

VOC = (𝜇A − 𝜇C )∕e.

(3)

The voltage of a battery cell in operation is typically smaller than the open circuit voltage VOC because of internal resistance and further losses. Upon charging, the whole process is reversed by applying an external voltage. Typically, the applied voltage must be larger than the open circuit voltage VOC to account for losses. For a rechargeable battery, the chemical reaction upon charging and discharging must be reversible. So far, the operation of a battery seems to be rather simple. However, there are many associated challenges. Not only is there a shuffling of ions that corresponds to charge and discharge, but the insertion and de-insertion of the ions in the electrodes is often accompanied by a volume change. This represents a particular problem for anodes based on silicon, which show a very favorable specific capacity but also a large volume change by a factor of 3 during cycling, which causes mechanical stress [14]. Furthermore, batteries do age, as the chemical reactions are not truly reversible, and are accompanied by some irreversible processes. Thus, the active materials and the electrolyte show degradation that limits the lifetime of a battery. It should be noted that rather harsh conditions are present in batteries. For example, the lowest unoccupied molecular level (LUMO) of a liquid electrolyte or the bottom of the conduction band of a solid electrolyte must be higher than the electrochemical potential 𝜇A of the anode, and the highest occupied molecular level (HOMO) of a liquid electrolyte or the top of the valence band of a solid electrolyte must be lower than the electrochemical potential 𝜇C of the cathode; otherwise the electrolyte can be reduced or become oxidized. As the typical voltage of a Li–ion battery is above 4  V, this substantially limits the selection of suitable electrolytes that should also allow high ionic mobility. However, if a passivating solid–electrolyte interphase (SEI) layer forms at the anode, the anode–electrolyte reaction can become blocked even if 𝜇A is above the LUMO of the electrolyte. There are further unwanted processes in batteries. In particular, Li–ion batteries exhibit dendrite growth [15, 16]. Their presence can lead to short circuits associated with a thermal runaway  [5] that, together with a flammable electrolyte, can cause battery fires. It is very important that the challenges briefly described above are addressed in theoretical studies. However, the interfaces between the electrodes and electrolytes in batteries are typically not very well characterized, in particular when an SEI is formed. This hinders any realistic atomistic modeling. Atomistic theoretical studies can still contribute significantly to better understanding the processes occurring in batteries, and thus can help in developing strategies to tackle these challenges. Representative examples will be shown in this review, but before doing so, we need to identify the appropriate theoretical techniques.

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3 Computational Methods Upon discharge, chemical energy stored in the battery is converted into electrical energy. This involves chemical reactions in the electrodes and at the interface between electrodes and electrolytes, i.e., bond-breaking and bond-making processes. In order to reliably describe such processes and to identify and understand the electronic factors underlying the reactions, a quantum chemical approach is necessary. The method of choice for describing processes in bulk and interface systems is periodic electronic structure calculations based on density functional theory (DFT). There are well-known shortcomings of DFT  [17], such as the underestimation of band gaps and failures in the description of strongly correlated systems, including some oxide materials. Still, DFT calculations combine numerical efficiency with sufficient reliability and accuracy for many properties relevant to batteries  [7]. For example, open circuit potentials and estimates of the gravimetric and volumetric density can readily be obtained through DFT calculations and used as a computational screening for promising cathode/anode pairs [18]. Still, as battery structures can be rather complex, particularly at the interface between electrode and electrolyte, DFT calculations are sometimes too numerically demanding to describe these structures. In the case of a liquid electrolyte, instead of explicitly considering the solvent molecules, they might be described within an implicit solvent model  [19], i.e., as a continuous dielectric. This approach is numerically attractive and yields reasonable trends for electrochemical electrode/electrolyte interfaces [20], but it is not clear how reliable the method is, as far as quantitative results are concerned. Atomistic simulations using force fields  [21], i.e., parameterized classical interaction potentials, are numerically very attractive, and allow even millions of atoms to be taken into account. Unfortunately, they are not able to describe chemical reactions appropriately. Quantum and classical molecular mechanics can be combined in a horizontal multiscale technique within the QM/MM approach [22]: the central portion of the system, which requires a chemically accurate treatment, is described with quantum mechanics (QM), whereas the environment is treated with classical molecular mechanics (MM). This is a very powerful approach, but it must be ensured that the interface between the quantum and the classical region is well-described. Reactive force field (ReaxFF) methods are able to describe chemical reactions  [23] through the incorporation of bond-order terms. Still, they are computationally much cheaper than quantum chemical calculations, and hence they offer a numerically attractive alternative. However, their construction is very time-consuming and scales exponentially with the number of elements included in the ReaxFF. Typically, only up to three elements can be taken into account in a ReaxFF parameterization  [24], which limits their usefulness for battery simulations. Traditional force fields can also be very helpful when structural information is to be obtained, for example, when the interfacial structure of SEI components

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in contact with the electrolyte are to be determined  [25]. Recently, numerical interpolation schemes for potential energy surfaces based on machine-learning techniques such as artificial neural networks have become popular [26, 27]. Once such interaction potentials are created, they enable numerically efficient atomistic simulations of complex structures and interfaces [28]. In this  review, we concentrate mainly on atomistic studies related to batteries based on periodic DFT calculations, as they allow the determination of structures and processes together with an analysis of the underlying electronic structure.

4 Descriptors A descriptor is an observable that can be directly linked to the description of a fundamental property. The use of descriptors has contributed to significant advances in research and understanding in fields as diverse as catalysis and pharmaceuticals. As an example, the oxygen binding energy on metal electrodes has been shown to be directly related to the turnover frequency of the oxygen reduction reaction [29], which is one of the basic reactions occurring in fuel cells and in metal–air batteries [30]. Descriptors fulfill two purposes. First, they facilitate a fundamental understanding of the underlying principles governing the performance of a material, process or device. Second, they enable effective screening of candidates for improving a desired property, because only the particular descriptor needs to be optimized. Thus, a systematic approach to materials and process development and discovery is possible. In the field of battery research, descriptors have not really been introduced yet. It might be that the operation of a battery is so complex that no simple correlations exist between system parameters and battery performance. It might also well be that such descriptors exist, but that no real efforts have been made to identify them. In the next section, we will discuss a possible descriptor for the occurrence of dendrite growth, namely the height of self-diffusion barriers.

5 Dendrite Growth in Batteries The phenomenon of dendritic growth represents a severe problem at the anodic side of Li–ion batteries in particular [30–34], as dendrite occurrence can lead to irreversible battery damage and hazards such as battery fires. Their formation is schematically sketched in Fig. 2. Dendrites are structures shaped like needles or bushes that form upon the deposition of Li at the anode side. Once they connect the anode with the cathode, short circuits occur, accompanied by strong heating. A flammable electrolyte can ignite, causing a battery fire. This process was identified as the cause of recent lithium–ion battery failures aboard commercial aircraft [35]. Note that Li dendrite growth also occurs at anodes not containing metallic lithium, in particular for high charge rates and/or at low operating temperatures [36, 37]. Even if no short circuits result from dendrites, their formation is associated with reduced cyclability, loss of anode material and electrolyte pollution [30–32, 38].

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Top Curr Chem (Z) (2018) 376:17 Fig. 2 Schematic sketch of dendrite growth in Li–ion batteries

It is fair to say that the mechanism of dendrite growth is not completely understood. Different mechanisms have been suggested, for example, that they are a consequence of local deviations in the surface charge caused by imperfections in the SEI or that they grow preferentially from existing protrusions [34, 39–41]. Molecular simulations based on coarse-grained models have demonstrated that the propensity for dendrite formation increases with electrode overpotential [42]. Interestingly enough, not all charge carriers forming metals show the same propensity towards dendrite growth. It has been observed that magnesium, in contrast to Li, does not form agglomerates on copper or gold substrates, but instead shows a trend to grow uniform structures [43, 44]. Mg is a promising candidate as an alternative to lithium in batteries [45, 46]. Its volumetric energy density is even higher than that of Li, as Mg can carry two elementary charge units. It also represents a more sustainable option, as Mg is much more abundant in the earth’s crust, which at the same time makes it economically very attractive. Note that many of the existing theories for the occurrence of dendrite growth are not element-specific but rather generic as far as the properties of the metal forming the dendrite are concerned. Hence, these models are not able to explain the different tendencies of Mg and Li towards dendrite growth. It is important to note that growth phenomena at interfaces are intimately linked to diffusion coefficient D and deposition flux F [17]. Note furthermore that the critical quantity entering nucleation theory is the ratio D/F  [47]. Consequently, increasing the deposition flux has the same effect as decreasing the diffusivity. The fact that dendrite growth occurs at high charge rates and/or at low operating temperatures [36, 38] is consistent with this notion, as the charge rate is directly related to the deposition flux, and temperature controls diffusion coefficients. In order to find clues as to why Mg and Li behave so differently with respect to dendrite growth, periodic DFT calculations were performed  [48] to determine the self-diffusion barriers of Mg and Li at the most favorable surface terminations, which are the hexagonal close-packed (0001) surface of the hcp metal Mg and the square (001) surface of the bcc metal Li. The self-diffusion barrier of Na(001) was also evaluated, as sodium is another promising alkali metal for battery applications  [49]. Note that in  particular  for (100) surfaces, the typical hopping process is not the most favorable (shown in Fig.  3a), but rather an exchange process is Reprinted from the journal

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Fig. 3 a, b Illustration of the hopping and exchange self-diffusion process. c Self-diffusion barrier heights of Li, Na and Mg derived from Ref. [48] (courtesy of Markus Jäckle)

favored [50–52] (illustrated in Fig. 3b), in which the adatom replaces a surface atom, which then pops up and leads to an effective adatom propagation. Whereas in the hopping mechanism the configuration at the transition state corresponds to a twofold coordination, in the exchange mechanism there are two threefold coordinated atoms at the transition state. This is more favorable, in particular for a trivalent metal such as Al [50], but other metals such as Ir also exhibit such a diffusion mechanism [51]. This mechanism can also be favorable for diffusion across steps [52]. The calculated self-diffusion barriers of Li, Na, and Mg [48] are plotted in Fig. 3c. First, it is obvious that on Li(001), the hopping mechanism is still more favorable than the exchange mechanism, but only slightly. More importantly, it is evident that the self-diffusion barrier of 0.02 eV on Mg(0001) is significantly smaller than the corresponding barriers on Li(001) and Na(001). For such a small diffusion barrier, deposited Mg atoms are very mobile so that they easily propagate on the surface until they become attached to an island edge. This leads to a rather smooth growth. For high diffusion barriers, on the other hand, the deposited adatoms stay where they landed, resulting in a rougher growth mode. These considerations are consistent with the observation that Mg does not exhibit dendrite growth, whereas Li does. However, one should note that the battery environment has not been taken into account at all in these calculations. The presence of the electrolyte and/or the SEI might change the diffusion properties significantly. Furthermore, the electrode potentials corresponding to the charge and discharge have not been considered. All these factors must be included in order to develop a realistic picture of dendrite growth in batteries. In addition, the determination of the self-diffusion barriers on flat terraces might not be sufficient. When an island is formed, it is important to consider whether an adatom deposited on the island stays on the island or whether it diffuses down to the lower terrace. At the same time, other adatoms might diffuse up to the island from the terrace. Down-diffusion leads to smooth surfaces, whereas up-diffusion results

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in rough surfaces. Using a kinetic modeling approach, researchers have derived a quantitative relation between the surface roughness and the ratio of up- and downdiffusion coefficients [53].

6 Structure of Interfaces in Electrochemical Storage Devices In the calculations presented so far, the presence of the electrolyte at the electrochemical electrode/electrolyte interface in batteries has not been taken into account at all. Of course, the properties of this interface are strongly influenced by the presence of the electrolyte. Still, the modeling of the electrolyte represents a theoretical and numerical challenge, in particular for liquid electrolytes. To describe them properly, theoretically and numerically demanding statistical averages must be performed. In order to avoid this costly task, a hierarchy of approximations has been developed. Instead of total energy, free energies must be evaluated, including entropic contributions. In a grand-canonical approach, the electrolyte is not considered explicitly, but as a reservoir that provides the charge carriers characterized by their electrochemical potential. In implicit solvent models, the presence of the liquid electrolyte is taken into account, but as a dielectric continuum. And finally, the liquid electrolyte can be described explicitly in an atomistic manner. These approaches will be described in the following. 6.1 Grand‑Canonical Approach to Consider the Presence of Electrolytes at Interfaces In the grand-canonical approach, the liquid electrolyte is regarded as a thermodynamic reservoir containing ions as charge carriers. These ions are characterized by their electrochemical potential that corresponds to the energy to take an ion from the reservoir or to add it to the reservoir. In thermal equilibrium, the appropriate thermodynamical potential describing the electrode/electrolyte interface in the presence of the ions i in the electrolyte is the Gibbs free energy G(T, p, {Ni }). The basic scheme is illustrated for a solvated ion species (X + (aq)) in Fig. 4. The structure of the interface between electrode and electrolyte is determined by the minimum of the surface free energy that can be expressed [54] as ( ) ∑ 1 G(U, {Ni }) − Ni 𝜇̃ i (U, ai ) , Δ𝛾(U, ai ) = (4) As i where the free energy must be derived in the interface region illustrated by the dashed box in Fig.  4. As is the surface area, U the electrode potential and ai the activity of the ions  i in the electrolyte. This surface free energy corresponds to a free energy of adsorption. The electrochemical potential 𝜇̃ i (U, ai ) is related to the solvation energy of ion species i as a function of the electrode potential and concentration. The determination of solvation energies is still also rather demanding, as it Reprinted from the journal

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Top Curr Chem (Z) (2018) 376:17 Fig. 4 Illustration of the grandcanonical scheme to determine the equilibrium structure of the electrode–electrolyte interface. The interface region is given by the area in the dashed box

involves thermodynamic integration schemes [21]. It turns out that it is in fact not necessary to evaluate these solvation energies, as noted by Nørskov et al. [29, 55] in an approach now coined computational hydrogen electrode (CHE). Within this concept, the standard electrode potentials of redox couples or redox potentials can be used to select the most convenient reference species. This is illustrated for the redox couple 12X2 ⇄ X+ + e−  [56] (see Fig. 4). The electrochemical potential of the solvated anion can be expressed as

𝜇(X ̃ + (aq)) + 𝜇(e− ) =

1 𝜇(X2 (g)) − e(USHE − U 0 ) + kB T ln aX + , 2

(5)

where U 0 is the reduction potential of the corresponding anion with respect to the potential of the standard hydrogen electrode (SHE) and aX + its activity coefficient. ̃ + (aq)) can be This means that the electrochemical potential of the solvated ion 𝜇(X derived from the chemical potential of the stable gas phase species 𝜇(X2 (g)). Up to now, the derivation is exact. Typically, the following approximations are made in applications based on the concept of the computational hydrogen electrode [57–59]. First, the chemical potential of the gas phase species is taken in the limit of zero temperature and pressure. Second, changes in the zero-point energies and entropy upon adsorption are neglected. This means that instead of the free energy, only total energies need to be calculated. The free energy of adsorption then becomes

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Δ𝛾(U, ai ) ≈

( ) 1 1 Eads (X2 ) − NX Δ𝜇̃ X (U, ai ) , As 2

(6)

where the adsorption energy Eads is evaluated with respect to the molecule A2 in the gas phase, and Δ𝜇̃ i (U, ai ) contains only the changes in the electrochemical potential as a function of electrode potential and activity, as given in Eq. (5). This expression only contains terms that can be conveniently calculated. We now illustrate this grand-canonical approach for the determination of the structure of Li intercalation cathodes. They typically consist of transition metal compounds (oxides/sulfates/fluorides) which contain admixed atomic species (Li, Na/Mg, N/F) and/or functional groups (PO4, SiO4) to stabilize the material against chemical and/or structural decomposition during delithiation. Technically, DFT calculations of these compounds are handicapped from the fact that strongly localized and correlated d-states of transition metal ions are typically not well described by standard DFT functionals. A convenient approach is here to use the DFT+U approach  [12] where U is an on-site Coulomb interaction parameter that is typically empirically determined. This approach has been used to determine the stable structure of Li2FeSiO4(010) as a function of the lithium chemical potential [60]. Li2FeSiO4 is a promising new electrode material for Li–ion batteries because of its abundance, low cost and safety of the elemental components [61, 62]. Compared to the wide-spread used cathode material LiFePO4, it exhibits a better electronic conductivity and higher theoretical capacity [63, 64] because in principle two Li ions per formula unit can be extracted or stored. Surfaces of transition metal compounds can often exhibit complicated reconstruction patterns [17, 65]. Different non-stoichiometric Li compositions of (010) surface and subsurface layers have been tested. The resulting free surface energies as a function of Li chemical potential are plotted in Fig. 5, the structures are illustrated in the upper panel. The nomenclature (n / m) has been chosen to denote the number of Li atoms per (1 × 1) unit cell in surface and subsurface Li layers. Note that the (2/4) structure corresponds to the stoichiometric termination; therefore, its stability does not depend on the Li chemical potential. The Li chemical potential is given with respect to a metallic Li(m) electrode (perpendicular dashed line at 0.0 eV). Thus, a direct correlation of the chemical potential with the applied voltage in the cell can be made. The other vertical line corresponds to the delithiation voltage in this material. Over the largest portion of this electrochemical window the stoichiometric (2/4) structure is most stable. However, the (1/4) structure becomes more stable at potentials below 3.03 eV. This means that a Li ion can already be extracted from the surface at a voltage that is below the open circuit voltage. This is because the Li ion binding energy at the surface is reduced with regard to the bulk binding energy. 6.2 Description of Electrolytes in Implicit Solvent Models In the example shown above, the influence of the presence of the electrolyte on the adsorption energy Eads was entirely neglected. This approximation might be Reprinted from the journal

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Fig. 5 (010) surface composition of Li 2 FeSiO 4 at various Li chemical potentials. The nomenclature is chosen according to the number of Li atoms per (1 × 1) unit cell in surface and subsurface Li layers (see pictograms). Reprinted from Ref. [60], with permission from Elsevier

justified in the case of an aqueous electrolyte, as water interacts relatively weakly with chemisorbed atoms and molecules [66]. However, as far as the organic electrolytes typically used in batteries are concerned, there have been almost no systematic studies about their influence on the interaction of charge carriers with the electrodes. As mentioned above, this is due to the high computational cost associated with a proper modeling of aqueous electrolytes, requiring expensive statistical averages. The statistical sampling can be avoided if the electrolyte is described in an averaged manner as a dielectric continuum [19, 68, 69] characterized by a dielectric constant. This is certainly a rather approximate method. Critical issues are a suitable short-range cavity parameterization and an appropriate description of the nonlinearity in the ionic response [70]. Still, the implicit solvent approach improves upon vacuum extrapolation techniques [71].

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We will illustrate this method using an example related to metal–air batteries. These types of batteries promise a very high energy density comparable to hydrocarbon fuels [30]. During discharge in the Li–air battery, metallic lithium is oxidized at the anode, whereas oxygen from the air is reduced at the cathode. However, up to now, metal–air batteries have exhibited low cyclability. Thus there is a strong need to better understand the processes occurring in these batteries. One recent combined experimental and theoretical study focused on the oxygen reduction reaction (ORR) for high-rate Zn–air batteries [67]. Zn–air batteries have several advantages. They have a low equilibrium potential enabling the use of aqueous electrolytes, they exhibit a high specific energy and good reversibility, and they are sustainable, exhibiting environmentally friendly compatibility, and are abundant in the earth’s crust [72]. In one study, instead of noble metal catalysts, nitrogen-doped graphene was studied as cathode material, which is known to be an efficient metal-free electrocatalyst for oxygen reduction  [73]. The experiments revealed that the O2 diffusion on the graphene electrode is more facile than in solution [67]. In order to understand this, diffusion paths of O2 on graphene were determined (see Fig. 6a) using periodic DFT calculations. In these calculations, the aqueous electrolyte was represented in an implicit solvent model [19]. The diffusion coefficients for the O2 solid-surface diffusion on graphene derived from the calculated barrier heights shown in Fig. 6b were

Fig. 6 a Head-on-armchair (H-A), head-on-zigzag (H-Z), side-on-armchair (S-A) and side-on-zigzag (S-Z) diffusion paths, and b their corresponding diffusion energy barriers derived from periodic DFT calculations describing the aqueous electrolyte in an implicit solvent model [19]. Schematic illustration of the molecular oxygen transport to the reactive sites on c Pt/C through liquid-phase diffusion (LPD) and on d nitrogen-doped graphene through LPD and solid-surface diffusion (SSD). Reprinted with permission from Ref. [67], Copyright 2017 American Chemical Society Reprinted from the journal

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found to be significantly smaller than that for liquid-phase diffusion, thus confirming the experimental results. On the basis of these results, two different models were derived for the O2 transport to the reactive sites on Pt/C cathodes (Fig. 6c) and on nitrogen-doped graphene (Fig. 6d). In another recent example of the application of the implicit solvent model in theoretical battery studies, surface solvation energies of crystalline LiF in various nonaqueous solvents were evaluated, demonstrating the strong dependence of the interfacial energy on the choice of battery solvent [74]. 6.3 Explicit Atomistic Modeling of Electrode/Electrolyte Interfaces It has already been mentioned that upon battery operation, a passivating solid–electrolyte interphase (SEI) layer forms. The exact structure of the SEI still remains unclear. Schematic drawings such as the one shown in Fig. 7 are used to illustrate the possible structure of the SEI, but it is still unclear whether such drawings are realistic. The SEI is formed from the solvent and electrolytic salt that are electrochemically reduced. It is composed of oligomers and inorganic crystals, as indicated in Fig. 7, and generates a barrier between the electrolyte and the anode, thus protecting the anode. Still, Li ion transport through the SEI has to be possible; otherwise the battery would no longer be operative. Hence, it important to identify and characterize the structure of the SEI. However, the atomistic modeling of the SEI represents a significant challenge. Because of its complexity, the SEI can hardly be modeled on a first-principles basis, but it can be addressed on a force-field level [76]. As an example, MD simulations of the Li+ transport through the dilithium ethylene dicarbonate (Li2EDC) component of the SEI [75] are presented. In this study, the force field was adjusted based on quantum chemical calculations. Two states of Li2EDC were modeled: a crystalline ordered state shown in Fig. 8a and a molten (or disordered) state illustrated in Fig. 8b. The ion transport in Li2EDC was examined by deriving ion self-diffusion coefficients for ordered and molten material from the MD simulations. Typically, nuclear quantum effects in the dynamics that might be relevant for hydrogen [77] are Fig. 7 Schematic illustration of the solid electrolyte interphase (SEI) forming at battery anodes

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Fig. 8 Snapshot from the MD simulations of dilithium ethylene dicarbonate in the ordered (a) and the amorphous (b) states at a temperature of 450  K. The Li+ ions are depicted as pink balls. c A representative cluster of crystalline dilithium ethylene dicarbonate. Reprinted with permission from Ref. [75], Copyright 2013 American Chemical Society

neglected. This can be justified by the fact that there are competing effects that are canceled to a large extent [78–80]. The MD simulations yielded activation energies for Li+ diffusion and conductivity in good agreement with experiment [75]. Because of its complexity, quantum chemical studies are limited to the initial stages of SEI formation [81–84], which are assumed to be the decomposition of the electrolyte such as ethylene carbonate (EC)  [85]. In order to develop a molecularscale understanding of the atomistic structure of the electrode/electrolyte interface in batteries, it is helpful to perform joint experimental–theoretical model studies with a high control  [86–88]. The adsorption of EC on Cu(111) was addressed in such a study. At a surface temperature of 80  K, a well-ordered commensurate EC adsorbate structure was observed in STM experiments. DFT calculations including dispersion corrections were performed in order to support the interpretation of the STM pictures. Isolated EC molecules adsorb in a flat configuration on Cu(111), as shown in Fig. 9a, b. Based on the experimentally observed periodicity of the EC adsorption, a structural model was proposed (Fig. 9c). Using the Tersoff–Hamann approximation [89], STM images were simulated and compared with the experimental images (see Fig. 9d). The good agreement between theory and experiment lends credibility to the proposed arrangement of the EC molecules on Cu(111). It turns out that the structure results from a compromise between molecule–surface and molecule–molecule interaction: the molecules do not all remain in the adsorption configuration of the isolated EC molecule on Cu(111). An analysis of the adsorption energy reveals that both the molecule–surface and the molecule–molecule interaction are governed by dispersion effects. Upon heating to 220 K, competing desorption and decomposition of the EC molecules into –C=O, –C–O–C–, –C–H and –C–C– compounds was observed by X-ray photoelectron spectroscopy, reflecting initial steps of SEI formation  [86]. Similar studies were performed addressing 1-ethyl-3-methylimidazolium chloride bis-(trifluoro-methyl-sulfonyl)-imide ([EMIM]+[TFSA]−) ionic liquids on Au(111)  [87, 88] and graphite  [88]. Ionic liquids (ILs) are room-temperature molten salts characterized by weak interactions due to charge delocalization on the ions. They represent promising candidate materials as alternative electrolytes [90]. Whereas EC is combustible at high temperature, ionic liquids exhibit low flammability, significant Reprinted from the journal

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Top Curr Chem (Z) (2018) 376:17 Fig. 9 Calculated energy minimum structures of an isolated ethylene carbonate (EC) molecule in side (a) and top (b) view and of an ordered EC adlayer (c) within the experimentally derived periodicity [86]. Carbon atoms are depicted in blue, oxygen in red and hydrogen in white. d An emulated STM image obtained within the Tersoff–Hamann scheme [89] is compared with an experimental STM image inserted in the bottom left corner. Reprinted with permission from Ref. [86], Copyright 2016 American Chemical Society

stability and high ionic conductivity. DFT calculations showed that ILs, as EC, interact with electrode surfaces mainly through dispersion forces [87, 88].

7 Atomistic Modeling of Bulk Electrode Properties In this review, we have concentrated mainly on the challenges in the modeling of interfaces between electrodes and electrolyte in batteries. Because of the liquid nature of many electrolytes, the description of these interfaces necessitates taking into account the statistical nature of bulk liquids, which is theoretically and numerically rather demanding. This is different as far as well-ordered crystalline electrode materials are concerned. Here, structure optimization is often sufficient for estimating thermodynamic properties such as the open circuit potential.

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Top Curr Chem (Z) (2018) 376:17 Fig. 10 Bulk structure of Pmn21 Li 2 FeSiO 4 together with an indication of Li diffusion channels (courtesy of Nicolas Hörmann)

Iono-covalent electrode materials are often highly anisotropic. This is illustrated in Fig.  10, where the bulk structure of Pmn21 Li2FeSiO4 is shown. As mentioned above, this silicate mineral is of interest as an electrode material for lithium ion batteries because of the low cost of the elemental components due to their abundance, together with high safety  [61, 62]. In addition, as in principle two Li ions per formula unit can be extracted or stored, it should exhibit a high theoretical capacity [63]. Still, oxide materials are typically insulators, i.e., they are bad electron conductors. Furthermore, they are often bad ion conductors, as one of the main selection criteria is the stability of the electrode materials in the charge/discharge cycle. The use of nanosized electrode particles can reduce these transport limitations  [91]. Regarding the strong anisotropy of these electrode materials, it is advantageous when the nanosized electrode crystals preferentially exhibit surface terminations that allow easy access to easy diffusion channels, as indicated in Fig.  10. The shape of crystallites is controlled by the surface energies, and the equilibrium shape can be derived based on the Wulff construction scheme  [17]. Using DFT calculations, it was shown that the non-polar (010) and (110) surfaces have the lowest surface energies and should be the most prominent surface terminations in equilibrium [61, 92]. The above discussion has already stressed the importance of facile diffusion for efficient charging and discharging. Electronic structure calculations can be very helpful in determining reaction barriers. Traditionally, layered rocksalt-type lithiumtransition metal oxides and ordered spinels have been used as cathode materials [12], whereas non-ordered materials have been considered to be inferior as far as transport properties are concerned, as no channels for facile diffusion exist. However, in a combined experimental and theoretical work, it has been shown that this “ordering paradigm” might not necessarily be justified [93]. DFT calculations, in combination with automatic transition state search routines [94, 95], enable the determination of diffusion paths and barriers for non-ordered environments, as illustrated in Fig. 11. Thus, it was shown that lithium diffusion in cation-disordered oxides can be facile due to percolation of active diffusion channels  [93], which opens up the route towards a new promising class of battery electrode materials [96, 97]. Reprinted from the journal

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Top Curr Chem (Z) (2018) 376:17 Fig. 11 Determination of diffusion paths with automatic transition search routines (courtesy of Holger Euchner)

8 Conclusions Although the operating principle of batteries is in principle rather simple, the improvement in the capacity and efficiency of batteries is not trivial. This is mainly due to the complexity of the interfaces and the fact that the selection of available materials is limited, as they must be stable under charge and discharge conditions. As the electrochemical energy storage is based on bond-making and bond-breaking processes, quantum chemistry tools are needed for a true comprehensive theoretical description. However, in spite of the ongoing increase in computer power and the development of more efficient methods, the complexity of electrochemical storage systems still presents a considerable numerical and theoretical challenge. Still, first-principles electronic structure calculations can contribute significantly to a better atomistic understanding of the structures and processes present in batteries. Together with molecular mechanics methods and continuum approaches, they represent an indispensable tool for improving the efficiency, stability and safety of batteries. Acknowledgements This review is based on the insights gained by working together with my excellent collaborators, among them Florian Buchner, Holger Euchner, Katrin Forster-Tonigold, Markus Jäckle and Nicolas Hörmann. I am also indebted to my colleagues Jürgen Behm, Oleg Borodin, Maximilian Fichtner, Martin Korth, Arnulf Latz and Wolfgang Schmickler for sharing their insights with me.

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Top Curr Chem (Z) (2018) 376:17 87. Buchner F, Forster-Tonigold K, Uhl B, Alwast D, Wagner N, Farkhondeh H, Groß A, Behm RJ (2013) Toward the microscopic identification of anions and cations at the ionic liquid|Ag(111) interface: a combined experimental and theoretical investigation. ACS Nano 7:7773 88. Buchner F, Forster-Tonigold K, Bozorgchenani M, Gross A, Behm RJ (2016) Interaction of a selfassembled ionic liquid layer with graphite(0001): a combined experimental and theoretical study. J Phys Chem Lett 7:226 89. Tersoff J, Hamann DR (1983) Theory and application for the scanning tunneling microscope. Phys Rev Lett 50:1998 90. Armand M, Endres F, MacFarlane DR, Ohno H, Scrosati B (2009) Ionic-liquid materials for the electrochemical challenges of the future. Nat Mater 8:621 91. Kubiak P, Pfanzelt M, Geserick J, Hörmann U, Hüsing N, Kaiser U, Wohlfahrt-Mehrens M (2009) Electrochemical evaluation of rutile TiO 2 nanoparticles as negative electrode for Li–ion batteries. J Power Sources 194:1099 92. Hörmann N, Groß A (2014) Polar surface energies of iono-covalent materials: implications of a charge-transfer model tested on Li 2 FeSiO 4 surfaces. ChemPhysChem 15:2058 93. Lee J, Urban A, Li X, Su D, Hautier G, Ceder G (2014) Unlocking the potential of cation-disordered oxides for rechargeable lithium batteries. Science 343:519 94. Henkelman G, Jónsson H (1999) A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J Chem Phys 111:7010 95. Henkelman G, Jónsson H (2000) Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J Chem Phys 113:9978 96. Ren S, Chen R, Maawad E, Dolotko O, Guda AA, Shapovalov V, Wang D, Hahn H, Fichtner M (2015) Improved voltage and cycling for Li+ intercalation in high-capacity disordered oxyfluoride cathodes. Adv Sci 2:1500128 97. Chen R, Ren S, Knapp M, Wang D, Witter R, Fichtner M, Hahn H (2015) Disordered lithium-rich oxyfluoride as a stable host for enhanced Li+ intercalation storage. Adv Energy Mater 5:1401814

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Top Curr Chem (Z) (2018) 376:16 https://doi.org/10.1007/s41061-018-0196-1 REVIEW

Interfaces and Materials in Lithium Ion Batteries: Challenges for Theoretical Electrochemistry Johannes Kasnatscheew1 · Ralf Wagner2 · Martin Winter1,2 · Isidora Cekic‑Laskovic1,2

Received: 21 June 2017 / Accepted: 9 April 2018 / Published online: 18 April 2018 © Springer International Publishing AG, part of Springer Nature 2018

Abstract Energy storage is considered a key technology for successful realization of renewable energies and electrification of the powertrain. This review discusses the lithium ion battery as the leading electrochemical storage technology, focusing on its main components, namely electrode(s) as active and electrolyte as inactive materials. State-of-the-art (SOTA) cathode and anode materials are reviewed, emphasizing viable approaches towards advancement of the overall performance and reliability of lithium ion batteries; however, existing challenges are not neglected. Liquid aprotic electrolytes for lithium ion batteries comprise a lithium ion conducting salt, a mixture of solvents and various additives. Due to its complexity and its role in a given cell chemistry, electrolyte, besides the cathode materials, is identified as most susceptible, as well as the most promising, component for further improvement of lithium ion batteries. The working principle of the most important commercial electrolyte additives is also discussed. With regard to new applications and new cell chemistries, e.g., operation at high temperature and high voltage, further improvements of both active and inactive materials are inevitable. In this regard, theoretical support by means of modeling, calculation and simulation approaches can be very helpful to ex ante pre-select and identify the aforementioned components suitable Chapter 2 was originally published as Kasnatscheew, J., Wagner, R., Winter, M. & Cekic-Laskovic, I. Top Curr Chem (Z) (2018) 376: 16. https://doi.org/10.1007/s41061-018-0196-1. * Johannes Kasnatscheew [email protected] * Isidora Cekic-Laskovic [email protected] 1

Helmholtz-Institute Münster, IEK-12, Forschungszentrum Jülich GmbH, Corrensstrasse 46, 48149 Münster, Germany

2

MEET Battery Research Center/Institute of Physical Chemistry, University of Münster, Corrensstrasse 46, 48149 Münster, Germany

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for a given cell chemistry as well as to understand degradation phenomena at the electrolyte/electrode interface. This overview highlights the advantages and limitations of SOTA lithium battery systems, aiming to encourage researchers to carry forward and strengthen the research towards advanced lithium ion batteries, tailored for specific applications. Keywords Electrochemical energy storage · Lithium ion battery · Electrode materials · Electrolyte · Electrolyte/electrode interface · Computational chemistry

1 Terminology The following definitions are used within the review. Term

Description

Active materials

Active materials participate in the electrochemical charge/discharge reaction in a cell

Adsorption

“An increase of the concentration of a solute in the vicinity of a solid surface, over that in the bulk of the solution, due to the attractive interaction between the solid immersed into the solution and the solute. Adsorption on a solid from a gaseous phase also occurs. It is generally considered to be a physical process” [1]

Alloy

An alloy consists of mixed metallic or intermetallic phases with no ordered structure

Anode

“The electrode where oxidation occurs in an electrochemical cell. It is the positive electrode in an electrolytic cell, while it is the negative electrode in a galvanic cell” [1]

Battery

“A device that stores electrical energy using electrochemical cells. Strictly speaking, a battery should consist of several, internally connected, electrochemical cells. However, in present usage all storage devices (single cell and multiple cell) are called batteries” [1]

Cathode

“The electrode where reduction occurs in an electrochemical cell. It is the negative electrode in an electrolytic cell, while it is the positive electrode in a galvanic cell” [1]

Cell voltage

“The electrical potential difference between the two electrodes of an electrochemical cell” [1]

Concentration polarization

“The polarization associated with the diffusional transport of the reactants to the electrode surface from the bulk of the electrolyte and the reverse transport of the products” [1]

Electrochemical cell

“A device that converts chemical energy into electrical energy or vice versa when a chemical reaction is occurring in the cell” [1]; “It can be either a galvanic cell, when the reactions are spontaneous, or an electrolytic cell, when the reactions are nonspontaneous” [2]

Electrode

“The two electronically conducting parts of an electrochemical cell. These can be simple metallic structures or much more complicated, composite structures” [1]

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Description

Electrolytic cell

“An electrochemical cell that converts electrical energy into chemical energy. The chemical reactions do not occur “spontaneously” at the electrodes when they are connected through an external circuit. The reaction must be forced by applying an external electrical current. It is used to store electrical energy in chemical form (rechargeable battery). It is also used to decompose or produce new chemicals by application of electrical power (electrolysis)” [1]

Galvanic (voltaic) cell

“An electrochemical cell that converts chemical energy into electrical energy. A cell in which chemical reactions occur spontaneously at the electrodes when they are connected through an external circuit, producing an electrical current” [1]

Half cell

“A somewhat archaic term, indicating a structure that contains an electrode and the surrounding electrolyte” [1]

Inactive materials

Inactive materials do not contribute to the energy storage related redox chemistry of the cell

Interface and interphase

“The inhomogeneous spacial region at the interface between two bulk phases in contact. The “interface” is a two-dimensional surface, while the “interphase” is a thin, but three-dimensional, volume” [1]

Intermetallic phase

An intermetallic phase has a defined stoichiometry and structure in an at least binary system of metals

Joule heating

Process whereby the energy of an electric current is converted into heat as it flows through a resistance

Mass transport

“The phenomenon of movement (transportation) of mass (in the form of molecules or ions) from one part of the system to another. This occurs through convection, diffusion, or electro migration” [1]

Oxidation

“The process in which a chemical species loses one or more electrons; it is the reversed process to the reduction” [2]

Redox couple

“Chemical species that has at least two oxidation states, and thus can act either as the reduced or the oxidized species (depending on the oxidation state)” [2]

Redox reaction

“A class of electrode reactions involving oxidation/reduction of two dissolved species” [1]

Reduction

“A process in which a chemical species gains one or more electrons; reversed process is called oxidation” [2]

Standard hydrogen electrode (SHE) The IUPAC (International Union of Pure and Applied Chemistry) defines SHE as follows: “The standard hydrogen electrode consists of a platinum electrode in contact with a solution of H+ at unit activity and saturated with H2 gas with a fugacity referred to the standard pressure of 105 Pa” [3]

2 Introduction to Electrochemical Energy Storage Devices An electrochemical capacitor (alternatively called a supercapacitor or ultracapacitor) is a device in which a typically high surface area electrode material, based mostly on carbon, is charged so that an excess charge layer at the electrode surface is created, Reprinted from the journal

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and oppositely charged ions form a layer in solution, such that an EDL with an electrical potential difference between solution and electrode is the result [4–7]. Simultaneous diminution of the layers in the solution and at the electrode surface by release of ions and charge in the electrode results in a rapid release of electric charge and a repeal in the electrical potential difference [6, 8–13]. Electrode materials and electrolytes for electrochemical capacitors are reviewed in [13–17]. In contrast, batteries generate electrical energy by conversion of chemical energy via redox reactions taking place at the active materials, namely the negative and positive electrode in one or more electrically interconnected electrochemical cells. Batteries can be classified into primary (non-rechargeable) and secondary (rechargeable) batteries, depending on whether they are capable of being recharged by applying an electric current [18]. During discharge, each cell gives a current Idis (A) at a voltage Vdis(q) (V), which is dependent on the state of charge of the cell, up to a defined period of time tdis (h). The current flow over time is defined as the discharge capacity (Qdis) tdis

Qdis = ∫ Idis dt. 0

(1)

This can be referred to by unit volume, as the volumetric discharge capacity (Ah L−1), or by unit weight, as the specific discharge capacity (Ah kg−1) [19]. The (relativized) theoretical specific capacity qth of a given electrode material depends on the number of electrons exchanged, z, and its molecular or atomic weight M (g mol−1). F is the Faraday constant (96,485 As mol−1).

qth =

zF M

(2)

The specific discharge energy (Edis) (Wh) supplied by any cell is determined by the discharge voltage Vdis(Q) as well as the obtained absolute discharge capacity (Qdis) Qdis

Edis = ∫ Vdis (Q)dQ. 0

(3)

Energy available per unit weight is called the specific energy (Wh  kg−1 or mWh  g−1), also called gravimetric energy density. On the other hand, the amount of energy that is stored per unit volume is called the volumetric energy density (Wh L−1), referred to simply as energy density in many reports [18–20]. The discharge power (Pdis) [specific power (W kg−1) and volumetric power density (W  L−1)] is determined by the discharge voltage Vdis as well as the discharge current Idis

Pdis = Vdis Idis = Ri (Idis )2 .

(4)

During discharge of the cell, an internal cell resistance (RI) (Ω) reduces Vdis compared to the open-circuit voltage (Voc) (V) by an overvoltage (η) (V). The magnitude of the overvoltage depends upon the value of the current drawn as well as the state

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of charge of the cell [21]. The overvoltage consumes part of the energy as irreversible Joule heat (J)

𝜂 = Ri Idis ,

(5)

Vdis = Voc − 𝜂(q, Idis ).

(6)

The thermodynamic value of the cell voltage under open circuit conditions is determined by the difference between the electrochemical potentials of the negative (𝜇̃ n ) and positive (𝜇̃ p) electrode (J  mol−1) including the Faraday constant [19, 22, 23]; which can also be expressed as the difference in standard electrode potential of positive ( Ep0) and negative ( En0) electrode: [21, 24]

| 𝜇̃ n − 𝜇̃ p | | | Voc = | | = Ep0 − En0 | F | | |

(7)

The standard electrode potential of an electrochemical reaction is commonly reported with respect to the standard hydrogen electrode (SHE) as shown in Table 1. The first primary cell, the voltaic pile, was developed by Volta between 1790 and 1800. It was made of elements based on copper disc/brine-soaked cardboard/zinc disc connected in series. Only 2  years later, Ritter built the first accumulator, by replacing the zinc discs in the voltaic pile by copper plates [26]. The first commercially successful rechargeable battery was the lead acid battery developed by Planté in 1859. The lead acid battery uses lead oxide as the positive electrode material,

Table 1 Standard electrode potential values of common battery materials in volts relative to the standard hydrogen electrode (SHE)a Half cell reaction

E°/V

Li+ (aq) + e− ↔ Li(s)

− 3.01

Li+ (aq) + C6 (s) + e− ↔ LiC6 (s)

− 2.9

Na+ (aq) + e− ↔ Na(s)

− 2.71

Mg2+ (aq) + 2e− ↔ Mg(s)

− 2.38

Cd(OH)2 (s) + 2e− ↔ Cd(s) + 2OH− (aq)

− 0.81

2+

Zn

− 0.76

−

+ 2e ↔ Zn(s) −

PbSO4 (s) + 2e ↔ Pb(s) +

− 0.36

SO2− 4 (aq)

2H+ + 2e− ↔ H2 (g)

0

Cu2+ + 2e− ↔ Cu(s)

+ 0.34

Ag2 O(s) + H2 O + 2e− ↔ 2Ag(s) + 2OH−

+ 0.35

NiOOH + H2 O + e− ↔ Ni(OH)2 + OH− (aq)

+ 0.45

Br2 (aq) + 2e− ↔ 2Br− (aq)

+ 1.08 + 1.36

Cl2 (g) + 2e− ↔ 2Cl− (aq) PbO2 (s) + a

SO2− 4 (aq)

+

−

+ 4H + 2e ↔ PbSO4 (s) + 2H2 O

+ 1.69

Data taken from [25]

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metallic lead as the negative electrode material and aqueous sulfuric acid as electrolyte. Practical lead acid batteries have a nominal voltage of 2 V and a specific energy of ≈ 35  Wh  kg−1 [25]. Even today, the lead acid battery powers numerous battery applications. The need for higher energy storage systems for advanced applications led to the development of nickel/cadmium (NiCd), nickel/metal hydride (NiMH) (both using aqueous KOH as electrolyte and having a nominal cell voltage of 1.2 V) and lithium ion batteries (LIBs) [25]. Detailed information on the aqueous battery systems lead acid, NiCd and NiMH is given in [18, 25]. Today, together with the lead acid battery, the LIB is the most important rechargeable battery technology, with double-digit compound annual growth rates. The liquid electrolyte in LIBs requires moving away from aqueous media, since water-based electrolytes have a too narrow electrochemical stability window regarding the operation voltage range of LIBs [27]. The use of aprotic liquid organic electrolytes adds some complexity to the picture, since electrochemistry and ion transport properties in these media are much less studied. Furthermore, due to the sensitivity to hydrolysis of certain cell components, in particular the electrolyte, LIBs have to be assembled in a dry atmosphere [28]. Further LIB technologies, such as Li/air [29–31], Li/S [29, 32, 33], Na-ion [34], Mg metal [35, 36], Ca metal [37, 38], Al metal [38–40], dualion [41–44] as well as lithium metal batteries, dual-ion batteries and LIBs based on organic electrode materials [45, 46] are still in the research and development stage and are detailed in the stated literature and in [47]. They are not discussed in the frame of this review.

3 Introduction to Lithium Ion Cell Chemistry Due to their flexibility in terms of cell chemistry, electrode (micro-) structure and design, LIBs can be constructed to meet a broad range of power to energy ratios (P/E), thus making them a most suitable battery technology for application in all kinds of electric vehicles with different P/E ratios, such as hybrid (HEV, P/E ≈ 15), plug-in hybrid (PHEV, P/E ≈ 8) and fully battery electric (BEV, P/E ≈ 3) [49]. In general, LIBs comprise a negative and positive electrode capable of Li+ ion insertion/de-insertion, and a separator that is soaked with a lithium salt containing mixture of liquid organic solvents to ensure the rapid transfer of Li+ ions within the cell [50, 51]. The separator, a porous polyolefin membrane with a thickness of 15–25  µm, acts as an electronic insulator and prevents direct electronic contact between the two electrodes. The electrode active materials, embedded in a mixture of conductive additive [52, 53] and binder [54], are coated on current collectors, where Cu foil (8–18 µm) is preferably used for the negative electrode [55] and Al foil (12–20 µm) for the positive electrode [46–59]. Figure 1 depicts a typical wound cell assembly with double-side-coated porous positive electrode, double-side-coated porous negative electrode separated by an inner and outer separator.

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Fig. 1 a Wound cell construction including negative and positive electrode, as well as inner and outer separator. b Double-side-coated negative and positive composite electrodes. c Scanning electron micrograph (SEM) top view on separator and SEM cross sections of double-side-coated positive and negative composite electrodes

During charging of a LIB, reduction takes place at the negative electrode. Thereby, the negative electrode is forced to accommodate electrons from the positive electrode, which flow through the external current circuit. Simultaneously, the negative electrode inserts Li+ ions, which are extracted at the positive electrode side into the solution phase and migrate and diffuse through the bulk electrolyte to the negative electrode side, to ensure the charge balance. As a result, the positive electrode active material is oxidized. In the case of the discharge process, the redox reactions are inverted. During the discharge process, the negative electrode acts as anode and the positive electrode as cathode. As seen in the overall reaction of the LIB depicted in Scheme 1, the active Li+ ions are shuttled between two insertion host electrodes during charge and discharge of the LIB. The electrochemical role of both electrodes changes between anode and cathode, depending on the direction of the current flow through the cell. However, throughout the literature and in the remainder of this manuscript, the positive electrode is named as the cathode and the negative electrode as the anode.

Scheme  1 Overall cell reaction during charge and discharge of a lithium ion battery (LIB) based on graphite as negative electrode active material and lithium transition metal oxide (TM = Mn, Co, Ni, etc.) as positive electrode active material

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4 Anode Materials for LIBs 4.1 Lithium Metal, the Ancestor Anode of LIB Electrodes Metallic Li is regarded as the most promising anode material for high energy density Li-based batteries, due to its outstanding properties. Among all metals, the Li/ Li+ redox couple has the lowest potential value (Table  1) and Li has the lightest weight, resulting in a low operation potential and a high specific capacity of Li metal anodes, respectively. However, the use of Li metal electrodes comes with serious safety issues upon repetitive charge and discharge of the cell, originating from extensive shape changes, inhomogeneous Li deposition and formation of high surface area Li, commonly referred as Li dendrites in the literature, when liquid organic solvent-based electrolytes are used [60–62]. In the worst case scenario, Li dendrites grow through the separator and locally short-circuit the cell [63]. Lithium metal polymer batteries, comprising a dry solid polymer electrolyte and a LiFePO4 cathode are already a practically used reality (Fig.  2). Specific ionic liquid-based electrolytes, also in composites with polymers, enable the use of the metallic Li electrode [64]. 4.2 Classification of Anode Materials As metallic Li is still a safety concern when used in the rechargeable mode, anode materials based on Li+ ion uptake have been pursued for LIBs. The materials can be classified into the following categories according to their type of reaction with the Li+ ion: insertion, alloying and conversion reactions (Fig. 3) [66]. Many metals can form alloys or intermetallic phases with Li; however, most of the literature is

Fig. 2 a Schematic illustration of a lithium metal polymer battery. b Cross-section SEM image of the cell. Adapted with permission from [65]. Copyright (2015) American Chemical Society

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Fig. 3 A schematic representation of the different reaction mechanisms observed in electrode materials for lithium-based batteries. Black circles Voids in the crystal structure, blue circles metal, yellow circles lithium. Reprinted with permission from [28]. Copyright (2009) Royal Society of Chemistry

devoted to Si [67] and Sn-based [51, 68] anode materials [51, 69–72]. Still, the main challenge arising with the use of Si, Sn (and other Li storage metals) as negative electrode active material is the severe volume change (up to 400%) that the Li storage metals experiences during Li+ ion uptake and release, thus leading to particle cracking and disintegration of the electrode structure [67]. Various approaches to overcome the challenges arising with the Li storage metal volume change have been reported, with the use of active-inactive composites (e.g., Si–C composites) as the most prominent ones. Si–C composite electrodes with Si content in a low singledigit range have already been commercialized. Recent research progress in so-called conversion reaction-based anodes has been reviewed in [73, 74]. The large voltage hysteresis in conversion materials is still a major obstacle leading to a low energy efficiency of these materials during charge and subsequent discharge [20, 75]. For this reason, conversion anodes are used only at a laboratory scale and will have no tangible effect on the LIB cell chemistry in the next years. Commercial LIBs use mainly insertion anode materials, such as graphite, hard carbon or lithium titanate (Li4Ti5O12, LTO). 4.3 Graphitic and Non‑Graphitic Carbon Anodes Carbon materials can be classified into graphitic (materials having a layered structure characterized by crystalline domains) and non-graphitic (disordered structure, characterized by amorphous domains). Depending on their ability to develop a graphite structure during heat treatment, non-graphitic carbons can be further Reprinted from the journal

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divided into graphitizing carbons (referred as soft carbons) and non-graphitizing carbons (referred as hard carbons) [51, 76]. Each type of carbon has its own current and potential characteristics of the Li+ ion intercalation/de-intercalation reaction. Graphitic carbons comprise stacked graphene layers in the stacking sequence AB (hexagonal graphite) or ABC (rhombohedral graphite), which are held together by weak van der Waal forces [77]. During electrochemically induced lithiation, a maximum content of one Li+ ion per six carbon host atoms can be stored, corresponding to a theoretical specific capacity of 372 mAh g−1. The process of Li+ ion insertion proceeds via the prismatic surface, and is accompanied by a change in the graphite stacking sequence to AA, thus leading to a change of the graphene interlayer distance of ≈ 10%. Thereby, Li+ ion insertion proceeds via a staging mechanism in which the Li+ ion fully intercalates into very distant graphene layer gaps before occupying the space between neighboring layers. The staging process is characterized by well-defined potential plateaus in the potential region between ≈ 0.25 and 0.05 V vs. Li/Li+ (Fig. 4) [51]. The plateaus arising in the potential profile are due to the coexistence of two phases (P) according to Gibbs phase rule.

 =C−P+2

(8)

The number of degrees of freedom (ℱ) is given by the number of components (C) present and the number of coexisting phases present. In the case of Li+ ion intercalation into graphite, there are two components, viz., the Li+ ion and the graphite host structure, as well as two coexisting phases. This means that if the values of two intensive thermodynamic parameters, such as temperature and pressure, are specified, no ℱ are left. Thus, there is no independent ℱ, which means that the electrochemical potential is constant over the lithiation degree (plateau region in the potential profile) in the specific two-phase region. More information on the Gibbs phase rule and its application in batteries can be found in [78]. Due to the low operation potential of graphite anodes, all known liquid aprotic electrolytes are

Fig. 4 The potential profile of graphite has several stages distinguished as a result of single and twophase regions

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thermodynamically unstable at the anode/electrolyte interface. However, the chargeconsuming reduction (irreversible qloss in Fig. 4) of the commonly used lithium hexafluorophosphate (LiPF6)/organic carbonate-based electrolyte in the initial charge/ discharge cycles, especially during the first charge of the cell, leads to the formation of a passivation layer, the well-known solid electrolyte interphase (SEI) [63], and thus to kinetic stability. In this regard, the electrolyte components with the lowest reductive stability react first [79]. In particular, Baluena et al. studied the reduction stability of solvents by means of computational chemistry and pointed out the importance of Li+ ion–solvent coordination for predicting stability limits [80, 81]. Film formation is related to the surface properties of the carbon/graphite material [82, 83] and the electrolyte composition used [84–86], and is associated with the irreversible capacity loss and electrolyte depletion. For detailed information on carbon anodes, the reader is referred to [79, 87]. 4.4 Lithium Titanate Lithium titanate spinel (Li4Ti5O12, LTO) is an alternative commercialized anode material, known for its long cycle life and improved safety characteristics compared to graphite anodes, especially at low temperature applications and fast charge rates [88, 89]. On the one hand, this is due to the high Li+ ion intercalation/de-intercalation potential of 1.55 V vs. Li/Li+, which is higher than most of the reduction onset potentials of common liquid aprotic electrolyte components. On the other hand, LTO undergoes nearly no volume change during Li+ ion uptake and is therefore considered as zero-strain insertion material [66]. However, the increased safety performance comes along with a lower theoretical specific capacity of only 175 mAh g−1, thus resulting in an overall low specific energy [25]. The recent development and application of LTO is reviewed in [90, 91].

5 Cathode Materials for Lithium Ion Batteries To date, there is a wide range of materials for positive electrodes (cathodes), belonging either to the group of insertion materials or to conversion materials [49, 92]. In this review, only the most relevant commercialized cathode materials are discussed. For further detailed information on cathode materials under development, much more specialized reviews are available elsewhere [92–95]. Within the class of insertion materials, most of them (in the discharged state) can be expressed chemically as a crystal composed of Li+ ions, transition metal (TM) cations and anions based on either -phosphates, -sulfides or -oxides (LiTMPO4, LiTMS2, LixTMyOz). Beyond the performance-related aspects, other features including high reversible specific capacity, high mean discharge potential and high rate capability, price, safety and toxicity need to be considered for selection as well. The classification of insertion cathode materials conventionally occurs according to the type of spatial Li+ ion transport within the crystal structure, which is either one, two or three dimensional (1D, 2D, 3D), as depicted in Fig. 5. Reprinted from the journal

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Fig. 5 Classifications of active materials with respect to the spatial Li+ ion transport pathway within the crystal structure

LiTMPO4 and LiTMS2-based electrodes belong to the 1D and the 2D family, respectively, revealing the olivine and layered crystal structure type. The LixTMyOz-based electrodes can be subdivided into LixTMyO2 and LixTMyO4 electrodes, which belong to the 2D (layered crystal structure type) and 3D (spinel crystal structure type) families. While the mean potential of each crystal structure is tailorable by variation of TMs, the theoretical specific capacity is limited by the respective molar mass according to Eq. 2. Consequently, the highest theoretical specific capacities can be assigned to layered oxides, making them the most promising cathode material candidates up to date. For instance, the theoretical specific capacities for prominent representatives of each crystal structure, that are LiFePO4 (LFP), LiTiS2 (LTS), LiNi1/3Mn1/3Co1/3O2 (NMC111) and LiNi0.5Mn1.5O4 (LNMO), amount to 170, 225, 278 and 148 mAh g−1, respectively, which finally points to the superior role of the layered oxides in this regard. Even though, in practice, the specific capacity utilization in layered oxides must be restricted for reversibility reasons, as the delithiation beyond a respective threshold value is accompanied by thermodynamic structural instabilities [96], layered oxides have dominated the LIB market in past decades [57, 97]. Because there is still large scope for specific energy improvement, research and development efforts for layered oxides are still intense. Generally, the characteristic layered oxide reactions upon delithiation (charge) and lithiation (discharge) are accompanied by a continuous increase and decrease of the electrode potential, as depicted in Fig. 6 using the example of NMC111 active material. Hence, the targeted goal of specific energy increase can be realized simply by the increase of the cathode charge potential. This would increase not only the discharge potential (Udis) (V), but also the specific discharge capacity (qdis), which both contribute to the increase in specific discharge energy according to Eq. 3 [98, 99]. However, these benefits are accompanied with a continuous increase in specific capacity loss (qloss), when a certain potential threshold value is exceeded. The increase of qloss is closely intertwined with undesired consequences with respect to cycle life

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Fig. 6 Initial charge/discharge potential curve as a function of the specific capacity of NMC111, exemplary representing a layered oxide. The increase of the charge potential would increase the specific capacity (q), but also the specific capacity loss (qloss)

and safety aspects. Recent studies revealed that the origin of qloss increase could be attributed predominately to structural intrinsic changes of the active material, leading finally to an impeded and incomplete lithiation during discharge [96, 100]. Furthermore, it could be pointed out that the specific capacity fade (limiting the cycle life) is dependent on the type of active material rather than solely the charge potential [101]. The exemplary comparison of the specific capacity fade of LNMO and NMC111 electrodes in Fig.  7 demonstrates that, despite a higher charge potential (4.95  V  vs.  Li/Li+ for LNMO) the specific capacity fade is even less than for the NMC111 electrode having lower charge potentials. For the same active material though, the specific capacity fade increases with the charge potential, which could 100 Normalized sp. capacity / %

Fig. 7 Charge/discharge cycling with normalized specific discharge capacities for LNMO/ Li (charged to 4.95 V vs. Li/ Li+) and NMC111/Li (charged to 4.60 V and 4.80 V vs. Li/Li+) half cells after formation. Data reevaluated from [102]

90 80 70 LNMO at 4.95 V NMC111 at 4.60 V NMC111 at 4.80 V

60 50

10

20

30

40

Cycle no.

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be attributed to increased structural instabilities associated with increased delithiation amounts, as pointed out in Fig. 6. Consequently, the key to the desired performance improvement is intertwined with improvements in the active material itself. Therefore, the relation between chemical composition, structure and properties needs to be characterized and understood. From a crystallographic point of view, the layered oxides are based on altering TM and Li+ ion layers, each residing in oxygen octahedral coordinated 3a and 3b sites, respectively (Fig. 8). Properties with respect to performance and stability of layered oxide-based active materials can be tailored via (1) coating of the active material surface and/or (2) variation of the TMs, which are based conventionally on Ni, Co and Mn including doping with other elements, and/or (3) overlithiating of the material leading to Li1+xTM1-xO2 type layered oxides. (1) The advantage of active material coating is associated with stabilization of the electrode/electrolyte interface towards parasitic side reactions and increasing thermal and electrochemical stability [103–105]. However, the implementation of inactive or less active mass through coating not only decreases the gravimetric energy density but also results in an additional resistance for Li+ ion migration, which needs to be outweighed prior to application. (2) Layered oxides can be composed of single or even mixtures of TMs enabling a wide range of possible combinations. A prominent, already commercialized, single TM-based active material is LiCoO2 (LCO), showing good electrochemical performance for capacity utilizations up to ≈ 50% of theoretical capacity. Exceeding this limit (e.g., in case of overcharge) leads to safety hazards, which are associated with O2 release attributable to chemical instability

Fig. 8 Left Crystal structure of layered oxide-based cathodes, revealing altering layers of Li+ (yellow bullets) and transition metals (TMs; coordinated within violet octahedra). Right Magnification including two TM layers and a Li+ layer. The oxygen (violet bullets) coordinated TMs reside in Wyckoff 3a sites, while the analogues coordinated Li+ resides in Wyckoff 3b sites. The Li+/Ni2+ mixing phenomenon is marked with a red double arrow. The pros and cons of each possible TM within layered oxide-based cathodes are highlighted. Reprinted with permission from [101]. Copyright (2017) John Wiley and Sons

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of LCO [106]. The specific capacity restrictions, safety issues, toxicity, costs and resource problem of Co have necessitated the search for alternative active materials [107]. The substitution of Co with Ni, yielding LiNiO2 (LNO), indeed enables a higher capacity utilization, as the Ni-based layered oxide is thought to be more chemically stable (less risk of oxygen release). However, the cycle life and electrochemical performance, especially at elevated rates, do not meet the requirements necessary for application in LIBs. On the one hand, this is associated with the Ni3+ suffering from structural distortions due to the Jahn–Teller effect [108]. On the other hand, the synthesis yields non-stoichiometric Li1-xNi1+xO2 compounds, resulting in Ni2+ ions placed within the Li+ ion layer, mitigating Li+ ion mobility within the Li+ ion layer for several reasons: (1) They act as obstacles interfering the Li+ ion migration path, due to increased electrostatic repulsion between Ni2+ and Li+ ions. (2) They decrease the slab space (c-direction) within the Li+ ion layer due to higher valence of Ni2+ ions compared to Li+ ions [95]. Partial substitution of Ni with Co and Al effectively reduces the cationic disorder and improves the thermal as well as electrochemical performance. The paradigm mixture LiNi0.8Co0.15Al0.05O2 (NCA) is a commercial material, which is used, for example, in Panasonic wound cells for Tesla BEVs [92]. With respect to cost issues and chemical stability, LiMnO2-based layered oxides were also considered for application in LIBs [109]. However, this material suffers from poor cycle life due to Jahn–Teller effect related structural instabilities and irreversible phase transformations attributable to its trivalent state (Mn3+) [110]. Interestingly, the tetravalent Mn (Mn4+) has a beneficial effect with respect to structural and thermal stability [109, 111]. However, as the average TM oxidation state within the LiTMO2 structure is TM3+, the desired Mn4+ can be realized only in combination with (at least) equal amounts of Ni2+. These valence states are obtained according to crystal field theory, when Mn3+ and Ni3+ are originally incorporated within the structure [112]. However, the associated Ni2+ is undesired, because its similar ionic radius to Li+ (69 vs. 76 pm) leads to a partial Li+/Ni2+ site exchange, known as Li+/Ni2+ mixing. This phenomenon, depicted in Fig.  8 (red arrow), leads to the presence of Ni2+ within the Li+ ion layer, leading to the undesired effects described above for LNO active material [113]. Interestingly, the implementation of Co3+, yielding the well-known LiNixMnyCozO2 (NMC; x + y + z = 1) family, suppresses the Li+/Ni2+ mixing extent, but at the expense of the disadvantages of the Co element [114, 115]. The pros and cons of the three individual TM are summarized in Fig. 8, pointing out the required optimized trade-off between electrochemical performance, structural stability and cost as well as cycle life [107]. (3) The overlithiation of the active material occurs at the cost of the amount of redox-active TM within the structure, which is consequently accompanied with a decrease in theoretical specific capacity. As the theoretical specific capacity is not utilized completely during LIB operation, overlithiation has its advantage in increasing the TMs average oxidation state. As pointed out above, the lower oxidation states of Ni (Ni2+) as well as Mn (Mn3+) cause severe performance disadvantages, which can be minimized by increasing the overlithiation degree. Besides this advantage of conventional LiTMO2 chemistry, overlithiated materials also reveal an uncommon chemistry, enabling specific capacities even higher than theoretical values. The Reprinted from the journal

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extra specific capacity in those materials is thought to originate from oxidation of the oxygen within the structure. Even though the specific capacity for this structure is remarkable, the reversibility upon charge/discharge cycling remains a big challenge [116, 117]. It is worth noting that, to date, the specific capacity bottleneck within a full cell setup is the positive electrode (cathode). Further improvements in specific capacities of the negative electrode (anode) are not significantly beneficial as long as the specific capacity of the cathode remains constant [47]. For reasons of simplicity, focusing only on the masses of the active materials for both cathode and anode, this correlation was calculated as depicted in Fig. 9. The increase of the specific capacity of the anode within a full cell approaches the specific capacity value of the cell-capacity-limiting electrode, i.e. the cathode, asymptotically. Improvements in specific anode capacity are noticeable only up to a certain point (≈ 1000 mAh g−1). For sure, it is still reasonable to focus on the anode, as graphite, as the state-of-the-art (SOTA) anode material, reaches a specific capacity of just 372 mAh g−1 (dashed line). However, the specific capacity improvement of the cell-capacity-limiting electrode, the cathode, would have a very beneficial impact on the overall specific full cell capacity, which points to the importance of exploratory research and development in this field [118]. Ab  initio computational modeling allows for prediction of the influence of different TMs and doping elements on the Li+ ion diffusion kinetics, thus guiding more effective experimental research [119].

6 Electrolytes for LIBs The ability to conduct ions, and in particular Li+ ions, is the main function of the electrolyte in LIBs. Within the LIB, the electrolyte belongs to the inactive materials; however, its effect on the chemical nature and morphology of the formed interphases at the electrode/electrolyte interfaces have a major influence on the cycle life, power capability 400 Full cell sp. capacity / mAh g -1

Fig. 9 Full cell specific capacities as a function of the anodespecific capacities for constantly held cathode-specific capacities of 150 and 300 mAh g−1. Dashed line Specific capacity of graphite anode material of 372 mAh g−1. For the calculation only the masses of the active materials are considered

Cathode: 150 mAh g-1 300 mAh g-1

300

200

100

0

0

1000

2000

3000

4000

Anode sp. capacity / mAh g-1

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and safety performance of the LIB. Research on electrolytes for lithium-based batteries can be grouped into ceramic solid electrolytes [120], polymeric electrolytes [121, 122], ionic liquid based electrolytes [123, 124], liquid organic electrolytes [125–128], liquid aqueous electrolytes [129], as well as hybrid electrolytes [64, 130]. However, most of the electrolytes used in commercial LIBs are liquid organic solvent-based electrolytes, comprising a Li salt dissolved in a blend of aprotic organic solvents. Surprisingly, as compared to research outcome devoted to cathode cell chemistries, advances in electrolyte research and development have been scarce over the past 25 years [127]. The LIB commercialized by Sony in 1991 comprised a LCO positive electrode, a non-graphitizing carbon negative electrode and LiPF6 dissolved in a mixture of propylene carbonate (PC) and diethyl carbonate (DEC) as electrolyte [131]. With the energetic advantage of highly graphitic carbon being used as negative electrode in LIBs, ethylene carbonate (EC) replaced PC and became an indispensable component of every electrolyte formulation [125]. The structures of aforementioned organic carbonates are presented in Table 2. Since then, the skeleton electrolyte based on LiPF6 in a mixture of EC and linear alkyl carbonates has not changed significantly. In liquid electrolytes, the ionic conductivity (κ) (Ω−1 cm−1) is determined by the ion concentration (cI) (mol L−1) and the ion mobility (uI) (m s−1 V−1) [132] ∑ |z |Fc u , 𝜅= | i| i i (9) i

|zi |e0 ui = | | . 6𝜋𝜂ri

(10)

Table 2 Melting point (Tm), boiling point (Tb), flash point (Tf), viscosity (η) and relative permitivity (εr) and of commonly used organic carbonate solvents, viz. ethylene carbonate (EC), propylene carbonate (PC), dimethyl carbonate (DMC), diethyl carbonate (DEC) and ethyl methyl carbonate (EMC)a Solvent

Structure

Tm/ °C

Tb/ °C

Tf/ °C

η/mPa s−1 (at 25 °C)

εr (at 25 °C)

EC

36

238

143

1.90 (40 °C)

90 (40 °C)

PC

− 49

242

138

2.50

65

DMC

5

90

17

0.59

3.1

DEC

− 74

127

25

0.75

2.8

EMC

− 53

108

23

0.65

3.0

a

Data taken from [126]

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Here, zI is the charge of the ion I, e0 is the unit charge (1.602 10−19 C), η is the temperature dependent dynamic viscosity of the solvent (kg s−1 m−1) and rI is the stokes radius (radius of the ion I including its solvation sphere) (m) [132]. Molecular dynamics simulation are a suitable tool to study Li+ ion coordination by the solvent molecules and the Li+-anion ion pair formation [133, 134], and can be considered as complementary method to the spectroscopic methods, such as Raman and NMR, to study the structure of the ion solvation shell [135]. In LiPF6-based electrolytes, solvated Li+ ions have a lower mobility than the less solvated PF6− ions, thus resulting in the transference number of Li+ ion in the range of 0.2–0.4 [125]. The transference number (tI) is the fraction of the total current that is transferred by a particular ion:

�I i � ti = ∑� � � � i �Ii �

(11)

In this regard, it is important to remember that the power performance of the LIB is determined only by the current carried by the Li+ ion. Furthermore, a low Li+ ion transference number leads at the same time to an increased anion movement and enrichment at the electrodes, causing concentration polarization [125]. Equation  9 is valid only for electrolyte salts that dissociate completely into fully solvated ions. However, with decrease of the relative permitivity (εr) of the used electrolyte solvents, complete dissociation can no longer be achieved. Part of the dissolved electrolyte salt remains undissociated, thus being present as contact ion pairs in the solution (Fig. 10). Since contact ion pairs are macroscopically neutral species, they do not contribute to the total conductivity of the electrolyte. In general, in electrolyte solvents having εr < 10, the amount of electrolyte salt that is dissociated into fully solvated ions is small except in very dilute solutions [132]. Whereas in electrolyte solvents with

Fig. 10 a Conductivity change as a function of increasing electrolyte salt concentration. b Conductivity change of a 1 M LiPF6 salt in a high relative permitivity solvent, such as ethylene carbonate (EC), as a function of increasing low viscosity solvent concentration, e.g., dimethyl carbonate (DMC). Redrawn from [47, 136]

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εr > 40, the fraction of electrolyte salt that forms contact ion pairs is small except in highly concentrated solutions [132]. Next to a high εr value, suitable solvent molecules need to have a low viscosity (η), according to Eqs. 9 and 10. Since solvents kinetically stable with Li combine either high viscosity and high relative permitivity or low viscosity and low relative permitivity, a solvent mixture, usually comprising solvents with high εr values and solvents with low η values, is used (Table 2). In almost all cases, electrolyte conductivity in mixed solvents is superior to that in single solvent-based electrolytes [125]. Semi-empirical quantum-mechanical (SQM) and density functional theory (DFT)-based COSMOtherm calculations can be used to estimate the melting/flash/boiling points, electrochemical stabilities and viscosities of electrolyte solvents [137, 138] and thus are very helpful for the preselection of suitable electrolyte components. However, performance deterioration and safety risks caused by the poor thermal and chemical stability of present liquid aprotic electrolytes limit their application in LIBs to operation temperatures < 50  °C [139]. While reactions at the graphite/ electrolyte interface have been studied intensively, the degradation reactions inside the bulk electrolyte induced by high voltage and high temperature, as well as the influence of the formed electrolyte decomposition products on battery safety and performance have been rarely discussed [139, 140]. Figure 11 shows the decomposition reaction of LiPF6 in the presence of protic impurities resulting in the formation of various organophosphates [141–143]. However, the hydrolysis of LiPF6/organic

Fig. 11 Proposed decomposition mechanism of LiPF6. Reprinted with permission from [144]. Copyright (2015) Elsevier Reprinted from the journal

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carbonate-based electrolytes is still not fully understood, and support from computational chemistry is rare [103, 139, 141]. According to Eq. 7, the thermodynamic cell voltage of a LIB is determined by the difference between the electrochemical potentials of the anode and cathode. When the graphite anode is used with conventional LiPF6/organic carbonate-based electrolyte, the value of the graphite electrochemical potential lies well above the energy level value of the lowest unoccupied molecular orbital (LUMO) of the electrolyte. Because of the thermodynamic instability at the graphite/electrolyte interface, the electrolyte is reduced, which describes the electron transfer (ET) from the graphite electrode to the LUMO of the electrolyte. The reduction proceeds unless a passivation layer, the well-known SEI [63, 145, 146], is formed and prevents ET, or at least dramatically slows it down, as shown schematically in Fig. 12. The SEI is ideally considered as an electronic insulator and at the same time selectively permeable for only Li+ ions [63]. Theoretically, a 5 V cathode material with an electrochemical potential lower than the energy level value of the electrolytes highest occupied molecular orbital (HOMO) leads to oxidation of the conventional LiPF6/ organic carbonate-based electrolyte. ET from the HOMO of the electrolyte to the cathode takes place unless an effective passivation layer is formed. In this regard, it has been reported that the general trends obtained from DFT-calculated HOMO energies and computed oxidative stability limits often correlate with the experimental oxidation potentials of anions [147, 148] and solvents [149–151]. The lower the HOMO energy level of the solvent, the more stable is this compound toward oxidation. However, computed stability limits of investigated compounds are often significantly higher than experimentally measured values [152], where recent results even point to oxidative stabilities > 5 V  vs. Li/Li+ of conventional electrolytes [153]. In this regard, it is important to consider the presence of solvent–solvent or solvent–ion complexes in the electrolyte, which can lead to significantly different

Fig. 12 Schematic energy diagram of a lithium ion battery (LIB) comprising graphite, 4 and 5 V cathode materials as well as an ideal thermodynamically stable electrolyte, a state-of-the-art (SOTA) LiPF6/ organic carbonate-based electrolyte and a high voltage (HV) thermodynamically stable electrolyte. The electrochemical stability window (ESW), the lowest unoccupied molecular orbital (LUMO) energy level and highest occupied molecular orbital (HOMO) energy level are shown

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electrochemical stability values compared to computing on isolated molecules [139, 154]. The LUMO energy level can be used to predict the reductive stability of the solvent [85, 155]. An understanding of electrochemical decomposition reactions is also important as it provides basic insights into the reactions and products involved in the formation of the electrode/electrolyte interphases [156, 157]. The calculation of oxidation and reduction potentials of electrolyte components serves to establish trends that can guide the selection of advanced electrolyte formulations [158]. Recent progress in research on high voltage stable electrolytes is reviewed in [159]. The most promising alternative solvent classes with increased oxidative stabilities are fluorinated carbonates [160–162], sulfones [149, 163], and aliphatic dinitriles [164, 165]. However, the high cost of production and poor compatibility with graphite anodes limit their applicability in LIBs. Today, nitriles are used only as co-solvents up to 10 vol% in commercial LIB electrolytes [159]. The use of electrolyte additives is one of the most economic and effective methods with which to tailor the performance of LIB with regard to desired functionality [166]. In general, the amount of an electrolyte additive is ≈ 5% either by weight or by volume in order not to change the bulk electrolyte properties [166]. Hundreds of different additives have been reported in the literature and can be classified according to their functionality (Fig. 13). Vinylene carbonate (VC) is by far the most widely used and intensively studied film-forming electrolyte additive for graphite-based anodes [125, 127]. A small amount of VC (in most cases 2% by weight) in the liquid aprotic electrolyte effectively reduces the irreversible capacity loss associated with the bulk electrolyte reduction on graphite anodes. In general, SEI-forming additives are reduced at the negative electrode prior to the bulk electrolyte components due to their higher reductive potential [166]. The reduction process is accompanied by the formation of insoluble decomposition products that are immobilized at the anode/ electrolyte interface in a film with thicknesses up to several tens of nanometers, thus shielding the bulk electrolyte from the charged electrode surface [166]. SEI-forming Fig. 13 Different additive target functions in the LIB

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additives not only reduce gas generation during the reduction process but also increase the stability of the SEI, e.g., at elevated temperatures [166]. The reaction mechanism of VC was elucidated by ab initio calculations to interpret and simulate XPS valence spectra to identify VC-derived decomposition products in the electrode/electrolyte interphases [167]. VC is radically polymerized on the anode surface, thus resulting in the formation of a thinner SEI when added to the conventional LiPF6/organic carbonate-based electrolyte (Fig.  14) [167]. However, theoretical modeling of the SEI, to obtain further insight into the interphasial structure, is rare [168–171]. Fluroroethylene carbonate (FEC) is the electrolyte additive most reported for EI formation on silicon-based electrodes [172, 173]. The improvement mechanism of FEC is still under debate [127, 174, 175]. Recently, Tateyama et al. studied the decomposition of FEC by means of computational modelling and stressed the role of LiF in the SEI composition acting as a glue for the organic SEI components, especially on silicon-based electrodes [174]. However, the composition of the FECderived SEI, the chemical reactions involved, and the reaction intermediates remain to be elucidated [174]. Biphenyl (BP) is by far the most used shutdown additive to increase the intrinsic safety of the LIB. At the potential of 4.54 V vs. Li/Li+, BP is oxidized and forms a highly resistive cathode passivation film containing poly(pphenylene) (Fig. 15) [176]. The co-generated protons diffuse to the anode side and are reduced to H2, leading to an increase in internal cell pressure [136]. At a defined pressure, the current interrupt device (CID) in the cell is activated and the current flow is interrupted [136]. Therefore, BP is used only in LIBs having a CID, e.g., in round cells.

Fig. 14 Schematic illustration of vinylene carbonate (VC)-induced solid electrolyte interphase (SEI) formation

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Fig. 15 Working principle of biphenyl (BP) as a shutdown additive

Due to the development of new cell chemistries, especially cathode materials with higher operation potentials, there is a need for the development of new shutdown additives with higher oxidation onset potential [177]. In this regard, quantum chemical calculations are useful screening tools with which to identify suitable candidates [176].

7 Conclusion Regarding energy and power design, LIBs have a clear advantage compared to other secondary battery technologies. Yet, research into new electrode materials to further increase energy density, power density, cycle life and safety at affordable cost continues. The design and development of new electrode materials and electrolyte components based on understanding of operation and failure mechanisms of the battery, also at the electrolyte/electrode interfaces is important to further advance the limits of power, safety and cycle life in the LIB. Despite the fact that electrolyte belongs to the group of inactive materials in the LIB, the physicochemical properties and characteristics of the electrolyte/electrode interfaces formed significantly determine power and safety. Computational modeling of electrolytes provides significant insight into the electrochemical and transport properties of the bulk electrolyte and electrolyte decomposition reactions as well as the characteristics of the formed electrolyte/electrode interphases, which can effectively support research and development of new electrolyte components. Nevertheless, a link between predicted parameters and experimental values is always necessary to assess whether or not, and how accurately, any computational method and strategy can be used in a predictive manner.

References 1. Electrochemistry Dictionary and Encyclopedia (2014) The electrochemical society. http://knowl edge.electrochem.org/ed/dict.htm 2. Zoski CG (2007) Handbook of electrochemistry. Elsevier, Amsterdam

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Top Curr Chem (Z) (2018) 376:7 https://doi.org/10.1007/s41061-018-0187-2 REVIEW

Assessment of Simple Models for Molecular Simulation of Ethylene Carbonate and Propylene Carbonate as Solvents for Electrolyte Solutions Mangesh I. Chaudhari1 · Ajay Muralidharan2 · Lawrence R. Pratt2 · Susan B. Rempe1

Received: 25 July 2017 / Accepted: 23 January 2018 / Published online: 12 February 2018 © The Author(s) 2018. This article is an open access publication

Abstract Progress in understanding liquid ethylene carbonate (EC) and propylene carbonate (PC) on the basis of molecular simulation, emphasizing simple models of interatomic forces, is reviewed. Results on the bulk liquids are examined from the perspective of anticipated applications to materials for electrical energy storage devices. Preliminary results on electrochemical double-layer capacitors based on carbon nanotube forests and on model solid-electrolyte interphase (SEI) layers of lithium ion batteries are considered as examples. The basic results discussed suggest that an empirically parameterized, non-polarizable force field can reproduce experimental structural, thermodynamic, and dielectric properties of EC and PC liquids with acceptable accuracy. More sophisticated force fields might include molecular polarizability and Buckingham-model description of inter-atomic overlap repulsions as extensions to Lennard-Jones models of van der Waals interactions. Simple approaches should be similarly successful also for applications to organic molecular ions in EC/PC solutions, but the important case of Li+ deserves special attention because of the particularly strong interactions of that small ion with neighboring solvent molecules. To treat the Li+ ions in liquid EC/PC solutions, we identify interaction models defined by empirically scaled partial charges for ion-solvent interactions. The empirical adjustments use more basic inputs, electronic structure calculations and ab initio molecular dynamics simulations, and also experimental results on Chapter 3 was originally published as Chaudhari, M. I., Muralidharan, A., Pratt, L. R. & Rempe, S. B. Top Curr Chem (Z) (2018) 376: 7. https://doi.org/10.1007/s41061-018-0187-2. * Susan B. Rempe [email protected] 1

Center for Biological and Engineering Sciences, Sandia National Laboratories, Albuquerque NM 87185, USA

2

Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans LA 70118, USA

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Li+ thermodynamics and transport in EC/PC solutions. Application of such models to the mechanism of Li+ transport in glassy SEI models emphasizes the advantage of long time-scale molecular dynamics studies of these non-equilibrium materials. Keywords Li-ion battery · Molecular dynamics simulations · Propylene carbonate · Ethylene carbonate

1 Introduction An electrochemical voltage window is a primary concern for electrical energy storage applications of an electrolyte system, e.g., for lithium ion batteries (LIBs) and electrochemical double-layer capacitors (EDLCs). That voltage window is a primary issue for the energy density, but also a consideration in addressing safety. As a practical matter, that voltage window concern excludes aqueous electrolyte solutions [1]. Non-aqueous electrolyte solutions [2] are well-recognized, but the molecular simulation experience with those systems is orders of magnitude more limited than for aqueous systems [3–5]. This is partly due to the broad importance of water as a liquid medium [6], but also due to vast chemical and compositional variety relevant for non-aqueous systems [7–10]. Understanding that daunting range of chemical possibilities, including assessment of voltage windows, has put natural emphasis on screening enabled by electronic structure computations of theoretical chemistry [11–13]. But macroscopic characteristics of these liquids—such as phase diagrams, dielectric responses, and fluid phase kinetics—are relevant too, and direct numerical simulation of the solutions help in that screening. Careful molecular simulation often requires validation of models and techniques, consideration of a range of thermodynamic states, and understanding the scale limitations of the results. Therefore it can be helpful for simulation work to examine relevant cases in depth to complement screening approaches. Recent work has aimed at filling in the simulation basis for study of non-aqueous electrolyte solutions, i.e., for ethylene carbonate (EC) and propylene carbonate (PC) systems, at a molecular level (Fig. 1). This report collects and discusses recent

Fig. 1 Chemical structures of ethylene carbonate (EC) and propylene carbonate (PC)

O H 2C

O

O

C

C O CH2

O H 2C

O CH CH3

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simulation results on these solvents to identify basic research that might help in further design of materials. Molecular simulation is a useful tool for development of new materials. Development of effective, simplified molecular simulation models would enable enlightening simulation of dynamical phenomena of specific interest for electrical energy storage systems, i.e., transport through inhomogeneous or non-equilibrium materials, or of annealing processes involving those non-equilibrium materials. Electrochemical double-layer capacitors (EDLCs), or supercapacitors [14], present cases of inhomogeneous materials. EDLCs based on carbon nanotube (CNT) forests provide a specific setting for molecular-scale examination of the dynamics of propylene carbonate solutions of complex salts [15], a setting where the underlying microstructure is comparatively unambiguous [16]. We note that a variety of solvent/electrolyte systems, including ionic liquids [10], are commonly considered with EDLCs. Nevertheless, molecular-scale descriptions that might explain the dependence on electrode microscale structures or of the rates of charging/discharging have not been carried through. Synthesis of CNTs [17–19] with well-characterized molecular-scale microstructure should assist in establishing the molecular theories sought to understand these systems fully. An even more prominent example of important molecular-scale kinetics involving inhomogeneous or non-equilibrium materials is that of Li+ ion transport through the solid electrolyte interphase (SEI) of lithium ion battery (LIB) [20]. The SEI of an LIB forms during initial charging/discharging cycles [21–23]. Solution components decompose [24], forming a passivating anode layer. Li+ ions travel through that complex organic material. The composition of the SEI depends on a variety of factors, including solvent and additives, ions, anode material, voltage, temperature and the use history. Understanding the atomic-scale mechanism of transport of Li+ ion through the SEI should assist in development of high-performance LIBs, through better characterization and control of the SEI layer. Molecular simulations might help to bridge the learning gap [8, 9, 25, 26]. Molecular calculations and simulations are typically a necessary prerequisite for basic molecular theories. Molecular calculations span a daunting range of algorithmic techniques, and a daunting range of space and time scales. For example, quantum calculations track electrons and can characterize decomposition of electrolytes at anode surfaces [8, 9, 22, 27, 28]. These methods include ab  initio molecular dynamics (AIMD), which have the drawback of computational expense and the concomitant limitation to small systems and time scales [29–31]. On the other hand, if chemical changes such as chemical bond rearrangement are essential to the study, AIMD provides natural perspectives on those phenomena. Classical molecular dynamics simulation with model molecular force fields— ‘force field molecular dynamics’ (FFMD)—inhabit a broader region of the simulation scale. Useful force field models can span a broad range of possibilities, from frankly ad hoc models, to models that are recognized as coarse-grained on a pragmatic basis, then including progressively more complicated models. Electron coordinates can be reintroduced into FFMD approaches by development of models that include molecular polarizabilities. Polarization of that type has been considered important for this problem [32]. The polarizable force field of Borodin et al. [7]. for Reprinted from the journal

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the carbonate solvents and SEI layer models [25, 26], has been applied to LiBF4 in PC [34]. Highly specialized force fields and parameters are not readily available for common molecular simulation packages. Additionally, their complexity limits their use for study of transport behaviors for novel materials that interrogate molecularly long correlation times. This overview focuses on the pragmatic middle of FFMD simulations focused on non-polarizable force fields with empirical parameters. 1.1 Methods and Force Fields The FFMD simulations discussed specifically here were carried out using the GROMACS simulation package [35]. Details of the calculations differ slightly between cases, as noted with those discussions below, but were always obtained with force fields of standard non-polarizable format. We note the success of empirical force fields for liquid water [3–5]. EC and PC liquid results here used all-atom optimized potentials for liquid simulation (OPLS-AA) force fields and parameters [36]. There were several distinct reasons for these choices, beginning with simplicity and accessibility of these molecular simulation basics. Another reason for the present simple choice of force field model is that we emphasize liquid phase thermal properties that are statistical challenges for molecular simulation. Thus, the ability to examine sufficiently long statistical series is an important consideration. Finally, we note the sufficiency of empirical potential structure refinement (EPSR) modeling for reproducing the neutron diffraction results with exactly the same forms [37]. Thus, the present simple force field models should be sufficient also for those important data. We identify secondary specific differences among those FFMD calculations discussed below, but we here provide several common features. These calculations adopted constant pressure simulation conditions with p = 1 atm on the basis of the Parrinello-Rahman barostat [38]. Temperatures were maintained with a Nosé-Hoover thermostat [39, 40]. A time step of 1 fs and time constant of 2.5 ps were used for the thermostat and barostat, respectively. Periodic boundary conditions were applied standardly to simulate bulk liquid conditions. The particle mesh Ewald method was used to compute electrostatic interactions, and Lennard-Jones interactions were cutoff at 1.2 nm. Long-ranged dispersion corrections were also applied. Bonds involving hydrogen atoms were constrained using the linear constraint solver (LINCS) algorithm [41]. Extensions of such a simple force field model are interesting for the chemical physics of these problems. A Buckingham [32, 42] model of van der Waals repulsions is an extended feature that is likely to be generally helpful compared to a traditional 1∕r12 (Lennard-Jones) model. We comment further about that extension below when we discuss solvation of Li+ ions in these carbonate liquids. Another interesting extension is the inclusion of solvent molecular polarizability in these force fields [32, 42]. This feature is likely to be specifically important for electrolytes— involving free ions—but we emphasize that dispersive van  der  Waals interactions are modeled separately in these forces fields. We note in passing that establishment

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of saturated solution conditions, perhaps involving ion pairing as a mechanism for phase separation, is primarily sensitive to (attractive) dispersive van der Waals interactions [43–45]. As with the common empirical force fields for liquid water simulation [3–5], the non-polarizable force field parameters should be recognized as effective values that approximate the outcomes obtained with more complicated force fields. 1.2 Plan of this Report We will collect and discuss molecular simulation results on the EC and PC liquids and on solutions with electrolytes relevant to EDLC capacitors based on CNT forests [44, 46–48]. We will emphasize macroscopic characteristics that are often considered in discussions of such applications, particularly interfacial structure, dielectric responses, and molecular mobilities. In focusing here on the molecular basis of macroscopic characteristics of these liquids, the present report aims to complement the recent review [49] that emphasized synthesis and catalysis. We take up the example of EDLCs based on CNT forests where the liquid carbonate solutions are integral components. We then include Li+ in these calculations [32, 50], leading to discussion of simulation of a model LIB SEI layer [42]. In closing this introduction, we reemphasize the common goal of devising highcapacity, fast-charging, safe electrical energy storage systems [21]. Commonly used electrical energy storage devices do present distinct material requirements. Therefore, breadth and fidelity in understanding possible materials should be an advantage. Indeed, other solvents have been considered in this context. For example, glycerol carbonate has been studied recently by neutron diffraction and modeling [37]. Nitriles have received extended study [1, 51–53], as has acetonitrile [54–62]. Of course, it is the non-aqueous conditions that are of interest here. But LIB applications have involved carbonate solvents, instead of nitriles [1], because of the role of carbonate molecules in chemical processes that form the SEI [63]. A recent study of PC/acetonitrile mixtures is striking due to the unusual solvent combination [64].

2 Ethylene Carbonate and Propylene Carbonate Liquids The vapor pressures of EC and PC are low in regimes of practical use [44, 66], and thus they are strongly bound liquids. We further characterize [46] this ‘strongly bound’ quality by the ratio Tc ∕Tt of their critical temperatures to their triplepoint temperatures. For the well-studied Lennard-Jones model liquid, this ratio is Tc ∕Tt = 1.9. But for liquid PC and EC, this ratio is 3.5 (PC) and 2.3 (EC). Acetonitrile and water, for which Tc ∕Tt ≈ 2.4, provide further comparisons [46]. Estimation of Tc for our standard simulation model of PC, on the basis of extrapolation of liquid-vapor surface tensions (Fig.  2), is remarkably accurate. Study of those interfaces shows that the plane of the PC molecular is statistically oriented parallel to the interfacial plane, with the methyl group directed toward the vapor phase. Planar stacking persists when liquid PC contacts a planar graphite surface

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0.8

p(uz )

1.5

0.6 1.0 assumed exponent: 5/4

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Tc = 763K (exp) 0.4 0.2

Tc ≈ 740K −0.6

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uz

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1.0

400

500 600 T (K)

[γ(T )/γ(300K)]4/5

1.0

700

2 1

r

m)

0

z (nm)

Fig. 2 (left) For PC molecules in the liquid-vapor interfacial layer at T = 300 K, the probability density for projection of the unit vector normal to the carbonate plane onto the axis, perpendicular to the interface. The inset in upper-right corner of that panel indicates the slab geometry used for these calculations [44, 65]. The ‘outer’ (vapor) direction corresponds to projections near 1.0. The most probable orientation aligns the carbonate plane parallel to the plane of the interface, with the methyl group extended toward the vapor phase. uz > 0.5 (𝜃 < 60◦) for about 50% of interfacial PC molecules. (right) Liquid-vapor interfacial tensions for PC, extrapolated to estimate the critical temperature Tc as shown. The surface tension for the lowest T shown here agrees well with the one experimental evaluation of that tension at T = 20◦ C. The estimated vapor pressures for these cases are roughly correct [66]. The inset on the right panel is a configuration drawn from the T = 600 K calculation, which thus gives an indication of the co-existing vapor. These results together provide support for the observed interface structures and suggest that the balance of attractive intermolecular interactions is realistic

4 r (nm)

Fig. 3 PC droplet on graphite. The left side is the observed millimeter-scale droplet [44]. The blue curve on the right side is the nanometer-scale simulated droplet shape, obtained with adjustment of the van  der  Waals interaction to match the experimental contact angle as described in that reference. The fringe on the right side of the simulated droplet illustrates nanometer-scale molecular layering of PC molecules in contact with the graphite surface

(Fig.  3), except that the methyl group is preferentially oriented toward the liquid phase in that case [44]. The relative orientation of near-neighbor PC molecules in the liquid (Fig. 4) again display this rough planar stacking motif, with the two nearest neighbors corresponding to a plane above and a plane below a distinguished PC molecule. The dipole moments of these stacked neighbors tend to be anti-parallel and this has by now been experimentally confirmed on the basis of neutron diffraction from PC and glycerol carbonate [37]. The liquid density of standardly simulated PC at p = 1  atm is several percent denser [44] than the experimental value near T = 300 K. The thermal expansion

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15 T = 320 K

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g (r)

n (r)

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PC

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0 0.2

0.4

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1.0 0.2

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r (nm)

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r (nm)

Fig. 4 Radial distribution functions associated with carbonyl carbon atoms. (black): Traditional radial distributions involving all carbonyl carbon atoms with the characteristic split primary peak, further quantified by the neighborship-ordered radial distribution functions for the closest (blue), 2nd-closest neighbors (red), and 3rd-closest neighbors (green) of a carbonyl carbon atom. The embedded molecular graphic illustrates that these close pairs exhibit stacking of carbonate planes and antiparallel dipole moments. The two closest neighbors saturate the closest peak of the traditional distribution function, and stacking of one plane on top and another on bottom achieves that

coefficient from the simulations under those conditions is highly accurate, although the isothermal compressibility is too small by about 50% [44]. We expect that discrepancy in the isothermal compressibility would be improved by effective replacement of Lennard-Jones 1∕r12 repulsions by Buckingham repulsions [32, 42]. 2.1 Molecular Mobilities Here we characterize the mobilities of EC and PC molecules in their liquid by the slope of the mean-squared displacement (msd) ⟨ ⟩ d Δr(t)2 (1) ∼ 6D , dt at long times t, thus evaluating the self-diffusion coefficient, D. But we can take that characterization deeper (Fig. 5) before considering those mobilities broadly (Fig. 6). The step deeper is to consider the velocity autocorrelation function (acf) [67] � � C(t) = ⟨𝐯(0) ⋅ 𝐯(t)⟩∕ v2 , (2) from which the mobilities

⟨ ⟩ d Δr(t)2 dt

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⟨ ⟩ = 2 v2

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∫0

C(𝜏)d𝜏,

(3)

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t v (τ ) · v (0) dτ (nm2 /ps) t (ps) 0  ∆r(t)2 nm2

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4

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Fig. 5 (top-left) Time correlation functions associated with the velocity of the center of mass of PC molecules in liquid PC at T = 300 K. For this strongly bound liquid, the velocity acf relaxes through negative values after several collision times. Consistent with this, the friction kernel 𝛾(t) relaxes over many collision times. This behavior has been attributed to attractive intermolecular interactions in these strongly bound liquids. (top-right) Mean-squared displacements of PC in liquid PC (dashed). The time derivative (following Eq.  3, blue solid curve) shows a prominent maximum due to the negative tail of the velocity autocorrelation function. After that maximum, the msd achieves a constant slope only slowly. This behavior is not evident, for example, in the hard-sphere liquid model [46]. (bottom) Similar plots for EC

may be then derived. Here the indicated velocities are those of the center of mass of the polyatomic EC/PC molecules. We also consider the friction kernel 𝛾(t) defined by [67]

m

t dC(t) =− 𝛾(t − 𝜏)C(𝜏)d𝜏 , ∫0 dt

(4)

with m as the mass of the molecule. 𝛾(t) characterizes the random forces on these molecules, and

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T (K) 600

400

350

300

-9 ethylene carbonate

ln D (cm2 /s)

-10

Qd = 3.6 kcal/mol -11 -12 -13

propylene carbonate Qd = 4.0 kcal/mol 1.5

2.0

2.5

3.0

3.5

103 /T (K) Fig. 6 Comparison of simulation [48] and experimental [70] values of EC/PC molecule self-diffusion coefficients, over a range of temperatures at constant ambient pressure. The experimental results were extracted from studies of LiPF 6 solutions. Qd is the activation energy parameter, ln D ∝ −Qd ∕kB T , identifying the slope of the indicated fitting lines

⟨ ⟩ 𝛾(0) = mΩ2 = F 2 ∕3kB T ,

(5)

emphasizes ⟨ ⟩ that connection with the forces on the molecules with Ω2 = F 2 ∕3mkB T. An interesting observation for these strongly bound liquids [46, 47, 68] (Fig.  5) is that C(t) exhibits a negative tail, i.e., relaxation through negative values for times longer than a collision time, and that negative tail substantially affects the evaluation of D through Eq. (3). Contrary to the standard Langevin picture [67], the friction kernel 𝛾(t) also persists in relaxation over the same timescales of many collision times. That longer-timescale relaxation has been attributed to attractive intermolecular interactions in these strongly bound liquids [46, 47, 68, 69], particularly for the mobility of ions in solution for which long-ranged attractive forces are defining qualities. For the neutral PC molecule, indeed, that slowly relaxing tail of 𝛾(t) diminishes for the highest Ts considered [46, 47]. Experimental results for D are only available for solutions of EC and PC with LiPF6 at 1M concentration [70]. Nevertheless, here we compare our computed results [48] to those mobilities (Fig. 6). Our results agree with those experimental values to within about a factor of 2, satisfactory accuracy here. This encouraging comparison supports the use of the present non-polarizable force field in the studies reviewed below. The temperature dependence of ln D is linear in 1/T over the range considered. Reprinted from the journal

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(b)

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3.0 τ = 31 ps (exp) 2.0 ethylene carbonate H ∗ = 3.1 kcal/mol

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propylene carbonate H ∗ = 3.5 kcal/mol

40 propylene carbonate

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103 /T (K)

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Fig. 7 a Static dielectric constants 𝜖∕𝜖0 (in open triangles) and b relaxation times 𝜏 for EC (black) and PC (red) at several temperatures. The experimental relaxation times indicated are those provided in the figure captions of the available experimental report [71], which incorporates an estimate of molecular polarizability and assumes a Debye relaxation model. Dashed lines are linear fits to the data, provided for visual guidance

2.2 Dielectric Constants and Relaxation Times The high dielectric constants of EC and PC liquids correlate naturally with the solubility of strong electrolytes, including lithium salts, in these solvents [72]. Dielectric characteristics are thus properties of first interest for these liquids. Dielectric constants and relaxation times are strongly temperature-dependent, and that might have consequences for battery efficiency and safety. Here, the computed static dielectric constants (Fig. 7a) are in good agreement with the experimental values for both PC and EC [44, 48, 62, 65], though at the lowest temperature here, the discrepancy is nearly 30% (too large) for EC. Dielectric relaxation characterizes the ability of the material polarization to follow a changing applied electric field [73]. Harmonic analysis of the field and the polarization leads to a frequency-dependent, complex dielectric constant [73–75]

𝜖(𝜔) = 𝜖 � (𝜔) − i𝜖 �� (𝜔).

(6)

with real and imaginary parts. 𝜖 (𝜔) describes frictional energy loss, and can be obtained from the polarization autocorrelation function [71, 75–77] ��

P(t) = ⟨M(0)M(t)⟩∕⟨M 2 ⟩,

(7)

PKWW (t) = exp[−(t∕𝜏)𝛽 ],

(8)

of the total dipole moment at time t, M(t), of the liquid. The acf P(t) is then fit to the Fourier transform of a stretched exponential (or Kohlrausch-Williams-Watts, KWW) model [78],

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where 𝛽 is the fitting parameter. Available experimental data and analysis of simulation data suggest that 𝛽 = 1 (Debye relaxation) is an accurate approximation for these systems. The agreement between computed and experimental relaxation times is encouraging: 𝜏 = 46 ps from experiment on PC at room temperature compared to 𝜏 = 48 ps from these simulations. Note that extraction of the experiment relaxation times utilized models incorporating electronic polarizability 𝜖(𝜔 = ∞)∕𝜖0, which we deliberately avoid here. Still, the relaxation times of 46 ps for PC, 31 ps for EC, and 8 ps for water emphasize [77] the comparative sluggishness of the carbonate solvents. This comparative sluggishness presents a severe challenge for simulation of these liquids on the basis of the more demanding simulation techniques such as AIMD. The temperature dependence of the relaxation times

𝜏 −1 = A exp(−H ∗ ∕kB T),

(9)

can be modeled with an activation energy, H . For simplicity, we assumed the preexponent factor A to be independent of T [71, 79, 80], and calculate H ∗ from the slope of the Arrhenius plot, ∗

ln 𝜏 ∝ H ∗ ∕kB T .

(10)

The computed H for EC (3.1 kcal/mol) and PC (3.5 kcal/mol) are within the range of activation enthalpies reported for liquid water (2.8 − 4.5 kcal/mol for 278K < T < 348 K) [81]. Though the present computational results cover a broad temperature range, fitting beyond a single activation energy has not been warranted so far. Still, it would be interesting, and maybe of practical relevance, for subsequent experiments and modeling to investigate super-cooled conditions more thoroughly. ∗

2.3 Non‑linear Polarization Response The molecular electric fields at play on a molecular scale in ionic solutions are often much stronger than the laboratory electric fields used to measure dielectric constants. Thus, the equilibrium polarization responses to strong fields (Fig. 8) are often queried, even though statistical mechanical theories are less firmly grounded then. Indeed, the underlying theory of non-linear polarization response has been reexamined recently from a basic perspective [88–90]. Still, it is now clear that long-standing simple models [83] can do a good job of fitting non-linear polarization responses in controlled settings [62, 84, 91]. Interesting recent work [62] studied PC, EC, dimethyl carbonate (DMC), acetonitrile, and EC/DMC mixtures, and observed electrofreezing in several of these cases. 2.4 Electrochemical Double‑Layer Capacitor Based on CNT Forests Beyond clear potential for practical significance, EDLCs based on CNT forests offer the possibilities of better molecular-scale understanding of those solutions in contact with charged electrodes. This possibility is enabled by the simplicity of the electrode Reprinted from the journal

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(Eext )

0

-1

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40 20 0

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2 3 Eext (V/nm)

4

( ) Fig. 8 For uniform liquid PC, 𝜀 Eext ∕𝜀0 − 1 as a function of external electric field strength, redrawn from Yang et  al. [82]. These molecular dynamics results were obtained for the uniform liquid with an applied uniform electric field. The error bars indicate a 95% confidence interval. The curve is the fitted Booth model [62, 83–86]. The shaded region identifies the low-field regime based on the Booth model and that empirical parameterization. Evidently, the high-field behavior is simple in the model and the simulation. These calculations have been reexamined [87], and refined and extended [62]. Distinct from these uniform liquid calculations [82], the inset suggests how molecular-scale electric fields might be approached, i.e., by investigation of common lab-scale potential changes over nanometer-scale gaps

chemistry and the fact that the microstructures of CNT forests can be simple and controlled over interesting ranges [94]. Thus EDLCs based on CNT forests provide a comparatively simple and controllable setting to learn about the molecular solutions. Outstanding practical questions that call for better basic molecular-scale understanding include (a) the dependence of the capacitance on electrostatic potential [92, 94] and (b) the dependence of capacitance on pore sizes for mesoporous electrode materials [95, 96]. Conclusive examination of those interesting questions will have to await further considerations. Here we make some primitive observations on work available so far. One consideration for simulating these systems is the modeling of the electrodes. The simple model exemplified in Fig. 9 sets fixed charges based on appropriate preliminary calculations [47, 92]. An alternative focuses on the conducting nature of the electrode and reformulates the simulations to incorporate a constraint of constant electric potential in a conducting phase [97–102]. The work of Wang et al. [97] studying LiClO4/acetonitrile between planar graphite electrodes with a constant potential MD calculation provided a clarifying example. The distribution of the fluctuating charges on electrode atoms was simple (unimodal) for cases exploring a voltage window below 4 V, though that situation changed markedly for net electric potential differences between the electrodes of 4 V and above. We note in passing that 4 V is close to the practical limit for the voltage window for experimental EDLC cases [94]. The complexities observed with the ultra-high potentials were associated with the depletion of the acetonitrile occupancy in Li+ inner shells for Li+ ions in close

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2

CNT center-axis

1 φ (V)

Pore

pore center-axis

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5

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Fig. 9 Left top: a snapshot of a simulation box [47, 92] containing 4 positively (left) and 4 negatively (right) charged CNTs, each of 360◦ C atoms, with ions filling the pore regions around CNT. A total charge of q = ±N e is set on each nanotube with N = (2, 4, 6, 8, 10) and a solution of 1 M TEABF 4 (tetraethylammonium tetrafluoroborate) electrolyte (blue and orange, respectively) in propylene carbonate (sticks). The highest charged case, then, has 223 C/gm, or adoption of 1300 m 2 /gm as a standard value for the specific area, 0.17 C/m 2 . The electrostatic potential was evaluated from the observed average charge density by numerical solution of the discretized Poisson equation [93]. Left bottom: a variation of electrostatic potential along the z-axis for a pore radius of R = 1.5 nm at a charge level of N = 6. Right: a cross-section perpendicular to the z-axis defining the pore radius and the location of pore and CNT axis

1.0

∆z (t)2 (nm2 )

0.8 vz (0) vz (t) / vz 2

0.010

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0.6 0.4 0.2

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DPC = 3.9 × 10−6 cm2 /s 0.5

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Fig. 10 Comparison of mobilities of PC molecules in bulk solution with PC molecules in the pore space of the CNT forest (Fig. 9) [47]. In this case, the CNTs are not charged and the pore radius (Fig. 9) is R = 1 nm. The indicated value of D (right panel) is for PC molecules in the bulk solution. Notice that the mobility of PC molecules in the pore looks diffusive at intermediate times, but not for longer times here. Further, the suggested intermediate-time diffusive motion is faster in the pore, presumably an effect of preferential orientation of PC molecules in the pore space Reprinted from the journal

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contact with the electrode. Those close contacts qualitatively change the density profiles of Li+ ions with respect to the electrode, but do not qualitatively change the density profiles of the bigger ClO4 − ion. The physical conclusion is that the EDLC/CNT calculations discussed above with molecular ions (Fig. 9) conservatively aim for a range in which they provide a reasonable initial step, perhaps subject to subsequent refinement. We note additionally that applications of constant potential MD calculations, implemented in simulation packages such as LAMMPS [103], have been limited so far in the number of electrodes and their configurations, specifically to two-planar electrodes. We take up the important special case of Li+ in the next section. We emphasize that realistic molecular models of EDLC/CNTs are feasible for direct numerical simulation of the pore filling and the electrical characteristics [47, 91, 92]. This reduces possible uncertainty about solution composition in the pore spaces and permits study of the kinetics of the filling in realistic settings. That the relevant molecular mobilities are different in the pore spaces is already clear (Fig. 10).

3 Empirically Scaled Partial Charges for Li+...Carbonate Interactions The results discussed in previous sections suggest that a parameterized, non-polarizable force field can reproduce experimental structural, thermodynamic, and dielectric properties of EC and PC liquids with acceptable accuracy [44, 46–48]. Next we consider the important case of addition of Li+ ions to EC and PC. A primary concern is a valid description of the thermodynamics of Li+-solvent interactions. In view of the strength of those interactions, and non-linear behaviors exhibited in Fig. 8, these thermodynamic issues are not taken for granted. In setting revised models, we considered partial charges, empirically scaled on the basis of electronic structure calculations and available experimental results. The electronic structure-based methods employed [50] are (a) quasi-chemical theory for the thermodynamics, and (b) AIMD calculations for structural and mobility information. We have compared results using partial charges available in the standard OPLSAA distribution for EC and PC solvents [104] to results derived from partial charges that were subsequently reduced to 90 and 80% of those values. Simulations treated a single Li+ ...PF6 − ion pair in both solvents. We compared structural and thermodynamics results with chemically based AIMD simulations. 3.1 Free Energy Results and Quasi‑Chemical Theory (QCT) QCT is based on the study of the occupancy of an inner shell of an Li+ ion, here, by the carbonyl O atoms of the solvent. QCT provides the free energy, specifically (ex) + the excess chemical potential, 𝜇Li + , for a solution phase Li [50]. We use the cluster QCT method [105, 106] ) ( (ex) (ex) (ex) (0) n 𝜇Li(sol) 𝜇Li , (11) + = −kT ln Kn 𝜌sol + + − n𝜇sol n

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Top Curr Chem (Z) (2018) 376:7 (ex) as a benchmark for comparison of QCT results for 𝜇Li + obtained from MD simulation with simple force fields. In the first term, Kn(0) is the equilibrium ratio for the Li+ -solvent (sol) association reaction

(12)

Li+ + n sol ⇌ Li(sol)n + ,

treated as in an ideal gas phase; hence the superscript (0). The solvent density, 𝜌sol, gauges the availability of solvent molecules to serve as ligands in this association, and this justifies the attention above to the equation of state of these liquids. The right-most term of Eq. (11) provides solvation of the Li(sol)n + complex by the solva(ex) (ex) tion environment external to it. That, 𝜇Li(sol) + − n𝜇sol , combination makes a favoran

ble contribution to the free energy. For analyzing the MD results, we use the direct QCT approach [105]

⟨ ⟩ (ex) (0) (n𝜆 ) + ln e𝜀∕RT ∣ n𝜆 + ln p(n𝜆 ) , 𝜇Li + ∕RT = − ln p

(13)

which is tautologically related to Eq.  (11) with the natural definition of the indicated probabilities [107]. 𝜀 is the binding energy of the Li+. The advantage of this simulation-based QCT is that it permits calculation of solvation free energies, and correlation of those results with observed solution features. The free energies of Li+ transfer ΔΔGLi+ to a carbonate solvent from water for the two QCT implementations (Fig. 11) compare accurate electronic structure calculations and classical FFMD simulation with simple force fields. The cluster QCT

∆∆GLi+ (kcal/mol)

Classical MD

G09 (n = 4)

20 15

EC (80% charge)

10 PC (90% charge)

Expt

5 0 Fig. 11 Transfer free energies, ΔΔGLi+, comparing FFMD direct QCT results (left) and cluster-QCT results (right) using the G09 electronic structure software package. The cluster QCT results for the free energy of Li+ transfer to PC from water agree with tabulated experimental values to within 1 kcal/mol [108]. Our experience using cluster QCT to predict ion hydration free energies [109–119] suggests that the G09 results have accuracy comparable to other ab initio predictions [120–123], and hence provide a useful benchmark for FFMD results Reprinted from the journal

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result for the free energy of Li+ transfer to PC from water agrees with the value tabulated by Marcus [108]. No experimental value is available for EC. The direct QCT evaluations of ΔΔGLi+ for the FFMD simulations agree reasonably with the cluster QCT electronic structure calculations when the partial charges of the force fields are scaled by 80% (EC) or 90% (PC). The direct QCT MD calculations agree to within 2 kcal/mol on the 10-kcal/mol difference in transfer free energies between PC and EC predicted by the cluster QCT calculations. Positive transfer free energies favor lithium ion solvation by water compared with either carbonate solvent. From the perspective of the cluster QCT calculations, the replacement free energy, reflecting the availability of the solvent molecules as ligands, is the foremost factor leading to that result. Comparing EC and PC transfer free energies, again from the perspective of cluster QCT, the solvation of the bare EC/PC molecules serving as ligands is decisive in arriving at a positive free energy of transfer from PC to EC, with EC being slightly smaller. 3.2 Radial Distribution Function Radial distributions (rdfs) of carbonyl O of EC and PC with Li+ are sensitive to partial charges of an FFMD model (Fig. 12). AIMD results of Li+ solvation in water [50] and PC agree with x-ray spectroscopy [34] and neutron diffraction [124, 125] results. Hence, we used AIMD for validation of FFMD results. The four-coordinate inner shell was observed in both AIMD and FFMD simulations of Li+ solvation in EC and PC. The AIMD results match those from previous calculations [126]. The coordination number of Li+ in PC using AIMD agrees with the 4.5 reported by neutron diffraction [125] and x-ray spectroscopy [34]. Interestingly, Bader charge analysis on AIMD configurations suggest that solvent molecules sometimes donate as much as 0.1 electron to an ion [29, 127]. The neutron and x-ray diffraction experiments have the peak position at 2.04 Å, which is slightly longer than all FFMD results (1.78–1.9 Å), but comparable to AIMD (2 Å) and polarizable force field results (1.95–2 Å). Yet, a four-coordinate inner solvation shell is seen consistently in all cases. The solvent density is less sensitive to these partial charges under the conditions of interest. Dielectric constants do change significantly with scaled partial charges, but the values realized are high enough that solvation characteristics are only slightly affected. 3.3 Ion Mobilities The Li+ msd results [128] were obtained from separate 1-ns simulations of one Li+ ...PF−6 ion pair in 249 EC and PC molecules, and compared with the experimental values obtained from nuclear magnetic resonance (NMR) results [70]. The results (Fig. 14) for 90% charged PC and 80% charged EC were closest to the experimental results. The transference number, tLi+, for Li+ can be calculated from ratios of diffusion constants, D, according to

tLi+ =

13

DLi+ . DLi + DPF6 − +

(14)

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Top Curr Chem (Z) (2018) 376:7 r(˚ A) 1.5

2.0

70

3.0

1.5

2.0

EC

2.5

3.0

EC

100%

60

8

AIMD

90%

50

6

40

80%

n(r)

gLiOc(r)

r(˚ A) 2.5

30

4

20

2

10

PC

80

50

8

AIMD

90%

60

6

80%

n(r)

gLiOc(r)

PC

100%

70

40

4

30 20

2

10 0

1.5

2.0

r(˚ A)

2.5

3.0

1.5

2.0

r(˚ A)

2.5

3.0

0

Fig. 12 Radial distributions of carbonyl O atoms from Li+ in (top) EC and (bottom) PC using (left) FFMD and (right) AIMD simulations. Running coordination numbers (dashed curves and right axes) show near-neighbor (inner-shell) occupancies. In the FFMD cases, partial charges on EC and PC molecules were reduced from 100 to 90%, and subsequently to 80%. AIMD results show that four solvent molecules fully saturate the Li+ coordination. The FFMD results demonstrate the importance of repulsions between near-neighbor (inner-shell) solvating molecules: the occupancy of the inner shell increases moderately, and inner-shell structures broaden, as the solvent partial charges are scaled down

The computed transference numbers of 0.35 (EC) and 0.31 (PC) are consistent with previous NMR [70] and impedance spectroscopy (EIS) [128] experiments. The diffusion constant value changes significantly with partial charges of solvent but the transference numbers are less sensitive. In summary, changes to the partial charges on PC and EC solvents alter solvation structure and transport properties of Li+ and PF−6 ions. Based on our results for radial distribution functions (Fig. 12), diffusion constants (Fig. 13), and transference numbers (Fig. 14), we identify 90% scaling of PC partial charges and 80% scaling for EC.

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8

ethylene carbonate

propylene carbonate

7

PF− 6

6 D × 10−10 (m2 /s)

Li+

5 4 3 2 1 0

100%

90%

80%

NMR

100%

90%

80%

NMR

Fig. 13 Diffusion constants were calculated from FFMD using the mean-squared displacement (msd) of Li+ and PF6 − ions in EC (left) and PC (right). The msd was calculated for 25 ps. Experimental values are taken from Hayamizu et al. [70] As evident from these plots, the diffusion constants match experimental values best for 80% of partial charges on EC and 90% on PC

1.2 ethylene carbonate

propylene carbonate

Transference number

1 0.8

PF− 6

0.6 0.4 0.2

Li+

100%

90%

80%

NMR

EIS

100%

90%

80%

NMR

EIS

Fig. 14 Transference numbers for Li+ and PF−6 in EC (left) and PC (right) were calculated using FFMD and Eq. 14. The NMR diffusion constants at 1 M salt concentration were used to calculate experimental transference numbers (NMR) [70] and the combined AC impedance and DC polarization results apply to 0.1 M salt concentration (EIS). The experimental results show little dependence on salt concentration, and the calculated results agree with the experimental numbers

4 Model solid electrolyte interphase layer The discussion above encourages us to apply such an empirical non-polarizable force field to study non-aqueous electrolytes more broadly. Thus we extended our

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EDC

1e-06

EC

T (K) 700 500 333 1e-04

1e-02

1e+00

T (K) 700 500 333 0.001

t (ns)

0.005

0.020

0.100

1e-05 1e-04 1e-03 1e-02 1e-01   ∆r(t)2 nm2

1e-05 1e-04 1e-03 1e-02 1e-01



∆r(t)2

nm2



Top Curr Chem (Z) (2018) 376:7

0.500

t (ps)

Fig. 15 Mean-squared displacements for Li+ in EDC and EC. The behavior in EDC at intermediate timescales 0.001 ns < t < 1 ns demonstrates trapping of the Li+ ion (gray shaded area). Ballistic motion is evident at short timescales, and diffusive motion at long timescales in both EDC and EC solvents. At high T, the trapping regime shrinks. Note the time scales differ dramatically between the left and right panels here. In the model SEI (left panel), trapping times are longer than nanoseconds. Thus for direct simulation of trapping, simulations should access multiples of that nanosecond time scale

effort to simulate Li+ ion transport within a model SEI layer of dilithium ethylene dicarbonate (EDC) [129]. The Li+ ion msd in EDC and EC solvents (Fig. 15) shows three distinct temporal regions corresponding to ballistic, trapping, and diffusive motions. The trapping region for Li+ ion is extended for glassy EDC material and has significant temperature dependence compared to liquid EC solvent. Further analysis [129] confirmed the glassy behavior of the EDC matrix.

5 Conclusions The basic results discussed suggest that an empirically parameterized, non-polarizable force field can reproduce experimental structural, thermodynamic, and dielectric properties of EC and PC liquids with acceptable accuracy. More sophisticated force fields might include molecular polarizability and Buckingham-model description of inter-atomic overlap repulsions as extensions of Lennard-Jones models of van der Waals interactions. Simple approaches should be similarly successful also for applications to organic molecular ions in EC/PC solutions, but the important case of Li+ deserves special attention because of the particularly strong interactions of that small ion with neighboring solvent molecules. To treat the Li+ ions in liquid EC/PC solutions, we identify interaction models defined by empirically scaled partial charges for ion-solvent interactions. The empirical adjustments use more basic inputs, electronic structure calculations and AIMD simulations, and also experimental results on Li+ thermodynamics and transport in EC/PC solutions. Application of such models to the mechanism of Li+ transport in glassy SEI models emphasizes the

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advantage of long time-scale molecular dynamics studies of these non-equilibrium materials. Acknowledgements Sandia National Laboratories (SNL) is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. This work is supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the US Department of Energy under contract no. DE-AC02-05CH11231, subcontract no. 7060634 under the Advanced Batteries Materials Research (BMR) Program and Sandia’s LDRD program (MIC and SBR). This work was performed, in part, at the Center for Integrated Nanotechnologies (CINT), an Office of Science User Facility operated for the U.S. DOE’s Office of Science by Los Alamos National Laboratory (contract DE-AC5206NA25296) and SNL. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Top Curr Chem (Z) (2018) 376:19 https://doi.org/10.1007/s41061-018-0195-2 REVIEW

Elucidating Solvation Structures for Rational Design of Multivalent Electrolytes—A Review Nav Nidhi Rajput1,4 · Trevor J. Seguin1,4 · Brandon M. Wood1,3,4 · Xiaohui Qu1,2 · Kristin A. Persson1,2,4

Received: 2 August 2017 / Accepted: 23 March 2018 / Published online: 26 April 2018 © The Author(s) 2018

Abstract Fundamental molecular-level understanding of functional properties of liquid solutions provides an important basis for designing optimized electrolytes for numerous applications. In particular, exhaustive knowledge of solvation structure, stability, and transport properties is critical for developing stable electrolytes for fast-charging and high-energy-density next-generation energy storage systems. Accordingly, there is growing interest in the rational design of electrolytes for beyond lithium-ion systems by tuning the molecular-level interactions of solvate species present in the electrolytes. Here we present a review of the solvation structure of multivalent electrolytes and its impact on the electrochemical performance of these batteries. A direct correlation between solvate species present in the solution and macroscopic properties of electrolytes is sparse for multivalent electrolytes and contradictory results have been reported in the literature. This review aims to illustrate the current understanding, compare results, and highlight future needs and directions to enable the deep understanding needed for the rational design of improved multivalent electrolytes. Chapter 4 was originally published as Rajput, N. N., Seguin, T. J., Wood, B. M., Qu, X. & Persson, K. A. Top Curr Chem (Z) (2018) 376: 19. https://doi.org/10.1007/s41061-018-0195-2. Nav Nidhi Rajput, Trevor J. Seguin, and Kristin A. Persson contributed equally to this work. * Kristin A. Persson [email protected] 1

Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

2

Department of Materials Science and Engineering, University of California, Berkeley, CA 94720-1760, USA

3

Graduate Group in Applied Science and Technology, University of California, Berkeley, CA 94720-1760, USA

4

Joint Center for Energy Storage Research (JCESR), Chicago, USA

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Keywords Multivalent electrolytes · Solvation structure · Renewable energy

1 Introduction A key challenge of modern society is the sustainability of energy supply with increasing demand and depleting fossil resources. We are on the verge of a power revolution, where we desire enhanced energy storage devices with higher energy density, faster charge/discharge capability, and longer life compared to existing technologies. Access to low-cost and environmentally benign energy storage devices will not only transform the world’s energy economy but also build a foundation for a carbon-free society. Li-ion batteries are considered a linchpin technology of energy storage because of their ubiquitous use in electric vehicles and electronic devices. However, current demands are pushing Li-ion technology to the limit of its capacity, which is raising serious safety concerns [1]. Even with the enhancement in energy density by 5% per year and a reduction of the cost by 8% per year, the Li-ion chemistry is perceived as incapable of meeting the high energy density, long cycle life, and low-cost requirements for future electric vehicles and electronic devices due to inherent materials limitations [2]. Hence, exploration of the vast space beyond Li-ion batteries to identify potentially safer, cheaper, and environmentally benign battery technologies is warranted. In this context, alternative technologies such as metal–air, redox flow, and multivalent batteries are investigated. Among several proposed post-Li-ion technologies, multivalent ion batteries have spurred renewed popularity in the last two decades owing to their theoretically high volumetric capacity, improved safety, and eco-friendliness as compared to state-of-art Li-ion batteries. As multivalent cations (Mg2+, Ca2+, Zn2+, Al3+, Y3+,…) proffer more than one electron per redox center, they are capable of delivering significantly higher energy density as compared to monovalent Li-ion and Na-ion batteries. Even though the concept of both divalent and trivalent batteries dates back to 1970s, rechargeable trivalent batteries remain in the realm of scientific curiosities [3, 4] and greater success of divalent chemistries abated the momentum of global research efforts on trivalent batteries [5–8]. A successful secondary multivalent battery requires a metal or metal alloy negative electrode, a high-potential cathode material enabling reversible intercalation, and a non-flammable electrolyte that can provide efficient transport of ions between anode and cathode while supporting the formation of functional solid–electrolyte interphase. A practical electrolyte enables both a stable solid-electrolyte  interphase (SEI), as well as facile ionic transfer through the interface. In many conventional electrolytes, divalent ion metals react with the electrolyte to form truly passivating surface films, which inhibit ionic transfer. For example, most magnesium analogues of lithium salts and typical solvents used in Li-ion batteries undergo decomposition at the Mg metal surface, resulting in a passivation layer that is both electronically as well as ionically insulating, hindering the cell chemistry [5, 9]. This is in contrast to commercial Liion technology, where the graphite SEI, once formed, prohibits further reactions and supports Li-ion diffusion.

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However, the limitations and design metric of different multivalent ions are quite different from each other. For example, Zn exhibits a less negative electrochemical potential as compared to the standard hydrogen electrode (− 0.8 V) than Ca (− 2.9 V) and Mg (− 2.4 V), however the volumetric capacity (5851 mA h/ml) of the Zn metal anode is larger than that of the more popularly studied Mg (3833  mA  h/ml). Additionally, Zn metal is prone to dendrite formation upon cycling, limiting the lifetime and safety of a Zn-ion battery. This was reported early in the reversible plating/stripping of zinc metal with aqueous electrolytes in which limited cycle life was observed [10]. However, more recent reports have shown markedly improved cycling performance, poising aqueous Zn-ion batteries as promising candidates for grid applications due to lifetime, cost, and durability considerations [11]. Good compatibility of Zn, particularly with conventional non-aqueous electrolytes, has also been observed [12]. Mg metal is less prone to dendrite formation, which makes it a potentially safer candidate system as compared to Li and Zn [13]. One of the main advantages in multivalent systems originates from volumetric energy gains on both electrodes, which directly impacts the resulting size of the battery and hence cost/kWh [14]. However, reversible multivalent chemistry is fraught with challenges; the major obstacles in the commercialization of Ca-ion and Mg-ion battery are the lack of suitable electrode materials in which ions can be inserted and extracted reversibly and supporting electrolytes that demonstrate the optimal conductivity, electrochemical stability window, and chemical compatibility with both electrode materials. While multivalent cations generally exhibit sluggish solid-state diffusion in most closepacked structures, recent investigations point to host structures with non-preferred coordination landscapes to achieve optimal mobility [15, 16]. Furthermore, while Zn exhibits good cyclability in several electrolytes [12, 17, 18], and a few electrolytes show reversible plating and stripping of Mg metal [19–22], Ca has been proclaimed impossible for rechargeable energy storage applications [23]. However, recently, electrolyte formulations of Ca(ClO4)2 and Ca(BF4)2 in ethylene carbonate and propylene carbonate were demonstrated on Ca metal, albeit exhibiting approximately a 2-V overpotential at elevated temperatures (50–100 °C) [24]. Recently, the solvation structure and local dynamics of the electrolyte, as a function of the liquid components and concentrations thereof, has garnered increased attention in order to elucidate critically important phenomena for battery performance. For example, equilibrium ion association constants and diffusion coefficients impact ionic conductivity [25], as well as the formation and stability of the electrode–electrolyte interface [26], which in turn influences electrode stability and kinetics. In spite of the effort devoted to developing future electrolytes for multivalent batteries, there are still many unanswered questions regarding the intricate relationship between the electrolyte composition, structure, and dynamics, and the nature of the passivation layer formed at the metal interface. A desirable, rational designer approach to functional electrolytes requires a fundamental understanding of the local inter-molecular interactions, e.g., the solvation structure of the liquid solution and its impact on properties such as conductivity, viscosity, stability of the solution species, and resulting SEI. The term “outer sphere ion pair or ion pair” in liquid solutions is described for the oppositely charged species bonded together by Reprinted from the journal

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simple electrostatic interactions, while species bound through short-range or covalent interactions in which a ligand temporarily donate a pair of electrons to fill an unoccupied orbital in the other atom (of neutral solvent molecule or negative ions) are described as “inner-sphere ion pair or complex” [27]. However, most methods of determining the association fail to distinguish between ion pair and complex formation. Also, since the solvated species are present in the solution through a series of equilibria, it is possible to observe simultaneous existence of different solvate species and complexes [27]. The outer sphere ion pairs are generally classified into four categories: (1) free ions, (2) solvent separated ion pairs (SSIPs), (3) contact ion pairs (CIPs), and (4) aggregates (AGGs). When both ions exhibit complete first solvation shells and do not share solvents, they are defined as free ions, however, when they share one or more solvent molecules, the solvate species is termed as SSIPs. When one to two and more than two counter-charged ionic species are present in the first solvation sphere of an ionic species, the ion pair is defined as CIP and AGG, respectively [28–30]. The true nature of the bonding is generally not known and some covalent character is expected to be present when ions are in close contact with each other. Both coulombic as well as covalent interaction energies contribute to the enthalpy term in free energy and the magnitude of enthalpy determines the extent of association between ions/molecules. Hence, the denomination of CIP and complex can sometimes be used interchangeably for the same species in the solution for e.g., MgCl+; similarly, higher AGGs are also termed as oligomers. Lastly, an ion pair complex is defined for a cationic and anionic complex that form an ion pair. In particular, when transition metal ions form a CIP or AGG with electron pair donors, they can form either cationic, anionic, or neutral complex. It is worth noting that when a monovalent salt (Z = 1) forms an ion pair, the net charge is zero with the formation of a CIP (e.g., [Li+-TFSI−]), similarly when a multivalent salt (Z > 1) forms an CIP the net charge is still zero (e.g., [Mg2+–SO42−]), however when a multivalent cation (Z > 1) forms an ion pair with a monovalent anion (Z′ = 1) the net charge is (Z–Z′) q (e.g., [Mg2+-TFSI−]−) [31]. It is well known that the structures of the active species in solution can significantly affect the kinetics of metal deposition and dynamics of charge-carrying species. In conventional electrolytes, the formation of ion pairs and AGGs are generally assumed to negatively affect the mobility of ions and the transference number, which in turn decreases the conductivity [32]. On the other hand, there is speculation that formation of CIPs in Li  salts with  low  dielectric solvents can increase the overall dielectric constant of the electrolyte, improve solvation of free species at higher concentration and hence enable higher conductivity [33]. Furthermore, the formation of ion pairs can shift the electrochemical window of the electrolyte and the chemical constitution of the SEI [26, 30]. Recent computational studies show the impact of the solvation structure on the stability of anions in the multivalent electrolytes [30, 34]. The solvation structure of a liquid electrolyte and formation of ion pairs are known to depend on various parameters such as the nature, charge, size of the ionic species, total concentration, the dielectric constant, as well as chelating properties of the solvent, and the temperature [35]. For example, it has been observed that larger cations have a higher tendency to form complexes [36]. Recent simulation studies of multivalent electrolytes also show that the nature and geometry

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of the solvent molecule also play an important role in determining the association of the ions in solution [30]. Approaches to design electrolytes by gaining an understanding of the solvation structure and ion pairing—and their effect on the stability of inorganic salts and organic solvent, ionic conductivity, viscosity are imperative in building metrics to identify electrolyte components and formulations with better stability, solvation, and conductivity [30]. Considering the crucial role of electrolytes in the development of high-energy-density and safer multivalent batteries, in this review article we aim to provide a comprehensive analysis of the composition and solvation structure, with a particular focus on ion association, and its impact on battery performance for a range of multivalent electrolytes, covering Ca2+, Mg2+, and Zn2+ systems. We also discuss key advancements, major hurdles, and possible future directions in the research of multivalent electrolytes.

2 Magnesium Electrolytes Mg metal possesses a multitude of exceptional properties such as high volumetric capacity (3832  mAh/ml), negative reduction potential (−  2.4  V vs. SHE), low equivalent weight (12.15 g/eq.), low cost (~ $2/kg), high melting point (922.15 K), eco-friendliness, and high abundance in the earth’s crust, making it a good candidate anode material for high-energy–density rechargeable batteries. However, the reductive reactivity of Mg metal with atmospheric gasses such as O2, H2O, CO2, and traditional non-aqueous electrolytes result in the formation of a passivation layer that is both electronically and ionically insulating. Furthermore, in contrast to Liion intercalation chemistry, very few solids are known to reversibly intercalate Mg2+ ions and no electrolytes have demonstrated the stability and conductivity required to enable a > 4.0-V electrochemical window while exhibiting reversible Mg metal stripping and deposition. Today’s Mg electrolytes  are limited by their (1) insufficient anodic stability, which makes them incompatible with high-voltage cathode materials, (2) inability for reversible electrodeposition, and (3) low conductivity. Hence, intense efforts have been devoted to developing novel electrolytes to enable high-energy–density Mg-ion batteries. The high negative potential and activity of Mg metal render aqueous Mg electrolytes impractical, resulting in a preference for non-aqueous Mg electrolyte solutions.  The difference in bonding and coordination environment of Mg ions in organomagnesium salts and simple Mg salts such as Mg(TFSI)2  and  Mg(BH4)2 impacts the performance. For example, it was observed that the electrolyte exhibiting the highest degree of covalent bonding with Mg2+ such as C2H5MgCl results in the formation of complex species that are capable of reversible electrodeposition at the metal anode. On the other hand, ionically bonded compounds such Mg(ClO4)2 and Mg(BF4)2 result in the formation of CIPs and AGGs, which were found to be capable of supporting intercalation in most solvents but fail to show reversible electrodeposition of Mg2+ [5]. Gregory suggested that salts with weakly covalent bonding between Mg2+ and a bulky anion, such as BBh2Ph2, would result in SSIPs or CIPs between covalently bonded complexes and promote both reversible electrodeposition as well as intercalation [5]. Hence, the Reprinted from the journal

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partial charge on the atoms and steric hindrance of the ligand attached to the metal ions have a significant effect on the interaction between metal cation and ligands, which ultimately control the reversible electrodeposition and intercalation of Mg2+ ions. 2.1 Simple Inorganic Mg Salts Conventional simple inorganic Mg salts, such as Mg(BF4)2, Mg(ClO4)2, Mg(CF3SO3)2, Mg(SO4)2, Mg(NO3)2, MgCl2, and Mg(PF6)2, suffer from poor solubility in most solvents (< 0.5 M in ether) such as esters, ethers, alkyl carbonates, and are found to be incompatible with reversible stripping/plating at the Mg metal anode [5, 37]. Early studies of Mg salts in conventional polar aprotic solvents, namely acetonitrile (AN), propylene carbonate (PC), and tetrahydrofuran (THF), demonstrate the formation of a passivation layer and very high impedance due to either the reduction of solvent molecules (AN, PC) or inactivity of the solvent (THF), which leads to the reduction of salt anions and the deposit of electronically insulting species on the metal surface [37–39]. This passivation film, which is formed as a result of reactions between the active metal and solution species, does not allow conduction of Mg2+ ions in contrast to the functional surface films (solid–electrolyte interface, SEI) that form on negative electrodes in commercially available Li-ion batteries. The solvation structure of multivalent ions is likely to play a crucial role in determining both the formation of passivation film at the negative electrode as well as intercalation of ions at the positive electrode. It has been established that divalent ions such as Mg2+, Zn2+, and Ca2+ tend to form more stable ion pairs in solution as compared to monovalent alkali metal ions [40, 41]. A systematic theoretical study of the binding energy between different mono- as well as multivalent ions with a gas-phase solvent molecule by Okoshi et al. [41] shows remarkably larger binding energies for multivalent ions as compared to monovalent ions (Fig.  1). Assuming Fig. 1 Relationships between de-solvation energies of Li ion and monovalent (Na: blue circle) ion and multivalent ion (Mg: red square) ions, as well as SbCl5: green triangle). The dashed line corresponds to the energies of Li ion. Republished with permission of Journal of the Electrochemical Society from ref 41; permission conveyed through Copyright Clearance Center, Inc

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that higher molecular binding energies correlate with larger de-solvation energies in the liquid phase, it is suggested that the kinetics of charge transfer in multivalent systems would be more sluggish. Even though Mg2+ (0.65  Å [42]) exhibits approximately the same size as Li+ (0.6 Å [42]), due to high charge density of magnesium, Mg electrolytes are highly prone to ion pair and complex formation, even at modest concentrations for a wide range of solvents [30, 32, 34, 43, 44]. Early work by Minofer et al. using MD simulations reported strong ion pair formation and even clustering in 0.5  M aqueous solution of Mg(OAc)2 [6]. However, only recently the detailed solvation structure of non-aqueous Mg electrolytes was explored, where Rajput et al. examined the impact of bulk Mg electrolyte properties on the performance of Mg-ion batteries using a high-throughput computational approach [7, 8]. Mg(TFSI)2 is one of the few simple salts known that can be easily dissolved in many organic solvents and ionic liquids and show very high anodic stability. However, its compatibility with the Mg metal anode is still in question and often high overpotential and low coulombic efficiency have been observed for deposition and dissolution [44, 45]. The bulky size and highly delocalized charges of TFSI− typically result in better dissociation and lesser tendency to form ion pairs. Also, the connected p-orbitals in the TFSI− anion lower the total energy of the molecule and contributes to its stability. However, an analysis of the solvation structure of Mg(TFSI)2 in diglyme using MD simulations and X-ray total scattering by Saul et al. reveal formation of CIPs even at a moderate concentration of 0.4 M, where Mg2+ is sixfold coordinated by oxygen atoms including both a TFSI− anion, and diglyme solvent molecules (Fig. 2), to form octahedral or distorted octahedral geometry in solution [43].  Recently, Raman spectroscopy also observed such sixfold coordination of Mg2+ ions in Mg(TFSI)2/glyme solution in which two ether oxygen atoms originate from monoglyme and four oxygen atoms from the TFSI− anion [43]. However, due to the high flexibility of glymes and different conformers of the TFSI− anion, the number of oxygen atoms donated by glymes and TFSI− anion can vary based on salt concentration. Both simulation and

Fig. 2 Solvation structure of Mg(TFSI)2/diglyme solution from r-weighted form of the d-PDFs, rG(r), highlights the well-defined inner sphere features and broader solvation shells at longer distances (top). Mg-X radial distribution functions from MD simulations (O: red, N: blue, C: grey, S: yellow). The corresponding simulation showing Mg2+ in space-filling format (magenta), TFSI_ and diglyme in stick format (bottom). Reproduced from Ref. 43 by permission of the PCCP Owner Societies

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experiment validate that the TFSI− anion coordinates with metal cations (Li+, Mg2+, Zn2+) through the oxygen atoms and not the nitrogen or fluorine [8, 43]. Mg2+ is also known to form larger complexes through bridge formation including two or more cations, especially at high concentrations [13, 15]. In electrolytes based on ionic liquids, such as Pyr14-TFSI or BMPyr-TFSI with Mg(TFSI)2, the Mg2+ cation is surrounded by three to four TFSI− anions with more bidentate and bridging TFSI– anions due to a higher population of TFSI− in the solution [44]. Such ion association not only alters the effective charge of the solvated ions ([Mgn(TFSI)m](m−2n)−) but also affects the dynamics of ionic species in the solution as well as kinetics/energetics for desolvation at an electrode–electrolyte interface [43]. The concentration of the solute is a critical parameter in determining the formation of different ionic species in the solution, which in turn control the electrochemical performance of the electrolyte. High-concentration (> 1 M) electrolytes are often preferred, as they can potentially provide high ionic conductivity that in turn lowers the system’s internal resistance [45]. Cyclic voltammograms of Mg(TFSI)2/diglyme suggest an increase in current density of magnesium deposition/dissolution with an increase in salt concentration from 0.1 M to 1.0 M and a decrease with further

Fig. 3 Representative simulation snapshot of a 0.1  M; b 1.5  M  Mg (TFSI)2/diglyme at 298  K. Mg depicted in pink in space-filling format, TFSI in licorice, and diglyme in line format; c and d show the zoomed image of solvation structure around an Mg ion in 0.1 M and 1.5 M concentrations, respectively. Reproduced from Ref. 45 by permission of The Royal Society of Chemistry

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increase in concentration [45]. For Mg(TFSI)2/diglyme classical MD simulations show the formation of SSIPs at low concentrations (< 0.4  M) and CIPs at higher concentrations, but no AGGs are observed even at 1.5 M due to the non-coordinating nature of TFSI− (Fig. 3a) [30]. However, higher numbers of monodentate coordination were observed at lower concentrations, whereas TFSI- anions show more bidentate coordination at higher concentrations  (Fig.  3b). The latter could significantly increase the desolvation energy, resulting in higher overpotential. Such increase in bidentate coordination, which increases the oxygen atom coordination with Mg2+, and CIP formation at higher concentration also negatively affects the ionic conductivity and transference number. Raman spectroscopy studies of the solvation environment of Mg(TFSI)2-ionic liquid also suggest the formation of both cis- and trans- conformer of TFSI− in the solution, with predominantly monodentate interactions between TFSI− and Mg2+ at low concentrations and bidentate interactions at high concentrations [46]. Hence, it likely that at low concentrations TFSI− anions which exist as CIPs are in the minimum energy transoid (CF3 groups on the opposite side of the S–N–S plane) state, while at higher concentrations, a slightly higher local minima cisoid (CF3 groups on the same side of the S–N–S plane) with ~ 3.5 kJ/ mol energy barrier compared to trans- conformer exists [28, 46]. Such increase in bi-dentate and bridging TFSI- affects the dynamical properties as well as the desolvation energy of ions in the solution. Different solvates of varying sizes, including free TFSI-, CIPs with mono and bidentate coordination and bridging aggregates with several metal centers have also been observed in the solution as a function of concentration [44–46]. The solvation structure depends strongly on the nature of the ligand, its geometry, and the concentration of the solute. Using MD simulations, Rajput et  al. reported that for most Mg salts, SSIPs are observed in high-donor-number solvents such as DMSO and in long-chain glymes (e.g., tetraglyme) due to their high oxygendonor denticity and flexibility to chelate around the Mg2+ [30]. Glymes are known to enhance the solvation of metal ions via ion–dipole interaction with the oxygen atoms exhibiting high electron donicity [20]. Kimura et  al. [47] also reported formation of SSIPs for Mg(TFSI)2/triglyme(G3) by forming an [Mg(G3)2]2+ cationic species for a concentration range of 0–1.6 M using Raman spectroscopy and DFT at the B3LYP/6-311 + G** level. The strong chelating effect of neutral glyme molecules on metal cations reduces the cation–anion interaction, which promotes SSIPs, as observed previously for Li salts [48]. Contrary to organic electrolytes such as Li salts in PC, Kimura et al. [47] observed an increase in ionicity (dissociativity) for Mg(TFSI)2/triglyme electrolyte with an increase in salt concentration. A systematic study by Watanabe et al. using impedance and pulsed-filed gradient spin-echo NMR also reported a similar increase in ionicity for Li(TFSI)2/triglyme in concentrated solutions (~ 3  M) [49, 50]. On the other hand, the MD simulations of Mg(TFSI)2 in short-chain glymes such as diglyme (G2) and dimethoxyethane (G1) reported formation of CIPs and AGGs, respectively [30]. From both MD simulations and Fourier-transform infrared (FTIR) analysis, it was inferred that the tendency of Mg salts to form ion pairs in glymes monotonically decreases with an increase in chain length of glymes [20, 30, 51]. Similar to Watanabe’s work on Li salt/glyme solution [49, 50], Watkins et al. [46] also reported an alternative class of ionic liquids known Reprinted from the journal

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as “solvate” ionic liquids for Mg salts/glyme solutions with a general formula of M(Glyme)m(X)n [M = Li, Mg; X = counter ion]. For a weakly Lewis basis anion such as TFSI−, M(Glyme)m(TFSI)n solutions behave as a typical ionic liquid with [M(Glyme)m]+ as the cationic species and exhibit properties similar to those of ionic liquids such as high oxidative stability, high thermal conductivity, high ionic conductivity, etc. [46, 50]. Solvated ionic liquid studies have primarily been performed for Li salts, and obtaining a detailed understanding of the properties of solvated ionic liquids for Mg electrolytes will be extremely beneficial. Some widely used solvents such as high dielectric constant nitrogen chelating acetonitrile (AN) (ε = 37) and tetrahydrofuran (THF) shows formation of AGGs for most Mg salts resulting in very low solubility [20, 30]. Significant ion pairing of the TFSI− anions with Li+ has also been observed in solvents such as glymes and acetonitrile, even at dilute concentrations [28, 52]. However, Raman spectroscopy results show a stronger interaction between Mg-TFSI than Li-TFSI due to the higher charge density and hardness of Mg2+ as compared to Li+ [46]. The size of the anions and charge distribution also play an important role in forming CIPs and AGGs, for example, the steric effects and delocalization of negative charge in TFSIanions reduce the tendency to form ion pair compared to the small-sized BH-4 and BF-4 anions. Hence, not just the dielectric constant of the solvent but also the size of the solvent and anions, donor number and denticity of solvents, and coordination property of the chelating ligands play a crucial role in determining the speciation of the solution. Even though numerous species have been reported in the literature for simple Mg salts, understanding the relationship between the solvation structure and the electrochemical properties of the electrolytes is still in its infancy. Mohtadi et al. [53] suggested that one possible reason for the failure of salts such as Mg(TFSI)2 in organic solvents could be the thermodynamic potential of Mg ion insertion into the host matrices. However, recent computational study suggests that intermediate reduced Mg1+ species can activate new decomposition modes for the species coordinated to the Mg ion in an ion paired configuration. Specifically, at Mg metal potentials, the ion pair undergoes partial reduction at the Mg cation center

Fig. 4 a Bond dissociation energy (BDE) of TFSI− anion in different chemical environments corresponding to well-solvated, Mg1+ ion paired and Mg2+ ion paired configurations from DFT calculations. Adapted with permission from Ref 30. Copyright 2015 American Chemical Society. b Energy-dispersive X-ray spectroscopy analysis of deposited Mg metal from a Mg(TFSI)2/diglyme electrolyte. Inset shows zoomed image at low energy. Reproduced from Ref. 45 by permission of The Royal Society of Chemistry. c Galvanostatic cycling of Mg/Mg cells at a rate of C/20 after the first cycle at C/40. Adapted with permission from Ref. 20. Copyright 2014 American Chemical Society

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(Mg2+ → Mg1+), which competes with the charge transfer mechanism and activates the anion to render it susceptible to decomposition, thereby limiting the cathodic stability of the electrolyte (Fig. 4a) [30]. Recent scanning electron microscopy study [45] of Mg(TFSI)2/diglyme solution for a concentration range from 0.1 to 1.5  M also observed trace signal of elements C, O, and F, confirming decomposition of anions possibly by initiation with C–S bond breaking or solvent molecules during cycling as observed in simulations (Fig. 4b), [30, 45]. Ha et al. [20] also observed a difference in cathodic stability behavior of Mg(TFSI)2/glymes electrolyte as a function of salt concentration (Fig. 4c), which is possibly due to an increase in ion pair formation as a function of increased concentration ultimately leading to enhanced decomposition of TFSI− as mentioned above. Conversely, anions that are known to support reversible plating/stripping of Mg metal, such as BH4−, exhibit stable bonds even when ion paired with the transient, highly reactive Mg+ species [30]. As discussed above, an increase in salt concentration is often known to lead to the formation of CIPs or AGGs, which in turn decreases the conductivity and increases the viscosity of the solution and is also likely to put a penalty on the stability of the delivery vehicle. It should also be noted that CIPs with multivalent ions, [Mg(TFSI)n](2−n), are cationic complexes, unlike the neutral CIPs, [Li(TFSI)n](1−n), formed with monovalent ions. Similarly, the AGGs that form, [Mgz(TFSI)n](2z−n), can exhibit neutral or anionic composite charges [30]. Hence the effect of CIPs and AGGs on the ionic conductivity and transference number in divalent cation electrolytes are likely quite different than for monovalent systems. At concentrations where CIPs and AGGs form, the conductivity in divalent systems can decrease due to the formation of neutral ion pairs or due to a decrease in the mobility of large chargecarrying species (Fig. 5a, b). Classical MD simulation studies of Mg(TFSI)2 demonstrate the formation of AGGs for Mg(TFSI)2 in short-chain glymes and acetonitrile and SSIPs in DMSO and tetraglyme, but the diffusion constant of ionic species was found to be faster in AN and short-chain glymes (Fig. 5c) [30]. The faster dynamics observed is likely due to lower viscosity in case of AN and weaker interaction between the ions and the solvent molecules in case of glymes. Hence, interestingly,

Fig. 5 a Concentration-dependent ionic conductivity and b diffusion coefficient of Mg(TFSI)2/diglyme electrolyte at a concentration range from 0.1 to 1.5 M. Reproduced from Ref. 45 by permission of The Royal Society of Chemistry. c Self-diffusion coefficients of Mg2+ and TFSI− in seven different solvents (shown on x-axis) displayed with error bars. Adapted with permission from Ref 30. Copyright 2015 American Chemical Society Reprinted from the journal

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depending on the properties of solvent molecules and the mechanism of diffusion, it is possible to have a faster mobility of large-size AGGs compared to smaller CIPs. Two modes of ion transport often discussed in the literature are structural and vehicular ion diffusion. Structural diffusion is defined as the exchange of counterion or solvent molecules in the first solvation shell of the metal cation, whereas vehicular diffusion is the motion of metal cation along with the molecules in the first solvation shell. Experimental conductivity measurement of Mg(TFSI)2-IL solution observed a decrease in conductivity as a function of salt concentration. Further PFG-NMR results show a decrease in the mobility of TFSI- and an increase in the viscosity of the solution due to increase in Mg2+–TFSI− association as the salt concentration increases. Jeremias et al. [44] suggested the possibility of structural diffusion in Mg(TFSI)2-IL electrolytes by exchange of TFSI− anions between “free” TFSI− and neighboring [Mgn(TFSI)m](m−2n)− clusters (Fig.  6). Bidentate TFSI− coordination was found to be stronger and stable as compared to bridge complexes. Hence, due to the strong interaction between bidentate TFSI− anions and Mg2+, the mobility of Mg clusters can be higher than the exchange rate of bidentate TFSI- anions. Such hopping of ions explains the non-linear trend of conductivity as a function

Fig. 6 Proposed mechanisms of structural diffusion in the Mg2+−IL electrolytes, where the dashed lines indicate interactions being formed (▶) and broken (●). The weakly coordinating monodentate and bridging TFSI− anions tend to rapidly exchange between different ionic clusters, resulting in a faster process. On the other hand, strong coordination of bidentate TFSI− anions results in a vehicular diffusion of the cluster followed by a slower process, which involves exchange of the bidentate anions via a bidentate to bridging mechanism. The Pyr1x+ cations are omitted for simplicity. Reprinted with permission from Ref 44. Copyright 2014 American Chemical Society

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of concentration observed by Jeremias et  al. and the faster diffusion observed for Mg(TFSI)2 from MD simulations by Rajput et  al. in acetonitrile and monoglyme solutions where AGGs were observed [30]. However, a deeper, detailed understanding of the effect of the molecular organization of the electrolyte and modes of ion transport on the diffusion coefficient, conductivity, and viscosity is desirable. Salama et  al. [54] combined DFT, NMR, and single-crystal X-ray diffraction (SCXRD) to explore the solvation structure of Mg(TFSI)2 in dimethoxyethane (DME). DME was found to be a promising solvent in both Li-oxygen and Li-sulfur chemistries and results in higher conductivity of the ionic species, while TFSI− -based salts are highly soluble due the delocalized charge and larger size of the TFSI− anion as discussed above. At all concentrations studied (0.05–1.3  M), the dissolution of Mg(TFSI)2 results in Mg.3DME as a stable moiety, where Mg2+ ions are encaged by three DME molecules (Fig. 7a). The Raman spectra results for Mg(TFSI)2/DME solution indicate the formation of either SSIPs or free TFSI- ions irrespective of the concentration (0.05–1.3 M) (Fig. 7b). These results are in disagreement with the previous simulation and experimental studies of Mg salt in glymes, which suggests the formation of CIPs and AGGs in short-chain glymes such as DME and diglyme [20, 30, 34, 44]. Indeed, the experimental conductivity measurements by Salama et al. show a decrease in conductivity after 0.9 M, indicating the formation of AGGs and increase in viscosity (Fig.  7c). Hence, it is surprising that Salama et al. observed SSIPs and free anions for Mg(TFSI)2/DME irrespective of the salt concentration. Even though spectroscopy techniques such as NMR and Raman are powerful techniques, they have been reported to be inadequate to provide reliable information about ion association equilibria [55]. As the detection limit of NMR [1] H and [13] C is typically low, it is possible that some minority species were not detected by the NMR studies performed by Salama et al. Several recent studies have reported enhancement in electrochemical performance through the current density and coulombic efficiency for reversible Mg deposition with the addition of MgCl2 to Mg salts such as Mg(TFSI)2 [56]. Although, while a detailed understanding of the species present in the solution in the mixed salt system is pending, a single-crystal diffraction and electrospray ionization mass

Fig. 7 a Refined SCXRD structure for MgTFSI2 single crystal, recrystallized from MgTFSI2/DME solution. b Raman spectra of pure DME (brown line), U-phase (orange line), L-phase (yellow line), 1.25 M MgTFSI2 solution in DME, and powder pure MgTFSI2: 750−900 cm−1 spectral region. c Conductivity measurements of MgTFSI2/DME solutions at various salt concentrations. Adapted with permission from Ref 54. Copyright 2016 American Chemical Society Reprinted from the journal

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Fig. 8 a Displacement of ellipsoid representation of [Mg2Cl3(THF)6]+[TFSI]−. b ESI–MS spectrum of 0.5  M  Mg(TFSI)2-MgCl2 at the ratio of 1:(0.5) in THF (experimental measurement in positive mode). Adapted with permission from Ref 56. Copyright 2016 American Chemical Society

spectroscopy (ESI–MS) study by Sa et al. reveal formation of an ion pair complex composed of a cation [Mg2Cl3(THF)6]+ and the [TFSI]_ anion (Fig. 8) in the solution [56]. The cationic species reported here is the widely accepted electroactive species present in the magnesium organohaloaluminate or organomagnesium electrolytes in THF responsible for the reversible magnesium deposition/dissolution. This suggests that irrespective of anions such as TFSI−, magnesium and chlorine have a strong tendency to form a bridge complex where chloride ions are shared by more than one magnesium ion. As previous simulation results suggested formation of AGGs in Mg(TFSI)2/THF solution [30], it is likely that the addition of MgCl2 results in a competing interaction between TFSI– and Cl– anions, where the strong electrostatic interactions between Mg2+-Cl− results in formation of a cationic complex species while the weaker ionic interaction between Mg2+-TFSI- results in formation of CIPs of TFSI- anion with the [MgxCly]+ complex. Mg(BH4)2 is an example of another simple and non-corrosive inorganic Mg salt that has gained much popularity over the last few years due to its compatibility with a Mg metal anode [57, 58]. Both Mohtadi et al. [53] and Shao et al. [57] reported significant ion pair and aggregate formation of Mg(BH4)2 in diglyme, dimethoxyethane, and THF solvents using IR and NMR spectroscopy analyses [53, 57]. Later MD simulations confirmed a strong tendency of Mg(BH4)2 to form CIPs and AGGs in most solvents except DMSO and tetraglyme [30]. Also, stronger interaction between Mg2+ and BH-4 was observed in THF as compared to DME in agreement with previous experimental results reported by Mohtadi et al. The interaction between Mg2+ and BH-4 was observed to be mediated through the Mg-H bond instead of the Mg-B bond, which results in a strong covalent bonding between Mg2+-BH-4, especially in weakly coordinating solvents [51, 57, 58]. Yuyan et al. investigated the effect of ligands on the electrochemical properties of Mg (BH4)2/glyme electrolytes [51]. They observed that the electrochemical performance (coulombic efficiency, overpotential, and current density) of Mg(BH4)2 is enhanced with an increase in the chain length of glyme from DME (G1) to tetraglyme (G4) (Fig. 9a). Classical MD simulations demonstrate that the Mg–O(Glyme) distance decreases and the coordination number of Mg–BH4 decreases monotonically with an increase in chain length of glymes from DME to tetraglyme, indicating stronger coordination between Mg2+

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Fig. 9 a Cyclic voltammograms (20 mVs_1) of 0.01 M Mg(BH4)2 in glymes on a Pt electrode. b Radial distribution function of Mg–O(solvent) of Mg(BH4)2 in DME, diglyme, triglyme, and tetraglyme from MD simulations. Reprinted from Ref. 51 with permission from Elsevier

and longer chain glymes (Fig. 9b). Similar trends of decreasing cation–anion coordination number with an increase in chain length of glymes were also reported for other Mg salts using MD simulations [30]. It should be noted that the donor number (DN), which is commonly referred to as an index of the Lewis base character of solvent, follows the order DME/monoglyme (24.0) > diglyme (19.5) > triglyme (-) > tetraglyme (16.6) [20] while their dielectric constant is very similar; approximately 7. However, the high oxygen donor denticity and flexibility with an increase in chain length improves the solvation of the metal cation with an increase in chain length. On the other hand, such improved solvation comes at the cost of slow mobility of ionic species, as suggested by the diffusion coefficient results from MD simulation, showing that the mobility of both cation and anion decreases monotonically with an increase in chain length of glymes [30]. Hence, a mixture of glymes is often used to obtain an optimal combination of dissociation and conductivity. Few studies have suggested that the addition of additives such as LiBH4 or other Mg salts reduces the strong interaction between Mg2+ and BH4−, resulting in an enhancement of the electrochemical performance. However, it is worth noticing that any addition of other electrochemically active species such as Li convolutes the evaluation of the role of the Mg electrochemical response [59]. Recently, Hu et al. investigated the solvation structures and dynamics of Mg(BH4)2 and Mg(TFSI)2 dissolved in diglyme (DGM) at various concentrations and ratios of Mg(BH4)2/ Mg(TFSI)2 using a combination of natural abundance 25Mg NMR, quantum chemistry calculations of 25Mg NMR chemical shifts, classical MD calculations, and electrochemical performance tests [60]. They observed that for 0.01  M  Mg(BH4)2 (which is the saturated concentration in DGM), the first solvation shell of a Mg2+ ion contains two BH4− anions and one DGM molecule as a tridentate chelating the Mg2+, while the second solvation shell consists of five DGM molecules (Fig.  10a Structure-A). In contrast, for the system of Mg(TFSI)2 in DGM, at dilute concentrations, TFSI- is fully dissociated from Mg2+ while at high concentration Mg2+ and TFSI- are only partially dissociated with CIPs formed between Mg2+ and TFSI− (Fig. 10a Structure-B). An exchange mechanism between solvation structures in the Reprinted from the journal

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Fig. 10 a The exchange mechanisms and solvation structures in the combined electrolyte containing both Mg(BH4)2 and Mg(TFSI)2 in diglyme (DGM), highlighting that Structure-A is changed to Structure-B via intermediate Structure-C. b Coordination number of Mg-BH4, Mg-TFSI and Mg-DGM in mixed solutions of Mg(BH4)2 and Mg(TFSI)2 (b) cyclic voltammetry of electrolyte solutions prepared in diglyme with different concentrations of Mg(BH⁠4) 2 and Mg(TFSI) 2 as labeled. The scan rate was 20 mV/s. Reprinted from Ref. 60 with permission from Nano Energy

combined electrolyte containing both Mg(BH4)2 and Mg(TFSI)2 in DGM was found to result in a single observed 25Mg NMR peak. Such solvent exchange is responsible for the more uncoordinated anions, improved stability, and ionic conductivity of the mixed anion composition as compared to each single anion solution. For the solvent exchange mechanism, an intermediate Structure-C (Fig.  10a) with its first solvation shell similar to Structure-A but with one BH-4 replaced by a TFSI- anion was found to be responsible for facilitating the process. Such stable Mg species in mixed Mg electrolytes [Mg-BH4-TFSI]/solvent, potentially reduce the possibility of the TFSI- anion decomposition that was observed in Mg(TFSI)2/DGM solutions in previous simulation results. By mixing two competing Mg salts, they were able to reduce the strong covalent interactions between Mg2+ and BH−4 anions. A small increase is observed in the coordination number of Mg-TFSI and a significant increase in the interaction of Mg2+ ions with glymes (Fig. 10b). The weakest interaction between Mg2+ ions with BH4− and TFSI− anions were observed when the ratio of Mg(BH4)2 and Mg(TFSI)2 is 1:4. Battery performance tests indicated that the efficiency of reversible plating/stripping of Mg strongly depends on the concentration and the ratios of Mg(BH4)2 and Mg(TFSI)2 in DGM that is optimal at the Mg(BH4)2 and Mg(TFSI)2 ratio of approximately 1:4, owing to both the enhanced molecular dynamics and the stability of the TFSI− anion (Fig. 10c). Excitingly, Mohtadi et al. recently introduced 3-D boron clusters as potential anions for Mg batteries. Monocarborane, CB11H12−, in an Mg(CB11H12)/tetraglyme electrolyte, was reported to be compatible with Mg metal and possess a high anodic stability (3.8 V vs. Mg/Mg2+) as well as relatively high conductivity (1.8 mS cm−1), marking a significant development in practical electrolytes for Mg batteries [61]. In the same study, X-ray diffraction analyses on crystallized Mg(CB11H12)2/dimethoxyethane and Mg(CB11H12)2/diglyme solutions showed the presence of SSIPs containing Mg2+ cations bound to solvent molecules in a hexacoordinate configuration. Following Mohtadi’s work, McArthur et al. [62] reported a smaller ten-vertex

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carborane anion-based Mg salt, [Mg2+][HCB9H91−]2 which form SSIPs as observed from 11B NMR spectrum and X-ray diffraction study with three DME molecules coordinated with Mg2+  in the solid state. Monocarborane is known to be chemically inert and weakly coordinating [61, 63], but further detailed examination of the solvation structure involving this salt from e.g., MD simulations or first-principles calculations is not yet available. Crystal structures and solution NMR data of various carborane salts show the preferred site of interaction for cations at boron atoms opposite the carbon atom of the anion, despite the carbon calculated to be the most negatively charged atom of the cage [64]. 2.2 Organometallic Compounds (Complex Salts) Organometallic complex electrolytes in ether solvents comprise some of the few Mg electrolytes known to demonstrate highly reversible electrodeposition due to the stability of the ethers, the RMgX compound, and the Mg(AR2R’2)2 with respect to the metal anode. These electrolytes are highly corrosive [65–67] and the metal deposition process is found to occur by complex adsorption phenomena. The first evidence demonstrating reversible electrodeposition of magnesium from solutions of Grignard reagents in ether solvents was provided by Gaddum back in 1927 [68]. Unfortunately, despite the high stability of organo-magnesium salts against the metallic magnesium surface, the strong reducing character, extremely poor ionic conductivity (few μS/cm), and insufficient anodic stability (< 1 V) curbed their practical applicability in Mg batteries [19, 65, 66]. Through the seminal work of Gregory et al., it was established that the addition of electron-withdrawing Lewis acids such as aluminum chlorides (AlCl3) with Lewis bases such as Grignard reagents (RMgCl) and dibutylmagnesium (Bu2Mg) can significantly enhance the oxidative stability by stabilizing the R-Mg bond in Grignard solutions [5]. In the last three decades, there have been continuous efforts in enhancing the anodic stability and conductivity of Grignard solutions by Lewis acid (aluminum or organoboron) neutralization while at the same time developing suitable cathode materials that can intercalate Mg ions in nonaqueous media. A breakthrough was made in 2000 when Aurbach et al. demonstrated the first successful prototype of a rechargeable Mg battery consisting of an Mg anode, a Chevrel phase molybdenum sulfide (Mo6S8) cathode, and a magnesium organohaloaluminate electrolyte solution. From meticulous screening of several electrolytes synthesized by the acid–base (RmMgCl2−m–R′nAlCl3−n) reactions, a complex obtained from the reaction of EtAlCl2 and Bu2Mg with a molar ratio of 2:1, namely the dichloro complex (DCC) dissolved in THF exhibited the highest anodic stability (~ 2.4 V vs. Mg/Mg2+), an impressive cycle life (> 2000 cycles), improved ionic conductivity of 1.4  mS/cm and an energy density of ~ 60  Wh/kg [19]. The question of which electroactive species governs the enhanced oxidative stability and highly reversible Mg deposition/dissolution in Grignard electrolytes has intrigued the scientific community. Figure 11a shows the widely accepted single-crystal structure observed in the DCC electrolytes, which was obtained by the addition of a nonpolar cosolvent such as hexane or by precipitation at low temperature [65, 66]. It was observed that Grignard solutions are composed of chloride-bridged species, Reprinted from the journal

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Fig. 11 a ORTEP plot of [(μ-Cl)3Mg2(THF)6]AlCl4. b [(μ-Cl)3Mg2(THF)6]AlPh3Cl [(μ-Cl)3Mg2(THF)6] AlCl4 (Mg, blue; Cl, green; Al, pink; C, gray; O, red). Reproduced from Ref. 75 with permission from The Royal Society of Chemistry. c ORTEP plot (25% thermal probability ellipsoids) of (Mg2(μCl)36THF) (HMDSAlCl3). Reproduced from Ref. 67 with permission from The Royal Society of Chemistry

where the active cation may include more than one Mg ion and exhibit a general structure of Mg2R3−nCl+n ROR while the aluminium-chloro-organo anions likely exhibit the general structure of AlCl4−nR−n [66, 69]. However, the accurate structures of the different electroactive species present in the solution in dynamic multiple equilibria as a result of transmetallation reaction cannot be revealed by crystallographic analysis [66]. The structure of the cationic and anionic species in the complex solution is dependent on the nature and ratio of the Lewis acid and base, the solvent, concentration, temperature, and nature of the ligand. For example, the electrochemical window of DCC electrolytes is known to be governed by the Lewis acidity of aluminum compounds and complex ionic species formed in the solution [70]. A comprehensive understanding of the effect of different parameters, such as acid–base ratio and nature of ligands on the formation of species in the solution, which controls the chemical and electrochemical properties, is found in the review article by Yoo et al. [69]. Most literature work on Mg organometallic salts refers to the Mg solvates as complexes and not ion pairs, possibly due to high tendency of the Cl− anion to donate a lone pair electron and form a chemical bond with Mg2+. Even though we have been unable to locate detailed analyses to confirm if the ligands are present in the inner or outer sphere of Mg2+, we refer to Mg species in organometallic solutions as complexes, consistent with available literature. Conversely, when a cation and anion complex is bound through electrostatic interaction, they are defined as an ion pair complex. NMR analysis by Gizbar et al. identified charged complexes formed by chlorine bridges, [Et2ClAl-Cl-AlClEt2]− and [MgCl]+ as the possible electroactive species present in the DCC electrolytes [71]. They suggested that the high conductivity observed at 2:1 acid:base ratio is a result of the formation of charged complexes [Et2ClAl-Cl-AlClEt2]− and [MgCl]+, while neutral complexes [MgCl2] formed at 1:1 ratio decrease the conductivity of the electrolyte solution.

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Many experimental studies including Raman spectroscopy, nuclear magnetic resonance (NMR) in solution phase, and X-ray diffraction (XRD) on the crystallized samples, Mg K-edge near X-ray absorption fine structure (NEXAFS) identified various species in multiple equilibria. These species include charged complexes such as [Mg2Cl3]+ and [MgCl]+ as the most general cation species where the inorganic ligand bonds directly to Mg and Mg is always found to be a hexa-coordinated. The majority anion species are of the form AlCl4−nR−n (1 ≤ n ≤ 3) and exhibit organic ligands which reside primarily bound to Al with tetrahedral coordination. Finally, neutral complexes, MgCl2 and AlCl3−nRn (1 ≤ n ≤ 3), are also evidenced [69, 71–73]. It is often suggested that the dimer cation [Mg2Cl3]+ exist in the solution through an equilibrium between MgCl+, and MgCl2. DFT calculations suggest that since the charged complex [AlCl4]− possess a low-lying HOMO frontier orbitals, the ion pair complex between [Mg2(μ-Cl3)THF6]+ and [AlCl4]− should have high anodic stability [67, 74]. The cationic complex [Mg2(μ-Cl3)THF6]+ adopts a pseudo-D3h symmetry where two magnesium atoms share three chlorine atoms and each magnesium has three THF ligands attached (Fig. 11a) [75]. Recently, Liu et  al. suggested a simple synthesis to form cationic complexes Mg2Cl3+ and MgCl+ in solution by using MgCl2 as a non-nucleophilic source of Mg2+ with an aluminum Lewis acid such as (AlEtCl2, AlPh3, and AlCl3) (Fig. 11a, b) [75]. They provided the first evidence of the THF-solvated MgCl+ complex present in the solution using SPIN-MS as traditionally used ESI–MS fails to detect weaker interactions such as Mg-THF [73]. However, contradictory results have been reported in the literature about the species present in solution and the exact solvation structure of Mg ions. Most experimental and simulation studies suggest hexa-coordinated Mg ions, whereas a few experimental studies using NEXAFS and Fouriertransformed extended X-ray absorption fine structure (EXAFS) and first-principlebased simulations reported a tetrahedral coordination for Mg2+ ions [70, 76]. A detailed study of the solvation structure of ionic species present in DCC solution was performed by Nakayama et  al. [70] using X-ray absorption fine structure (XAFS) and Fourier-transformed extended X-ray absorption fine structure (EXAFS). By comparing the coordination environment of Mg(AlCl2EtBu)2/THF with BuMgCl/ THF and Mg(ClO4)2/H2O, it was concluded that the coordination number of Mg and Al are 2/3 in Mg(AlCl2EtBu)2/THF and BuMgCl/THF compared to those in aqueous Mg(ClO4)2/H2O and Al(NO3)2 solutions. The presence of second and third solvation shell for Mg indicated the formation of oligomers while monomers were observed for Al complexes. Contrary to previous reports, they observed tetrahedral coordination for both Mg and Al, where the coordination number of Al varies between 4 and 6 depending on the pH of the solution within the range of 3 < pH < 7 (Fig. 12a). They reported (Mg2Cl2THF4)2+, (R2AlCl2)−, and (R2AlCl3)− as the active ionic species present in the solution responsible for the electrochemical performance of the DCC electrolytes. The first-principle molecular dynamics (FPMD) simulations based studies using DFT (PBE-GGA) by Wan et al. also found the sixfold coordination Mg structures energetically unstable (Fig. 13b below) [76]. They reported tetrahedral coordination of Mg and occasional observation of fivefold coordination in the cationic complexes often known as dimer structures in the electrolyte. They concluded that six-fold Mg species can only be established in the solid phase. However, Reprinted from the journal

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Fig. 12 Complex structures of Mg electrolytes. a, b Tetrahedral dimer structure of neutral Mg complex in 0.25 M BuMgCl/THF: Mg2Cl2Bu2THF2. c, d Tetrahedral dimer structure of dicationic Mg complex in 0.25  M MgAlCl2EtBu2/THF: Mg2Cl2THF42+. e Tetrahedral monomer structures of Al complexes in 0.25 M MgAlCl2EtBu2/THF, and their equilibrium, where R = Et or Bu. Republished with permission of Journal of the Electrochemical Society from Ref 70; permission conveyed through Copyright Clearance Center, Inc. DFT-PBE optimized solvation structures for Mg2Cl3+·4THF in approximate (f) C3v and (g) D2h symmetry and Mg2Cl4·5THF in approximate (h) C3v and (i) D2h symmetry. Reprinted with permission from Ref 76. Copyright 2014 American Chemical Society

Fig. 13 ORTEP plot (50% thermal probability ellipsoids) of [Mg2(μ -Cl)3THF6] [HMDSAlCl3]THF. Hydrogen atoms are omitted for clarity. Reproduced from Ref. 86 with permission from The Royal Society of Chemistry

as previously noted, this is clearly not the case for aqueous solutions. Furthermore, classical molecular dynamics simulations results by Wan et  al. using optimized potential for liquid simulations (OPLS) force field parameters failed to reproduce the tetrahedral solvation structure and instead demonstrated sixfold coordination. Cheng et al. pointed out the importance of the nature of the solvent in determining the solvation structure. Using Raman spectroscopy, NMR and single-crystal XRD, they identified a tetra-coordinated doubly charged cation complex, [Mg2(μ-Cl)2DME4]2+ when dimethoxyethane (DME) was used as a solvent instead of THF for which they

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observed six-coordinated cation complex, [Mg2(μ-Cl)3THF6]+ [77]. The tetra-coordinated cation complex with DME solvent was found to be highly active for reversible Mg electrodeposition. They suggested that the six-coordinated complexes such as MgCl+ and Mg2Cl3+ are unlikely to form because DME is sterically unable to fulfill the coordination number of six. However, in contrast—six-coordination of Mg2+ in simple inorganic salts such Mg(TFSI)2 has been observed previously in DME solution using molecular simulations [30]. The electrochemical window of the DCC electrolyte was still narrow and limited by the relatively weak Al-C bond, which breaks through a β-H elimination reaction [65, 78]. To overcome the problems of DCC electrolytes, Mizrahi et  al. [79] developed the all-phenyl complex (APC) electrolyte solutions by replacing the alkyl ligands with phenyl. By using phenyl as organic ligands, an enhanced ESW of 3.3  V vs. Mg on a Pt working electrode, low overpotential, 100% cycling efficiency, and specific conductivity of ~ 2–5 mS/cm was achieved. Raman spectroscopy, together with DFT, NMR, and single-crystal XRD suggested MgxCl+y (MgCl+, Mg2Cl3+, MgCl2) as the majority Mg species, where Mg is always six-coordinated and AlCl4−nPh−n (n = 0–4) and Ph4Al− as the major anionic species features consistently tetra-coordinated Al [74, 79]. Neutral complexes, such as MgCl2, were not observed for the best-performing electrolyte with 2:1 ratio of PhMgCl and AlCl3, which results in better ionic conductivity [79]. Some air-sensitive nucleophilic species such as Ph2Mg and PhMgCl along with minor ratios of PhAlCl2, Ph4Al_, AlCl4− were also predicted to be present in the solution. In both DCC and APC electrolytes, ether solvents are part of the actual solvation structure and play an important role in stabilizing the ionic species, but APC electrolytes form a variety of aluminum compounds unlike DCC electrolytes. Early studies reported that the highly nucleophilic and corrosive nature of APC solutions makes them incompatible with electrophilic cathode materials (such as sulfur and oxygen) and electrophilic solvents (such as esters and carbonates) and also prohibits their use with aluminum current collectors [21, 67]. However, full operation of APC electrolytes with Chevrel phaseMo6S8, TiS2, and V2O5 cathodes has already been demonstrated by adding either LiCl or MgCl2 as additives [80, 81]. Pan et al. demonstrated enhanced electrochemical performance for APC salts in Mg-Mo6S8 with the addition of MgCl2 salt and they observed a typical dimer structure Mg2(μ-Cl3) from single-crystal X-ray diffraction [82]. Hence, it is likely that addition of MgCl2 does not change the active species of APC salts but rather drive the Schlenk equilibrium to generate more electroactive species. However, the addition of MgCl2 is likely to make APC salts more corrosive [54, 83]. To enhance air and moisture stability of the Lewis bases, a few groups suggested replacement of (R = Ph) with (R = OPh) and observed complex ion pair formation between [Mg2Cl3]+ and [Al(OR)4]−, but these electrolytes  still exhibit a highly corrosive nature due to the high chlorine content [84, 85]. Nelson et  al. further tried to enhance the performance by using the Lewis acid Al(OPh)3 to reduce the chlorine content. Using NMR and ESI–MS, they suggested two distinct active Mg2+ charged complexes in solution, [Mg2Cl3(THF)4]+ and [Mg2(OPh3) Cl(THF)2]+, where magnesium is five-coordinated. The anion complex was identified as [Al(Ph)4]- with Al in tetrahedral coordination.

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In 2011, Kim et al. proposed a strategy using non-nucleophilic Hauser bases salt comprising hexamethyldisilazide magnesium chloride (HMDSMgCl) electrolyte which demonstrates good compatibility with the electrophilic sulfur cathode [21]. Similar to DCC and APC the crystal structure of HMDSMgCl electrolytes show a typical dimer cation complex [Mg(μ − Cl)3THF6]+ and [HMDSAlCl3]− as the anion complex (Fig. 11c). The cationic species observed from single-crystal X-ray diffraction in DCC, APC, and HMDSMgCl in THF show a dimeric magnesium complex, where two magnesium ions share three chlorine atoms forming a bridge complex and each magnesium ion is solvated by three THF molecules [86]. Mg was found to be hexa-coordinated and the counter-anion Al species as tetra-coordinated in all three electrolytes in a majority of experimental studies. Zhao-Karger et al. confirmed the crystal structure of [HMDSMgCl] observed by Kim et al. using NMR for the ratio of 1:2 for HMDSMgCl and AlCl3, while other ratios studied from NMR did not yield the same crystal structure (Fig. 13) [86]. Recently, Pan et al. demonstrated that addition of ionic liquids such as N,N-diethyl-N-methyl-N-(2-methoxyethyl)ammonium bis(trifluoromethanesulfonyl)imide (DEME-TFSI) can enhance the ionic conductivity of Mg(HMDS)2-MgCl2/THF electrolyte [87]. The highly dissociative DEME-TFSI salt was found to form free ions up till 53.2 mol% of DEMETFSI in 0.5 M Mg(HMDS)2-MgCl2/THF. This highly dissociative ionic liquid does not affect the first coordination sphere of Mg(HMDS)2-MgCl2/THF, but disrupts the second solvation shell. A single peak observed in NMR suggested a rapid exchange or dissociation in the solution by disrupting the complex ion pair formed between and [HMDSMgCl2]− and forming a weak ion pair between and [TFSI]−. Such rapid exchange of ions can possibly result in structural diffusion, leading to enhanced ionic conductivity and current density of the solution. It should be noted that the structure of the cation complex observed here ([{(THF)3MgCl}2-µ-Cl]+) is different than the typical dimer cation complex  observed in the previous study for organometallic electrolyte where three chlorine ions are shared by two magnesium ions, whereas here only one chlorine forms the bridge between two magnesium ions. Organic boron based Mg complex (OMBCs) salts were initially studied by Gregory in 1990 and later by Aurbach in 2002, but they were found to be limited by low cycling efficiency and anodic stability [5, 66]. Recently Guo et al. [88] developed an OMBC through reaction of tri(3,5-dimethylphenyl)borane (Mes3B) and PhMgCl in THF. Even though exact intermediates species present in the solution are unclear, based on the single-crystal XRD, NMR, Raman and fluorescence spectra analyses, they reported the same cation complexes (Mg2Cl3+, MgCl+) as observed in DCC, APC and HMDSMgCl electrolytes as the main cationic species and Ph2Mg and [Mes3BPh]− as anionic species present in the solution. The XRD results suggested the presence of ion paired [Mg2Cl3-THF6]+ [Mes3BPh]−, where the anion is tetrahedrally coordinated, while the cation shows a typical bridged structure of magnesium atoms hexa-coordinated by three chlorine and six THF molecules (Fig. 14). Further, fluorescence spectroscopy for different ratios of Mes3B mixed with PhMgCl and Raman spectroscopy analysis suggested the presence of weak interactions between [Mes3BPh]− and [Ph2Mg] through the formation of aggregates or π–π interactions, which results in high anodic stability of the Mes3B-(PhMgCl)2 electrolyte solution.

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Fig. 14 a 11B NMR spectra measured with boron-based electrolyte solutions of Mes3B/THF (a), Mes3B–PhMgCl/THF(b), Mes3B–(PhMgCl)2/THF (c), (b) ORTEP drawing of the molecular structure of the crystallized Mes3B–(PhMgCl)2 complex electrolyte. Hydrogen atoms have been omitted for clarity. Reproduced from Ref .88 with permission from The Royal Society of Chemistry

Doe et  al. reported the first simple all-inorganic Mg electrolyte by in  situ reaction between MgCl2 and AlCl3 in ethereal solutions, namely the magnesium aluminum chloride complex electrolytes (MACC). The MACC electrolyte shows a high anodic stability of ~ 3.3  V with good reversible deposition/dissolution, however, the reported enhanced performance after conditioning remains a mystery and

Fig. 15 Formation free energy (in eV) of magnesium-chloride complexes as a function of THF coordination for a MgCl + (monomer), b Mg2Cl3+(dimer), c Mg3Cl5+ (trimer), and d MgCl2. Arrows indicate the most stable THF coordination environment for each complex. Snapshots of the most stable magnesium-chloride complexes are also depicted. Ref. 90 - Published by The Royal Society of Chemistry Reprinted from the journal

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the performance deteriorates after the few cycles [89]. Canepa et  al. [90] coupled ab initio calculations with molecular dynamics simulations to investigate the functional species and the structural evolution during electrochemical cycling. In agreement with Wan et  al. and Nakayana et  al. results for DCC electrolytes, Canepa et  al. observed fourfold coordination for monomers (MgCl+ and MgCl2) and fivefold coordination for dimers (Mg2Cl3+) (Fig.  15). Some experimental studies suggested the formation of trimers and multimeric units in MACC electrolytes [89] and Canepa et al. reported a sixfold coordination of trimer (Mg3Cl5+) complexes [91]. However, Canepa et al. predicted dimers and trimers to be metastable under normal thermodynamic conditions, suggesting that a dimer structure might become accessible with the reduction of the THF chemical potential (e.g., drying). In contrast to these results, other experimental studies using X-ray diffraction, Raman, and NMR spectroscopy revealed hexa-coordinated structure of Mg ions in the MACC electrolytes for both monomer MgCl+ as well as dimer Mg2Cl3+ complexes. Four-fold coordination was observed in aluminum complexes, where (AlCl2+THF2), (AlCl2+ THF2), AlCl3 (THF) and AlCl4− were suggested as the stable species in the solution while no polymeric species were observed. Contrary to experimental studies, the simulation does not report the formation of other higher-order magnesium-chloro structures, rather suggests agglomeration of MgCl+…MgCl2, which could be interpreted as higher-order clusters in spectroscopic measurements [90, 91]. We note that dimers or other higher-order complexes would be favored under drying conditions due to lack of solvent molecules or solvent polymerization. It was speculated that enhanced electrochemical performance after conditioning is due to increase in the concentration of active species (MgCl+ and AlCl4−) in the solution. Conversely, resting the electrolyte, a process known as ‘aging’, deteriorates the electrochemical performance of MACC electrolytes, which was correlated with the drastic decrease in the concentration of electroactive species in the solution. 2.3 Aqueous Mg Electrolytes Water is an excellent solvent for the divalent cations considered here, hence aqueous electrolytes are expected to exhibit improved solubility for Mg salts. However, conversely, aqueous electrolytes are limited by the inherent water molecular electrochemical stability window of 1.5 V and passivation of the Mg metal anode. For reasons discussed above, there are sparse studies on aqueous Mg electrolytes for energy storage and those available report mainly simple salts such as Mg(SO4)2, Mg(ClO4)2, Mg(NO3)2 and MgCl2. But very recently Seoung-Bum et. al demonstrated reversible cycling of the Mg/V2O5 full cell in a 0.5 M Mg(TFSI)2/PC electrolyte containing 3 M water. They suggested that presence of small amount of water supports the intercalation of Mg ions in V2O5. Since  water is well known to passivate the Mg metal anode, they employed a protective artificial polymeric interphase to suppress the electrochemical decomposition of water-containing carbonate based electrolyte. However, details of the active species present in the electrolyte is not known at this point [92]. Due to the excellent hydration of Mg, exhibiting a preferred octahedral first-shell solvation structure [93], most simple salt aqueous solutions are reported

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not to exhibit ion pairs below 2 M [94, 95]. Yagi et al. evaluated the Mg(SO4)2 electrolyte performance and concluded that dehydration plays an important role [96]. As aforementioned, a large desolvation energy is expected in the case of complete desolvation, and partial dehydration at the electrode interface alleviates the penalty of this process. While some hydration may benefit intercalation in oxides [97, 98], it is expected that ions with smaller hydration numbers exhibit less detrimental impact on the host structure [99]. Buchner et  al. reveal the dependence of the hydration number on the concentration of Mg(SO4)2 [100]. It was deduced that the effective hydration number decreases from ~ 14 at infinite dilution to ~ 10 at high concentrations (> 1 M) of Mg(SO4)2. We note that this effective hydration number includes not only the first solvation shell but also the second solvation shell where the H2O molecule that are “irrotationally bounded” [100]. Raman spectroscopy confirmed the formation of both CIPs and AGGs in (> 1 M) Mg(SO4)2 aqueous solutions [100, 101], which reduces the hydration numbers, in turn affecting the electrolyte electrochemical properties. The association constants of Mg(SO4)2 were also experimentally determined [40, 102]. However, the direct effect of ion pair formation on electrochemical performance was not investigated. Several early reports demonstrated that additions of water can facilitate the desolvation process as well as insertion into various vanadium metal oxides as a result of the strong solvation structure between water and Mg2+ [102–110]. The highest specific charge, 170 Ah/kg, was attained in a 1 M Mg(ClO4)2 + 1 M H2O solution in acetonitrile, which coincides with a 1:1 ratio between Mg2+ and H2O [110]. Similarly, Song et  al. [111] reported reversible intercalation in a MnO2 nanowire electrode with gold current collector and a water-containing Mg(ClO4)2/PC electrolyte where the highest performance was observed at a ratio of Mg2+ to H2O ratio of 1:6. However, co-intercalation of water, while alleviating the desolvation process, tends to compromise the structural integrity of the electrode material and hence the cycling stability. In contrast to non-aqueous solutions, aqueous MgCl2 electrolytes have been reported to exhibit weak ion-pairing tendencies (0.2  M Cl−, 1.4  Mg2+, 3  M ionic strength in a Mg2+–Na+–Cl−–ClO4− system) from both potentiometric and osmometric measurements [112]. Furthermore, the association constant of Mg2+−Cl− is 25.6 times smaller than Mg(SO4)2 in aqueous solutions [102], indicating that the Mg2+–Cl− ion pair is significantly weaker than for Mg(SO4)2. For Cl− and SO [42] − , the ion pair stability with divalent metal ions decreases from Ca2+ to Mg2+, which supports the speculation that the hydration number of Mg2+ is larger than that of Ca2+ [40]. 2.4 Mg Polymer Electrolytes Polymer electrolytes hold the promise of electrochemical and thermal stability, which are important regardless of the specific chemistry. A primary challenge that remains for practical battery applications of polymer electrolytes is effectively managing the tradeoff between ion transport and other physical or chemical properties, such as mechanical or thermal stability. Solvation structure and specifically Reprinted from the journal

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ion pairing impacts transport properties and is the focus of this section. Lithium poly(ethylene oxide) (PEO) electrolytes have been well characterized and provide a useful starting point for the discussion of multivalent ions. Despite PEO having a modest dielectric constant (~ 7.5) [113], it has been reported both experimentally and computationally that CIPs do not appear to form until high salt concentrations, where the number of ether oxygens (EO) per metal cation nearly matches the average coordination number for both Li (5 EO) and Mg (6 EO) with TFSI anion. Mao et  al. [114, 115] used neutron diffraction isotopic substitution (NDIS) to identify the solvation structure of high molecular weight, amorphous PEO LiTFSI. It was found that, on average, no CIPs were present in P(EO)7.5LiTFSI at room temperature. Although no CIPs were present, broad peaks around 4.85 and 5.5  Å in the pair distribution function were suggested to be the result of SSIPs. Conductivity data provides similar evidence. Conductivity of binary liquid electrolytes generally increases with salt concentration until a maximum is reached where the formation of neutral IPs or neutral ion AGGs lead to a reduction in conductivity [116]. This analysis is complicated for systems where charged IPs or AGGs contribute to conductivity. It was recently demonstrated that charged AGGs (i.e., triplets) are important for transport in highly concentrated PEO LiTFSI [117]. Additionally, in the case of polymers, increased ion concentration reduces segmental motion, further complicating the connection between a maximum in conductivity and the formation of neutral IPs or AGGs. Nevertheless, in the case of high molecular weight PEO (5 and 20 kg/mol) a maximum in conductivity at 363 K and 373 K is reached in the range between P(EO)15LiTFSI and P(EO)10LiTFSI [118, 119], which at least in part, indicates formation of neutral CIPs or AGGs at higher salt concentrations. Combining NDIS and conductivity data, it appears that SSIPs are present at EO:Li ratios between 10 and 7.5, leading to a reduction in conductivity. Conventional spectroscopic methods such as IR or Raman, do not typically detect SSIPs, however, these methods can be advantageous for identifying CIPs [4]. IR and Raman studies of high molecular weight amorphous PEO LiTFSI seem to be in agreement that little to no CIPs are present when EO:Li is greater than or equal to 8 [120, 121], and a substantial fraction of CIPs (~ 24%) are present when EO:Li is equal to 6 [121]. It is worth noting that Edman saw little evidence of CIPs in roomtemperature samples that were not preheated to the amorphous regime at the same salt concentration [121]. This was attributed to slow recrystallization of salt-rich PEO, and  is evidence that crystalline regions solvate Li salts at higher concentrations than amorphous regions. A molecular dynamics study of P(EO)7.5LiTFSI at 393  K reported 4.6 oxygen atoms in the first coordination shell, 3.85 from EO, and 0.5 from TFSI anion (it is unclear why these do not sum to 4.6) [122]. The elevated presence of CIPs compared to experiment at this salt concentration may be due to the challenge of obtaining accurate electrostatic interactions including polarization for concentrated solutions. A few simulation snapshots are shown in Fig. 16 to help visualize the local environment around the cations in the PEO matrix. Overall, the picture that emerges for high molecular weight amorphous P(EO)n LiTFSI is that SSIPs are favorable between n = 15 and n = 10 and CIPs begin to be favorable when n < 7.5; CIPs make up a substantial fraction when n = 6.

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Fig. 16 Snapshots from simulations of PEO/LiTFSI at 423  K (a, b, d) for EO:Li = 20:1 and c for EO:Li = 10:1. Hydrogen atoms are not shown for clarity. Only atoms within 4.0 Å of each Li + are shown. Reprinted with permission from Ref. 112. Copyright 2006 American Chemical Society

Table 1 Comparison of the CIP regime, the point at which there are more CIPs than SSIPs and free ions, for a variety of electrolyte systems and the methods that aided in this determination Electrolyte system

CIPs regime

Methods

P(EO)nLiTFSI

n ≤ 7.5

NDIS [114], FTIR [120, 123], Ramen [120], Conductivity [118, 119]

P(EO)nMg(TFSI)2

n 0, b c f with the Li reference state as Li 2 O 2 , and ΔGXO > 0, where the two criteria account for thermodynamic a stability against direct oxidation and to Li2 O2-mediated oxidation, respectively

( ) 1 2Li2 O2 + 2b X + c − O2 → Li2 O + 2LiXb Oc ; 2

( 2Li2 O2 + X +

) a − 1 O2 → 2Li2 O + XOa ; 2

(13)

(14)

Other decomposition pathways involving direction oxidation and lithium-peroxidemediated oxidation can occur too: ( ) c+a−2 Li2 O2 + (b + 1)X + O2 → LiXb Oc + XOa ; (15) 2 In Eqs. (11)–(15), a, b, and c depend on the specific oxidation state of X in the compound. For transition metals with multiple oxidation states, there are a range of possible decomposition pathways. While the considered pathways do not represent a comprehensive list of all possible decomposition paths, we believe that trends in cathode stability can be established to a reasonable degree of accuracy by studying trends in the considered decomposition reactions. However, kinetics can play an important role, and a detailed framework that includes the effects of kinetics is still to be developed. Based on the considered pathways, the driving force for oxidative instability depends primarily on (i) the stability of the lithium-peroxide-mediated oxide formed with the cathode relative to that of the lithium peroxide, and (ii) the stability of the cathode material relative to its oxide. Reprinted from the journal

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In a similar manner, we show the decomposition pathways for a carbon cathode with the associated free-energy change per Li at 300 K as (16)

C + O2 → CO2 ; ΔG = −4.08 eV 1 Li2 O2 + C + O2 → Li2 CO3 ; 2

ΔG = −2.91 eV

1 2Li2 O2 + C + O2 → Li2 O + Li2 CO3 ; 2

ΔG = −1.35 eV

1 2Li2 O2 + C + O2 → Li2 O + CO2 ; ΔG = −1.99 eV 2

3 2Li2 O2 + 2C + O2 → Li2 CO3 + CO2 ; 2

ΔG = −4.95 eV

(17)

(18)

(19)

(20)

This suggests that there is a huge thermodynamic driving force for lithium peroxide on the C cathode to undergo highly exothermic reactions. It is worth emphasizing that this is due to carbon’s tendency to form an oxide (carbonate) that is more stable than lithium peroxide. This interfacial stability issue has been experimentally well documented in nonaqueous Li–O2 batteries  [17, 93]. However, during discharge, after a few monolayers of Li2CO3 have formed at the C–Li2O2 interface, there is a lithium carbonate layer between lithium peroxide and C, preventing further decomposition. Similarly, when comparing this to the stability of the secondary discharge product, an important implication for cathode design emerges. Since the free energy of Li2O is less than that of Li2O2, the driving force for the decomposition of Li2O to Li2CO3 is higher than that for Li2O2 decomposition (Li2 O + C + 21 O2 → Li2 CO3 ;ΔG = −2.95 eV). This implies that the secondary discharge product, Li2O, is highly undesirable for both rechargeable chemistry and in the context of stability to decomposition. Similarly, we consider the stability of transition metals, which are potential cathode materials for the Li–O2 battery. In this case, there are two thermodynamic driving forces for decomposition: (i) direct transition metal oxidation and (ii) mixed lithium—transition metal oxide formation. Using similar arguments to those presented for the C cathode, to a first approximation, the criteria for transition metal stability f f are ΔGmetaloxide > 0, and ΔGLi−metaloxide > 0 with Li2 O2 as the reference state for Li. First-order screening shows that early transition metals (e.g., Sc, Ti, V, Cr, W, Mo, Sn, Ni, Co) typically form stable oxides and are poor choices for Li–O2 cathodes. Noble metals are promising for nonaqueous Li–O2 electrochemistry since they are stable under the oxidizing conditions employed and there is no thermodynamic driving force for the formation of a mixed oxide relative to lithium peroxide. We believe that this approach can be extended to screen within other material classes (such as

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oxides, nitrides, and sulfides) based on stability under the specified operating conditions. It is worth pointing out that initially during the discharging phase and towards the end of the charging phase, the electrode is directly in contact with the electrolyte, so additional stability criteria relating to electrode–electrolyte interactions need to be considered. In summary, using a thermodynamic analysis, we have explored the design principles needed to meet three key criteria for a Li–O2 cathode: (i) selectivity towards the primary discharge product, (ii) low nucleation overpotential, and (iii) stability against decomposition. Specific facets of Ag and Au are capable of nucleating the primary discharge product, Li2O2, with very low overpotentials. An approach based on the thermodynamic driving force for evaluating the stability of cathode materials has been presented. According to the stability criteria established in this study, cathode materials that resist oxide formation and do not form mixed oxides in the presence of lithium peroxide are promising cathode candidates.

4 Conclusions The principles for the synergistic design of electrode and electrolytes for practical nonaqueous Li–O2 batteries have been presented. A beyond-Edisonian approach to material selection is crucial to the development of practical Li–O2 batteries. Datadriven high-throughput approaches are likely to play a major role in the identification of a stable electrode and electrolyte. Acknowledgements A.K., D.K., and V.V. acknowledge helpful discussions with John W. Lawson, NASA Ames Research Center. A.K. and V.V. acknowledge support from the Convergent Aeronautics Solutions (CAS) project under the NASA Aeronautics Research Mission Directorate. D.K. and V.V. also acknowledge support from the National Science Foundation CAREER award CBET-1554273, and the National Science Foundation Collaborative Research award CBET-1604898.

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