Article pubs.acs.org/JPCC Ion Association in Aprotic Solvents for Lithium Ion Batteries Requires Discrete−Continuum Approach: Lithium Bis(oxalato)borate in Ethylene Carbonate Based Mixtures † † ‡ § Oleksandr M. Korsun, Oleg N. Kalugin,*, Igor O. Fritsky, and Oleg V. Prezhdo*, † Department of Inorganic Chemistry, V. N. Karazin Kharkiv National University, Kharkiv 61022, Ukraine ‡ Department of Physical Chemistry, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine § Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States ABSTRACT: Ion association in solutions of lithium salts in mixtures of alkyl carbonates carries significant impact on the performance of lithium ion batteries. Focusing on lithium bis(oxalato)borate, LiBOB, in binary solvents based on ethylene carbonate, EC, we show that neither continuum nor discrete solvation approaches are capable of predicting physically meaningful results. So-called mixed or the discrete−continuum solvation approach, based on explicit consideration of an ion solvatocomplex combined with estimation of the medium polarization effect, is required in order to characterize the ion association at the quantitative level. The calculated changes of the Gibbs free energy are overestimated by nearly an order of magnitude by the purely continuum and purely discrete approaches, with the values having the opposite signs. The physically balanced discrete−continuum description predicts weak ion association. The numerical data obtained with density functional theory are validated using coupled-cluster calculations and experimental X-ray data. The study contributes to resolution of the challenge in solvation modeling in general, and develops a reliable, practical method that can be used to screen ion association in a broad range of ion−molecular mixtures for lithium ion batteries, especially for the solutions of LiBOB in EC based mixtures. 1. INTRODUCTION lithium salts is quite rare. Recently the mixed approach has + Lithium ion batteries (LIBs) constitute a key component of been used to investigate the solvation free energies of the Li ion in acetonitrile,5 to characterize ion clustering for the most modern portable electronic devices and vehicles. 6 Electrolyte solutions used in the batteries consist of a particular Li[PF6] electrolyte in acetonitrile, and to demonstrate that the structure of the Li+ first solvation shell can be predicted well in lithium salt dissolved in a mixture of aprotic organic solvents, 7 such as cyclic and linear carbonates or esters.1 One of the most an organic carbonate mixture. important physicochemical properties of the salts is high In this work, we show that neither continuum nor discrete Downloaded via UNIV OF SOUTHERN CALIFORNIA on November 7, 2019 at 23:09:00 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. solubility with minimal ion association (assoc) in a given solvation models can provide a satisfactory description of ion solvation and association in a typical LIB system. A mixed solvent mixture. These operating conditions are necessary for − ensuring maximal electrical conductivity and, as a consequence, discrete continuum description is required in order to obtain a high specific power of LIBs.2 physically reasonable representation. We demonstrate with a From the thermodynamic point of view, minimal ion popular lithium salt, dissolved in the EC based mixture of polar association corresponds to maximal change in the standard aprotic solvents, that the pure models err by nearly an order of Δ o − magnitude and that the mentioned errors have opposite signs. Gibbs free energy of ion association, assocGT = RT ln Kassoc. An experimental determination of the ion association constant, The errors are corrected in the mixed approach, which considers explicitly the first solvation shell of the solute particle Kassoc, is quite a labor- and time-consuming procedure. Therefore, a reliable prediction of the sign and magnitude of and treats the rest of the solvent as a polarizable medium. The Δ o method predicts a small degree of ion association. The assocGT by molecular modeling constitutes an important task. A theoretical method capable of this task will have a significant described approach can be used to screen a large number of impact on selection and development of novel lithium salts and systems suitable for LIB applications, assisting in design of polar aprotic cosolvents for design of advanced LIBs. Several quantum-chemical approaches have been considered, Received: June 13, 2016 most of which focus on aqueous media.3,4 Application of the Revised: June 24, 2016 discrete−continuum approach to nonaqueous solutions of Published: June 28, 2016 © 2016 American Chemical Society 16545 DOI: 10.1021/acs.jpcc.6b05963 J. Phys. Chem. C 2016, 120, 16545−16552 The Journal of Physical Chemistry C Article novel and more efficient electrolyte solutions. The computa- 298.15 K. The enthalpy and entropy changes show weak tionally efficient level is validated using both higher level variation over a broad temperature range. The changes in ion Δ o Δ o computations and experimental data. association enthalpy ( assocH298) and entropy ( assocS298)as Δ o Lithium bis(oxalato)borate (Li[B(C2O4)2], LiBOB) has been well as solvation Gibbs free energy ( solvGT) depend on the Δ o Δ o extensively studied as a highly promising electrolyte for use in accuracy of the enthalpy ( solvH298) and entropy ( solvS298)of LIBs. For example, LiBOB solutions in alkyl carbonates have solvation of the ions and IP. The thermodynamic potentials can been found much more thermally stable than the widely used be predicted using quantum-chemical calculations for the gas Li[PF6] solutions. Also, the performance of lithiated graphite and condensed phases. The latter data can be obtained with the electrodes appears to be much better with LiBOB solutions self-consistent reaction field (SCRF) methods.10,11 8 than with any other known lithium salt solutions. 2.1. Approaches. In order to calculate the Gibbs free It is known that there exists no suitable single solvent, energy and equilibrium constant of ion association, we consider exhibiting both high dielectric constant and low viscosity. These three solvation approaches (A). According to the first one, solvent properties are needed to ensure good lithium salt continuum model (AI), the bare ions and IP are placed in a solubility and high ion mobility, correspondingly. Currently, structureless polarized continuum (c) with the dielectric ethylene carbonate (EC) is a commonly used component in 1 constant of the solvent. The second, discrete solvation many LIB electrolyte solutions. The dimethyl carbonate approach (AII), involves an explicit consideration of the (DMC), diethyl carbonate (DEC), or ethylmethyl carbonate solvatocomplexes of the ions and IP in the gas phase, including (EMC) are usually added to EC as nonviscous cosolvents. solvent molecules most strongly interacting with the solutes. A The current study elucidates the utility of continuum, − combination of the approaches mentioned above constitutes discrete, and mixed discrete continuum solvation approaches the mixed or discrete−continuum framework (AIII). in application to association of the Li+ cation with the − − Application of AI is straightforward. It involves computation [B(C2O4)2] anion (BOB ). The previously unstudied ≈ of the properties of the ions and IP in the gas phase and in the EC:DMC binary mixture with the 7:3 weight or 70%:30% structureless polarized continuum of the solvent mixture. AII mole ratio is chosen as the solvent. The EC:DMC binary requires gas phase calculations on a series of ion−molecular mixtures with the component molar ratio ranging from and IP−molecular solvatocomplexes. According to AIII, the 50%:50% to 75%:25% exhibit sufficiently high dielectric most exergonic cation, anion, and IP solvatocomplexes from constants and relatively low viscosities, making them 9 AII should be considered in the solvent continuum, as in AI. appropriate for applications in the LIB technology. The In principle, a fully atomistic description of the solvent is main goal of the present study is to develop and validate an − approach that allows one to describe the ion association at the preferable to a continuum or discrete continuum model. At quantitative level without a need to refer to any experimental the same time, an explicit solvent model has its own limitations, data. This task is important for advancing LIBs using the novel for instance, due to approximations of a particular density electrolytes and solvent mixtures. functional, a basis set, or the size of the solvent shell that can be included in an explicit calculation given available computational 2. THEORETICAL METHODOLODY resources. Working within the limits of the current theoretical − approximations for the explicit and continuum descriptions of For the target ion association process, Li+ + BOB = − (solv) (solv) the solvent, we demonstrate that the mixed discrete− [Li+BOB ] , the change in the corresponding standard (solv) continuum provides the best results, while, at the same time, thermodynamic potential (Δ Φo) at the arbitrary temper- assoc T remaining computationally efficient. ature (T) can be calculated using The separation between the explicit and continuum fi Δ Φ=Δo Φ−ΔΦo o (Li+− ) −ΔΦo (BOB ) components of the mixed model is de ned by solid physical assoc TTTTassoc(g) solv solv arguments. The explicit part includes the first