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Ion Association in Aprotic for Lithium Batteries Requires Discrete−Continuum Approach: Lithium Bis(oxalato)borate in Ethylene Carbonate Based † † ‡ § Oleksandr M. Korsun, Oleg N. Kalugin,*, Igor O. Fritsky, and Oleg V. Prezhdo*, † Department of Inorganic , 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: in 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 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 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 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 ,5 to characterize ion clustering for the most modern portable electronic devices and vehicles. 6 solutions used in the batteries consist of a particular Li[PF6] electrolyte in acetonitrile, and to demonstrate that the structure of the Li+ first can be predicted well in lithium dissolved in a 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. 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 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 and 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 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 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 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 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 physical assoc TTTTassoc(g) solv solv arguments. The explicit part includes the first solvation shell of o +− +Δsolv ΦT([Li BOB ]) (1) the ions and IP surrounded by the most strongly interacting and abundant solvent molecules. Including the first solvation Δ Φo Here, assoc(g) T is the change in the standard thermodynamic + shell of the solvent without account for polarization of the potential for the gas phase (g) association process, Li (g) + fi − + − Δ Φo remainder of the solvent leads to signi cant errors in solvation BOB (g) =[LiBOB ](g),and solv T are the standard thermodynamics. Similarly, representing the entire complex by thermodynamic potential changes for solvation (solv) of the fi + − + − a continuum model ignores speci c interactions between the Li and BOB ions and the [Li BOB ] ion pair (IP). Note that, fi Δ Φo solute and the rst solvation shell, providing another source of in addition to eq 1, the solv T value for a particle P in an error. The combination of the two descriptions gives a sound arbitrary solvent can be computed rigorously according to approach, in which the two errors cancel. oo o o ΔsolvΦ=ΦTT(PP ) () −Φ T (solvent) −Φ T ((g) ) Chart 1 represents the set of solvation processes involving + − + − (2) Li and BOB ions and the [Li BOB ] IP and that are needed Δ Φo for the thermodynamic calculations of solv 298 within the Taking into account that a statistical mechanical treatment of three approaches. The chart also shows the ion association the condensed phases is expensive, instead, eq 3 is widely used Δ Φo Φ processes, for which the assoc 298 values ( = H, S, G) were in the framework of quantum-chemical calculations of the computed in the EC:DMC (7:3) binary solvent mixture. Due Δ Φo solv T potentials. to high dipole moment and favorable geometry, the EC oo o has a higher affinity to the bare ions and IP than the ΔsolvΦ≡Φ−ΦTT()PP ((solv) ) T ( P(g) ) (3) DMC molecule, as observed experimentally for the Li+ ion.12,13 The changes in the standard Gibbs free energy during ion In combination with a considerably larger EC in a Δ o Δ o association ( assocGT) and solvation ( solvGT) can be obtained mixture with DMC, one expects preferential solvation of the using the corresponding enthalpy and entropy data at T = ion species by EC molecules. This expectation is enhanced

16546 DOI: 10.1021/acs.jpcc.6b05963 J. Phys. Chem. C 2016, 120, 16545−16552 The Journal of Physical Chemistry C Article

Chart 1. Investigated Processes for the Solution of the more traditional PCM model. It is known in the case of the Li+ LiBOB Salt in the EC:DMC (7:3) Binary Solvent Mixture, ion that the van der Waals radius has to be scaled up Obtained within the Continuum (AI), Discrete (AII), and significantly to obtain good results.5 The solute energies were a Mixed (AIII) Solvation Approaches computed in a solvent cavity with the isodensity surface contour equal to 0.0002 e·bohr−3. The solution standard state was customarily defined to have the 1 mol·L−1 for all solute particles, while at the same time, neglecting solute−solute interactions. 2.3. Validation. The calculation results were validated by comparison of the B3LYP/6-31+G(2d) level of theory with the reference coupled-cluster calculations and X-ray experimental data. The aug-cc-pVDZ and 6-31+G(2d) basis sets were used in the CCSD(full) method. Geometric properties and dipole ag, gas phase; c, continuum; n =1−5, coordination numbers of the Li+ moment of the EC molecule, geometric properties of the BOB− + # − ion in the [Li(EC)n] solvatocomplexes, = A D, coordination types fi − # − ion, and the potential energy pro le of the ion molecular of the EC molecule in the [BOB(EC) ] solvatocomplexes defined in interaction for the [Li(EC)]+ solvatocomplex were selected for Figure 2i−l; m = 1, 2, coordination numbers of the Li+ ion by EC in − validation. The experimental data for the EC molecule in the + − the [Li (EC)mBOB ] solvatocomplexes. crystal and liquid states, as well as for the BOB ion in the ≈ MeBOBs (Me = Li, Na, K) and [Li(EC)4]BOB crystals, were further by the higher, 70% molar content of EC relative to used for the comparison. Some geometrical parameters and ≈ − 30% DMC. dipole moment of the EC molecule and BOB ion obtained 2.2. Computations. The quantum-chemical calculations from the quantum-chemical calculations and experiments are were carried out with Gaussian 03.14 The 6-31+G(2d) basis set 15 presented in Tables 1 and 2, respectively. and the B3LYP exchange-correlational functional were used. The data of Tables 1 and 2 show excellent agreement The geometry optimization was done in two steps. First, the between the reference and basic levels of theory, and between local minimum on the potential energy surface was founded the theories and the X-ray experiments. This fact indicates that using numerical second derivatives with respect to the nuclear the B3LYP/6-31+G(2d) method is able to reproduce the coordinates. Then, the optimization was continued with the structure and charge distribution of the molecular and ionic more robust analytical second derivatives. The latter also gave species. Figure 1 shows the basic and reference profiles of the harmonic vibrational frequencies needed for thermodynamic potential energy surface for the gas phase [Li(EC)]+ analysis. The analytic second derivatives were particularly solvatocomplex as a function of the ion−molecule distance. important for the construction of the solvent-saturated Figure 1 shows that the overall shape and location of the solvation shells for the AII approach, since these derivatives minimum on the potential energy curve relevant to the were used to confirm that the found structures corresponded to ° solvation process agree between the basic, B3LYP/6-31+G(2d), local minima. The pressure p = 101325 Pa (1 atm), and the and highly rigorous, CCSD(full)/aug-cc-pVDZ, theory levels. It most abundant isotopes were used for the thermodynamic data is known that in some cases B3LYP can overestimate the calculation within the ideal gas approximation (gas standard solvent binding energy;7 however, it is not the case here, as state). The basis set superposition error was taken into account evidenced by the data of Figure 1. Thus, the B3LYP/ using the counterpoise correction. 16 6-31+G(2d) description provides a good representation of The isodensity polarizable continuum model (IPCM) with the ion−molecule interaction involved in the solvation process. the dielectric constant of 51.0 for the EC:DMC (7:3) binary solvent17 was applied to represent the structureless solvent continuum in methods AI and AIII. Note that the SCRF 3. RESULTS AND DISCUSSION computations employing the IPCM technique do not require a 3.1.1. Solvatocomplexes Formation. The gas phase predefined or manually scaled atomic radii, in contrast to the structures of the BOB− ion, [Li+BOB−] IP, EC molecule, and

d a μ C Table 1. Selected Bond Distances ( ), Angles ( ), and Dipole Moment ( ) of the EC ( 2) Molecule Obtained Using the Basic, B3LYP/6-31+G(2d), and Reference, CCSD(full)/aug-cc-pVDZ and 6-31+G(2d), Levels of Quantum-Chemical a Theory in Gas Phase and Those Deduced from the X-ray Experiments for the Condensed Phases

param CCSD(full)/aug-cc-pVDZ B3LYP/6-31+G(2d) CCSD(full)/6-31+G(2d) X-ray for crystal18/liquid19 ± d(C(c)O(c)), Å 1.196 1.191 1.187 1.15/1.20 0.09 ± d(OC(c)), Å 1.365 1.359 1.354 1.33/1.34 0.12 d(CO), Å 1.442 1.434 1.432 1.40/1.46 ± 0.13 d(CC), Å 1.533 1.534 1.525 1.52/1.52 ± 0.11 d(CH), Å 1.097/1.101 1.092/1.096 1.094/1.099 − a(OC(c)O(c)), deg 124.76 124.84 124.80 124.5/ − a(OC(c)O), deg 110.48 110.32 110.40 111.0/ − a(COC(c)), deg 108.93 109.83 109.00 109.0/ a(CCO), deg 102.51 103.03 102.31 102.0/− a(HCO), deg 108.53/108.72 108.53/108.51 108.68/108.69 μ, D 5.47 5.54 5.61 aThe subscript “(c)” designates the carbonyl group.

16547 DOI: 10.1021/acs.jpcc.6b05963 J. Phys. Chem. C 2016, 120, 16545−16552 The Journal of Physical Chemistry C Article d a − D Table 2. Selected Bond Distances ( ) and Valence Angles ( ) of the BOB ( 2d) Ion Obtained Using the Basic, B3LYP/ 6-31+G(2d), and Reference, CCSD(full)/aug-cc-pVDZ and 6-31+G(2d), Levels of Quantum-Chemical Theory in Gas Phase a and Those Deduced from the X-ray Experiments for the Crystals

I 20 21 parameter CCSD(full)/aug-cc-pVDZ B3LYP/6-31+G(2d) X-ray after Me BOBs X-ray for [Li(EC)4]BOB d(OB), Å 1.483 1.473 1.474 1.4707 d(CO), Å 1.334 1.328 1.326 1.3320

d(O(c)C), Å 1.209 1.203 1.198 1.1908 d(CC), Å 1.553 1.554 1.538 1.536

a(O(c)CO), deg 126.49 126.46 127.4

a(O(c)CC), deg 125.93 126.37 124.5 a(OCC), deg 107.58 107.17 108.0 a(OBO), deg 105.43/111.53 105.06/111.72 109.5 aThe subscript “(c)” designates the carbonyl group.

fi + Figure 1. Potential energy pro les, E, of the gas phase [Li(EC)] (C2) − solvatocomplex along the lithium oxygen coordinate, d(LiO(c)), obtained using the basic, B3LYP/6-31+G(2d) (blue circles), and reference, CCSD(full)/aug-cc-pVDZ (dark red diamonds), levels of quantum-chemical theory. The subscript “(c)” designates the carbonyl group. The basic curve is shifted up by 0.86 Ha.

+ − # − # − the [Li(EC)n] (n =1 5), [BOB(EC) ] ( = A D), and + − [Li (EC)mBOB ](m = 1, 2) solvatocomplexes are shown in Figure 2. Table 3 contains selected geometric data for the EC − + − + Figure 2. Gas phase optimized structures of the BOB− ion (a), the molecule, BOB ion, [Li BOB ] ion pair, and the [Li(EC)n] − + − + + and [Li (EC) BOB ] solvatocomplexes. The data were [Li BOB ] ion pair (b), the EC molecule (c), and the [Li(EC)1−5] m − A−D − − + − computed in the gas phase at the B3LYP/6-31+G(2d) level (d h), [BOB(EC) ] (i l), and [Li (EC)1,2BOB ](m,n) + solvatocomplexes. Symbols A−D refer to coordination types of the of theory. The Li ion strongly polarizes the carbonyl groups of − − − − EC molecule with respect to the BOB ion in the [BOB(EC)A D] the coordinated EC molecules and BOB ioninthe fi + + − + − structures shown in the gure. [Li(EC)n] ,[LiBOB ], and [Li (EC)mBOB ] structures. This action results in the substantial lengthening of the double fi Δ o − · −1 bonds of the coordinated species. As the rst coordination should be extremely stable, since G298 = 486.7 kJ mol , i.e., sphere around the Li+ ion gets saturated, the distances from Li+ considerably less than zero. The IP stability arises due to both to the carbonyl oxygen atoms are increasing, and the Coulomb interaction and chelate bonding of Li+ by the BOB− corresponding valence angles are decreasing, as a result of ion (see Figure 2b). + ligand repulsion and incrementing. Changes in the Gibbs free energy for the Li (g) + nEC(g) = + The standard changes in the calculated thermodynamic [Li(EC)n] (g) processes are negative and decrease to + − + − − · −1 potentials of the [Li BOB ] IP, and the [Li(EC)n] (n =1 5), 369.3 kJ mol for the four-coordinated solvatocomplex # − # − + − − ffi [BOB(EC) ] ( = A D), and [Li (EC)mBOB ](m =1,2) (see Figure 2d g). Taking into account the higher a nity of solvatocomplexes formation in the gas phase are collected in the EC molecules to the bare Li+ ion compared to DMC and Δ Φo ΔΦo ≈ ≈ Table 4. This table contain assoc(g) 298 potentials ( 298 the larger EC mole fraction, 70% vs 30% for DMC, it is + − fi values for the [Li BOB ](g)) that are signi cant for eq 1 reasonable to expect that the most exergonic solvatocomplex, + application. The data of Table 4 show that the contact IP [Li(EC)4] , as determined in the gas phase cluster calculation,

16548 DOI: 10.1021/acs.jpcc.6b05963 J. Phys. Chem. C 2016, 120, 16545−16552 The Journal of Physical Chemistry C Article

Table 3. Selected Bond Distances (d) and Valence Angles (a) of the EC Molecule, BOB− ion, [Li+BOB−] Ion Pair, and the + + − [Li(EC)n] (n =1−5) and [Li (EC)mBOB ](m = 1, 2) Solvatocomplexes Obtained Using the Basic, B3LYP/6-31+G(2d), Level a of Theory in Gas Phase (See Figure 2a−h,m,n)

particle d(O(c)C(c)), Å d(LiO(c)), Å a(LiO(c)C(c)), deg

EC (C2) 1.191 + [Li(EC)] (C2) 1.224 1.734 180.0 + [Li(EC)2] 1.216 1.783 180.0 + [Li(EC)3] 1.208 1.849, 1.851, 1.850 171.8, 166.4, 174.0 + [Li(EC)4] 1.204, 1.203, 1.204, 1.204 1.943, 1.927, 1.940, 1.932 144.6, 153.8, 142.3, 146.8 + [Li(EC)5] 1.202, 1.200, 1.202, 1.199, 1.198 1.998, 2.148, 1.993, 2.266, 1.955 134.9, 139.3, 136.5, 138.7, 174.5 − BOB (D2d) 1.203 + − [Li BOB ](C2v) 1.230/1.192 1.893 101.9 [Li+(EC)BOB−] 1.225/1.194,1.193//1.208 1.957, 1.956//1.848 103.1//151.7 + − [Li (EC)2BOB ] 1.217/1.195, 1.196//1.205, 1.207 2.053, 2.049//1.909, 1.957 102.2, 102.3//134.9, 129.2 aThe subscript “(c)” designates the carbonyl group.

ΔE ΔUo ΔHo ΔSo Table 4. Changes in Potential Energy ( ), Standard Internal Energy ( 298), Enthalpy ( 298), Entropy ( 298), and Gibbs ΔGo + − + n − # − # Free Energy ( 298) of Gas Phase (g) Formation of the [Li BOB ] Ion Pair, and the [Li(EC)n] ( =1 5), [BOB(EC) ] ( = + − a A−D), and [Li (EC)mBOB ](m = 1, 2) Solvatocomplexes

Δ · −1 Δ o · −1 Δ o · −1 Δ o · −1· −1 Δ o · −1 complex formation process E,kJmol U298,kJmol H298,kJmol S298,Jmol K G298,kJmol +−+− Li(g)+= BOB (g) [Li BOB ] (g) −523.9 −517.3 −519.7 −110.9 −486.7 ++ LiEC[Li(EC)](g)+= (g) (g) −212.4 −205.3 −207.8 −86.3 −182.0 +++= − − − − − Li(g) 2EC (g) [Li(EC) 2 ] (g) 374.1 357.2 362.2 188.1 306.1 +++= − − − − − Li(g) 3EC (g) [Li(EC) 3 ] (g) 469.0 446.1 453.5 310.3 361.0 +++= − − − − − Li(g) 4EC (g) [Li(EC) 4 ] (g) 523.9 493.4 503.3 449.6 369.3 +++= − − − − − Li(g) 5EC (g) [Li(EC) 5 ] (g) 531.4 496.8 509.2 604.0 329.1

−−A − − − − − BOB(g)+= EC (g) [BOB(EC) ] (g) 46.1 37.8 40.3 94.0 12.3 −−B − − − − − BOB(g)+= EC (g) [BOB(EC) ] (g) 37.1 28.9 31.4 85.4 5.9 −−C − − − − − BOB(g)+= EC (g) [BOB(EC) ] (g) 40.1 31.9 34.4 68.0 14.1 −−D − − − − − BOB(g)+= EC (g) [BOB(EC) ] (g) 40.0 34.3 36.8 105.3 5.4

+− + − [Li BOB ](g)+= EC (g) [Li (EC)BOB ] (g) −101.5 −92.2 −94.7 −94.9 −66.4 +− + − [Li BOB ](g)+= 2EC (g) [Li (EC) 2 BOB ] (g) −166.8 −149.1 −154.1 −245.7 −80.8 aThe symbols A, B, C, and D refer to coordination types of the EC molecule with respect to the BOB− ion in the [BOB(EC)A−D]− structures (see Figure 2i−l).

+ should dominate in solution, and fractions of other previously as a possible form of the [Li(EC)n] in solvatocomplexes should be small.12,22,23 The difference in solution.7,24,26,27 Due to translational dynamics and strong + − + the Gibbs free energy of formation of the [Li(EC)3] and dipole dipole repulsions of EC molecules in [Li(EC)5] , the + · −1 [Li(EC)4] solvatocomplexes is less than 10 kJ mol , whereas latter is expected to be unstable in the bulk solution. the corresponding potential energy difference is much greater, Ion−dipole interactions between the BOB− ion and EC · −1 Δ o approaching 50 kJ mol . The example described above molecules are extremely weak. The G298 values for the demonstrates that it is very important to consider the Gibbs [BOB(EC)#]− formation, where # = A−D is the EC free energy rather than the potential energy changes. The latter coordination type (see Figure 2i−l), vary only from is used often for the thermodynamic characterization of various −5.4 kJ·mol−1 (type D)to−14.1 kJ·mol−1 (type C). Such processes, since potential energy can be easily obtained from low values can be explained by the large size of the BOB− ion, quantum-chemical calculations.24,25 An even stronger case is resulting in low specific density of the negative charge. + + − formation of the [Li(EC)5] (see Figure 2h) from [Li(EC)4] . Consequently, the BOB anion cannot be strongly solvated This process has a negative potential energy change and a in solution even by highly polar molecules such as EC. positive Gibbs free energy change. Thus, this unfavorable The lithium site of the [Li+BOB−] contact IP is not sterically process can be predicted erroneously as favorable based on the saturated and can additionally attach one or two EC molecules ff + potential energy di erence alone. The [Li(EC)5] solvatocom- (see Figure 2m,n). These processes are not as exergonic as Δ o − · −1 + plex ( G298 = 329.1 kJ mol ) has not been discussed formation of the [Li(EC)n] solvatocomplexes discussed above.

16549 DOI: 10.1021/acs.jpcc.6b05963 J. Phys. Chem. C 2016, 120, 16545−16552 The Journal of Physical Chemistry C Article

Δ Ho Δ So Δ Go Table 5. Changes in Standard Enthalpy ( solv(A) 298), Entropy ( solv(A) 298), and Gibbs Free Energy ( solv(A) 298) of Solvation of the EC Molecule, the Li+ and BOB− ions, and the [Li+BOB−] Ion Pair in the EC:DMC (7:3) Binary Solvent, Obtained Using the Continuum (I), Discrete (II), and Mixed (III) Solvation Approaches (A) (g, Gas; c, Continuum)

Δ o · −1 Δ o · −1· −1 Δ o · −1 particle A solvation process solv(A)H298,kJmol solv(A)S298,Jmol K solv(A)G298,kJmol

EC I ECEC(g)= (c) −26.1 −45.5 −12.6

+ ++ Li I LiLi(g)= (c) −587.1 −26.6 −579.2 +++= − − − II Li(g) 4EC (g) [Li(EC) 4 ] (g) 503.3 449.6 369.3 ++= − − − I [Li(EC)4 ](g) [Li(EC)4 ] (c) 152.8 26.6 144.9 +++= − − − III Li(g) 4EC (c) [Li(EC) 4 ] (c) 551.5 294.0 463.9 − −− BOB I BOB(g)= BOB (c) −172.1 −26.6 −164.2 −−C − − − II BOB(g)+= EC (g) [BOB(EC) ] (g) 34.4 68.0 14.1 −− III BOB(g)+= 0EC (c) BOB (c) −172.1 −26.6 −164.2

+ − +− +− [Li BOB ]I [Li BOB ](g)= [Li BOB ] (c) −51.9 −26.6 −44.0 +− + − II [Li BOB ](g)+= 2EC (g) [Li (EC) 2 BOB ] (g) −154.1 −245.7 −80.8 +−+− I [Li (EC)2(g)2(c) BOB ]= [Li (EC) BOB ] −65.0 −26.6 −57.1 +− + − III [Li BOB ](g)+= 2EC (c) [Li (EC) 2 BOB ] (c) −166.8 −181.2 −112.8

Δ o + − ⎛ ⎛ ⎞⎞ The corresponding G298 values for the [Li (EC)BOB ] and 298.15R + − − − · −1 oo⎜ ⎜ ⎟⎟ [Li (EC)2BOB ] are 66.4 and 80.8 kJ mol . In other Δsolv(I)SRV 298 =−⎜ln ln o ⎟ − ⎝ ⎝ ⎠⎠ words, the first EC molecule binds to [Li+BOB ] quite p ffi −−11 strongly, while the a nity of the second EC molecule to the IP =−26.58 J · mol · K (5) monosolvate is small and comparable to the free Gibbs energy # − of the [BOB(EC) ] formation. The two explicit EC molecules Since different standard states for the solvent and solute are ffi 28 are su cient for the complete saturation of the lithium usually used, the Vo value for EC in eqs 4 and 5, the molar + − solvation shell in the [Li BOB ] IP. Therefore, the volume that is accessible for the particular cosolvent molecules + of Li in the solvated cation as well as in target EC:DMC (7:3) binary solvent mixture, was in the solvated IP is defined by the carbonyl oxygen atoms and preliminarily calculated from experimental data29 and sub- o × −4 3· −1 is equal to four. stituted on VEC = 1.024 10 m mol . According to the gas phase calculations (Table 4), the The changes in the standard thermodynamic potentials of + C − Δ Φo [Li(EC)4] cation, the [BOB(EC) ] anion, and the solvation within AIII, solv(III) 298, can be found as linear + − [Li (EC)2BOB ] IP solvatocomplexes are the most stable combinations of the corresponding data obtained within AI and species. Therefore, these species were chosen in the framework AII (see Chart 1). of the discrete (AII) approach to characterize ion association of 3.2. Solvation Data. The changes in the standard enthalpy, LiBOB in the EC:DMC (7:3) binary mixture. entropy, and Gibbs free energy of the solvation processes are 3.1.2. SCRF Application. The SCRF quantum-chemical summarized in Table 5 for the different solvation approaches + − + − Δ Φo fi calculations of the bare Li and BOB ions, the [Li BOB ] IP, ( solv(A) 298). In spite of a signi cant dipole moment value + + − the EC molecule, and the [Li(EC)4] and [Li (EC)2BOB ] even in the gas phase, the EC molecules gives a very small Δ o − · −1 + solvatocomplexes were carried out using the experimental value magnitude of solv(I)G298 = 12.6 kJ mol . The bare Li ion of dielectric constant (51.0) of the EC:DMC (7:3) binary has a small radius and, consequently, a high polarizing action. mixture.17 The changes in the standard enthalpy of solvation Hence, its transfer into the structureless continuum is within the simplest AI model, Δ Ho , were estimated characterized by an extremely negative change in the standard solv(I) 298 − according to Gibbs free energy, which is equal to −579.2 kJ·mol 1. The same + value for the saturated [Li(EC)4] solvatocomplex is almost o oo Δsolv(I)HEpVR 298 =Δsolv(I) + −298.15 four times smaller by module, because of the size increase upon Δ o binding of the four EC molecules. The solv(III)G298 value for −1 + ≡Δsolv(I)E −2.38 kJ · mol (4) the Li ion is intermediate between those for the AI and AII models and is equal to −463.9 kJ·mol−1. Δ o −1 Here, solv(I)E is the potential energy change during the Taking into account that Δ G = −164.2 kJ·mol for − solv(I) 298 solvation within AI, and Vo = 0.001 m3·mol 1 is the standard the bare BOB− ion, its symmetric polarization by the molar volume that is accessible for the solute particle in the structureless continuum is almost 10 times more exergonic, solution standard state. as compared with the formation of [BOB(EC)C]− anion in the The isothermal compression stage of solvation decreases the gas phase. Therefore, consideration of any EC unsaturated translational entropy of transferring particles within the AI solvatocomplexes involving the BOB− ion is not reasonable Δ Φo ≡ Δ Φo model. Those changes in the standard entropy of solvation, and, as consequence, we have taken solv(III) 298 solv(I) 298 Δ o solv(I)S298, were taken into account with (see Table 5).

16550 DOI: 10.1021/acs.jpcc.6b05963 J. Phys. Chem. C 2016, 120, 16545−16552 The Journal of Physical Chemistry C Article

Δ Ho Δ So Δ Go Table 6. Changes in Standard Enthalpy ( assoc(A) 298), Entropy ( assoc(A) 298), and Gibbs Free Energy ( assoc(A) 298) during Ion Association for the LiBOB Salt in the EC:DMC (7:3) Binary Solvent, Obtained Using the Continuum (I), Discrete (II), and Mixed (III) Solvation Approaches (A) (g, Gas; c, Continuum)

Δ o · −1 Δ o · −1· −1 Δ o · −1 A association process assoc(A)H298,kJmol assoc(A)S298,Jmol K assoc(A)G298,kJmol +−+− I Li(c)+= BOB (c) [Li BOB ] (c) +187.6 −84.3 +212.7 +++−+=C + − − II [Li(EC)4 ](g) [BOB(EC) ](g) [Li (EC)2(g)(g BOB ] 3EC ) 136.1 +161.0 184.1 +−+−+= + III [Li(EC)4 ](c) BOB(c) [Li (EC) 2 BOB ] (c) 2EC (c) +37.1 +28.6 +28.6

As for the neutral [Li+BOB−] IP as well as for the more 4. CONCLUSIONS + − spatial extended [Li (EC)2BOB ] neutral solvatocomplex, the In conclusion, we showed that neither continuum nor discrete Δ o − · −1 corresponding solv(I)G298 values are around 50 kJ mol , that − solvation models are capable of describing ion association of is almost a factor of 3 smaller than for the bare BOB ion. lithium salt in highly polar solvent mixtures and that a Δ o + − Simultaneously, the solv(II)G298 value for the [Li BOB ]IPis combined discrete−continuum (mixed) treatment is required. − · −1 only equal to 80.8 kJ mol . Consequently, both discrete and Using these approaches, we performed quantum-chemical + − continuum contributions to solvation of the [Li BOB ] IP are calculations of the changes in the standard enthalpy, entropy, significant and are accounted for within the AIII model. The and Gibbs free energy of the ion association process for corresponding change in the standard Gibbs free energy is solution of the LiBOB salt in the EC:DMC (7:3) binary − equal to −112.8 kJ·mol 1. solvent. This is the first theoretical prediction for the solvated 3.3. Ion Association. Table 6 presents the changes in the [Li+BOB−] IP formation from the solvated Li+ and BOB− ions standard enthalpy, entropy, and Gibbs free energy for the Li+ in an EC based solvent mixture. The results show that accurate − and BOB ion association, obtained within the three different description of the Li+ ion solvation requires both continuum Δ Φo solvation approaches ( assoc(A) 298). The potentials were polarization of the solvent medium and binding of the four calculated according to eq 1 using the corresponding explicit EC molecules. On the contrary, in solvation of the Δ Φo − assoc(g) 298 values from Table 4 for the IP formation in the BOB anion is dominated polarization by the highly polar Δ Φo structureless solvent continuum. Explicit interaction of polar gas phase and the solv(A) 298 data for the solvation processes − from Table 5. Solvation model AI predicts positive values of the EC molecules with the BOB ion is extremely weak. The Δ Ho and Δ Go . The values are similar and are discrete and continuum contributions to the Gibbs free energy assoc(I) 298 assoc(I) 298 + − around 200 kJ·mol−1, since the entropic factor is unessential. of solvation of the [Li BOB ] IP are relatively small and are Thus, the continuum solvation approach predicts an unphysical similar. Therefore, both components should be taken into + − behavior: ion association is impossible for the LiBOB solution account in order to describe the [Li BOB ] IP solvation, and − in the EC:DMC (7:3) binary solvent at any temperature, this can be achieved only with the mixed discrete continuum because the entropic contribution is not properly taken into model. account. Libration of the three EC molecules upon ion Most importantly, the discrete and continuum components association according to solvation model AII leads to a large to the Gibbs free energies of the ion association process are − − large and have opposite signs. The continuum approach positive change in Δ So = 161.0 J·mol 1·K 1. The assoc(II) 298 predicts no association, while the discrete description produces corresponding Δ Ho value is strongly exothermic. As a assoc(II) 298 complete association. Both results are unphysical and contradict consequence, the discrete approach predicts a large negative − Δ o − · −1 between themselves. The mixed discrete continuum model value of assoc(II)G298 = 184.1 kJ mol : ion is combines both contributions. The resulting Gibbs free energy impossible at any temperature. The corresponding Kassoc is 32 of ion association is an order of magnitude smaller, predicting around 10 . That is, the discrete model sharply overestimates reasonably weak association. The conclusions drawn in the the hypothetical ion association. Such a value of Kassoc would − current work are particularly important for the selection of make the lithium salt with a large anion, such as BOB , totally − 1,9 novel aprotic electrolyte salt solutions. The mixed discrete insoluble even in the highly . Solvation continuum approach resolves the problems in determining the model AIII produces moderately positive values of all extent of ion association and can be used to screen the Δ Φo fi assoc(III) 298 potentials. Their absolute values are signi cantly properties of a broad range of ion−molecular mixtures for LIBs. smaller than the corresponding magnitudes obtained within AI and AII. Substitution of the two EC molecules in the ■ AUTHOR INFORMATION + [Li(EC)4] solvatocomplex by the in abstracto nonsolvated − Corresponding Authors and continuum polarized BOB anion explains qualitatively the * Δ o (O.N.K.) E-mail: [email protected]. Tel.: +380 50 positive assoc(III)S298 value. The entropic contribution does not Δ o 3032813. exceed the assoc(III)H298 contribution. As a result, the mixed or * − Δ o (O.V.P.) E-mail: [email protected]. Tel.: +1 213 8213116. discrete continuum approach gives assoc(III)G298 = 28.6 kJ·mol−1, corresponding to K on the order of 10−5. This Notes assoc fi result allows one to conclude that LiBOB in the EC:DMC The authors declare no competing nancial interest. (7:3) binary mixture is associated weakly, which is favorable for the LIBs applications. The predictions made in the present ■ ACKNOWLEDGMENTS work could be verified experimentally by conductometry This work was performed using computational facilities of the method or IR/Raman and NMR , as has been joint computational cluster of SSI “Institute for Single Crystals” achieved previously for Li+ ion solvation in other solvents.30 and Institute for Scintillation Materials of the National

16551 DOI: 10.1021/acs.jpcc.6b05963 J. Phys. Chem. C 2016, 120, 16545−16552 The Journal of Physical Chemistry C Article

Academy of Science of Ukraine incorporated into the Ukrainian (18) Brown, C. The Crystal Structure of Ethylene Carbonate. Acta National Grid. O.M.K. and O.N.K. acknowledge the Fund of Crystallogr. 1954, 7,92−96. (19) Soetens, J.-C.; Millot, C.; Maigret, B.; Bako,́ I. Molecular the Ministry of Education and Science of Ukraine for the − financial support (Grant Nos. 0113U002426, 0116U000834). Dynamics Simulation and X Ray Diffraction Studies of Ethylene Carbonate, and Dimethyl Carbonate in Liquid O.V.P. acknowledges support of the U.S. Department of Energy Phase. J. Mol. Liq. 2001, 92, 201−216. (Grant No. DE-SC0014429) and is grateful to the Russian (20) Zavalij, P. Y.; Yang, S.; Whittingham, M. S. Structures of Science Foundation for financial support of the calculations, Potassium, Sodium and Lithium Bis(Oxalato)Borate Salts from Project No. 14-43-00052, organization Photochemistry Powder Diffraction Data. Acta Crystallogr., Sect. B: Struct. Sci. 2003, Center RAS. 59, 753−759. 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16552 DOI: 10.1021/acs.jpcc.6b05963 J. Phys. Chem. C 2016, 120, 16545−16552