Electrolyte Solvation and Ionic Association: VI. Acetonitrile-Lithium Salt Mixtures: Highly Associated Salts Revisited

In order to investigate the highly associated electrolytes, the previously developed Atomistic Polarizable Potential for Liquids, Electrolytes, and Polymers (APPLE&P) many-body force fields (FFs) have been extended to (AN)_n-LiCF₃SO₃ and (AN)_n-LiCF₃CO₂ electrolytes and revised for the (AN)_n-LiBF₄ electrolytes. A detailed description of the FF functional form is given elsewhere,⁸ but the main features are listed below. APPLE&P utilizes a Buckingham potential, also called exp-6, in conjunction with permanent charges situated on the atomic sites for the electrolyte components simulated in this work. The polarization interactions are represented by the induced isotropic atomic dipoles. Thole screening with the parameter a_T = 0.2 was used to screen the interactions between the induced dipoles in the short range. Atoms connected by bonds (1-2) and bends (1-2-3) were excluded from the list of non-bonded interactions. Atoms connected by 3 or more bonds (1-4 interactions) had full non-bonded interactions with the exception of the 1-4 interaction between the permanent charges and the induced dipoles which were scaled by 0.8.

Permanent charges for the anions (BF₄⁻, CF₃SO₃⁻ and CF₃CO₂⁻) were determined by fitting the electrostatic potential around the anions calculated at the MP2/Tz level, where Tz denotes the aug-cc-pvTz basis set.⁸ The bond length and natural bending angles were fit to geometries obtained at the MP2/aug-cc-pvTz level. The dihedral parameters for the CF₃-group rotation were fit to MP2/Tz energies. For the CF₃CO₂⁻ anion, a set of atomic polarizabilities was transferred from the CH₃OCO₂⁻ anion FF.⁹ For the CF₃SO₃⁻ anion, the atomic polarizabilities for O, C and F were taken from the revised N(SO₂CF₃)₂⁻ (i.e., TFSI⁻) FF,¹⁰ while the S polarizability was adjusted to match the average anion molecular polarizability of 7.35 Å³ obtained from the M05-2X/aug-cc-pvTz calculations. The atomic polarizabilities of BF₄⁻ were taken from the previous version of the FF without modification.⁸ The exp-6 repulsion-dispersion parameters obtained from the TFSI⁻ and CH₃OCO₂⁻ FFs^2,9 were transferred to CF₃SO₃⁻ and CF₃CO₂⁻, respectively. After this, additional small adjustments were made to the Li...F and Li...S repulsive parameters in order to improve the description of the Li⁺BF₄⁻ and Li⁺CF₃SO₃⁻ binding energies obtained from the high-level quantum chemistry (QC) calculations described below.

In order to evaluate the ability of the developed FFs to predict the binding energies of (Li⁺CF₃SO₃⁻)_m and (Li⁺CF₃CO₂⁻)_m complexes (m = 1, 2, 3), a set of QC calculations was performed using the Gaussian g09 package¹¹ for the geometries shown in SI Figs. S1 and S2. The most accurate G4MP2 calculations were performed only for the smallest salt complexes with m = 1 and 2 because the G4MP2 calculations become prohibitively expensive (computationally) for the larger clusters with m = 3. DFT methods are the most suitable for the calculations of binding energies for the larger m = 3 clusters, provided that an adequate functional is used. A number of DFT functionals have therefore been evaluated with regard to their ability to describe the binding energies of the (Li⁺anion⁻)_m clusters with the results reported in Tables I and II and Figs. S1 and S2. These latter binding energies were not corrected for the basis set superposition error (BSSE), however, as many DFT functionals are parameterized without BSSE corrections. Instead, the BSSE corrections are given in parentheses as an estimation of the accuracy of the DFT calculations (Tables I and II).

The M06-L functional predicts binding energies that have the best agreement with the G4MP2 benchmark calculations with an accuracy comparable to or even better than the significantly more computationally expensive MP2/Tz calculations. Specifically, the M06-L results yielded binding energies slightly larger than those from the G4MP2 calculations if uncorrected for BSSE, while after BSSE correction the M06-L results tend to be slightly lower than the G4MP2 values. The M05-2X and B3LYP functionals, on the other hand, predict significantly higher binding energies than those from the G4MP2, MP2/Tz and M06-L calculations. Such high values are consistent with earlier calculations for solvent-Li⁺ and anion-Li⁺ complexes.^1–5 The M06-L/6-311+G^** level was therefore chosen as the most reliable for the investigation of the larger ion clusters.

An examination of Tables I and II reveals that the binding energies of the (Li⁺CF₃CO₂⁻)_m complexes obtained from both the QC and FF calculations are systematically higher than the binding energies in the corresponding (Li⁺CF₃SO₃⁻)_m complexes. Moreover, the FFs predict that the coordination in the (Li⁺CF₃CO₂⁻)_m and (Li⁺CF₃SO₃⁻)_m complexes (m = 1, 2, 3) is due to Li⁺ cation coordination by the anion oxygens, with the exception of the (Li⁺CF₃CO₂⁻)₁ (II) and (Li⁺CF₃CO₂⁻)₃ (II) complexes (Fig. S2) for which a Li⁺ cation is coordinated to a fluorine atom from the CF₃ group. For the later complexes, the binding energies from the MM calculations using the FF are significantly lower than the binding energies from the DFT and QC calculations (Table II). Attempts to improve the agreement for (Li⁺CF₃CO₂⁻)₁ by reducing the F-Li repulsion shifted the Li⁺ cation too close to the fluorine atom (relative to the QC results). The binding energy of the (Li⁺CF₃CO₂⁻)₁ (II) complex, however, is more than 8 kcal mol⁻¹ higher than the binding energy of the (Li⁺CF₃CO₂⁻)₁ (I) complex where the Li⁺ cation has bidentate coordination with the CF₃CO₂⁻ oxygen atoms. It is therefore reasonable to assume that the population of such higher energy complexes will be quite low and are thus not critical to the realistic representation of the solvates within the MD simulations. An examination of the binding energies indicates that the (Li⁺CF₃SO₃⁻)₃ (II) complex (Fig. S1) is approximately 10 kcal mol⁻¹ more stable than than the corresponding (I) complex from both the DFT and FF calculations (Table I). The FF calculations indicate that the stabilization of complex (II) vs. (I) is largely due to a significantly larger polarization (5 kcal mol⁻¹) from the two Li⁺ cations grouped together in complex (II). In addition, complex (II) also has less bend distortion than is found for complex (I).

MD simulations were performed on the solvent AN doped with LiCF₃SO₃ or LiCF₃CO₂ (AN:Li = 30, 20, 10, 5, 2) and LiBF₄ (AN:Li = 30, 20, 10, 5). The compositions of the simulation cells are given in Tables III–V. A previously used MD simulation methodology for the (AN)_n-LiX mixtures has been followed.¹ Equilibration and production runs were performed using NPT and NVT ensembles, respectively. The NPT and NVT run times are summarized in Tables III–V. The distribution of residence times for the solvent and anions present in the Li⁺ cation first coordination shells were calculated using:

where H(t) is 1 if a particular AN molecule or anion is involved in coordinating a given Li⁺ cation...and zero otherwise. The brackets indicate averaging over all of the Li⁺ cations and multiple time origins, as well as normalization such that P_Li-X(0) = 1. The residence time for each species in the Li⁺ cation coordination shells was calculated as the time integral of stretched exponential exp(−(t/τ)^β) fits to the P_Li-X(t) distribution functions.

MD simulations were previously reported for (AN)_n-LiBF₄ mixtures,¹ but these have been revised here as it was found that a newly refined FF for the BF₄⁻ anion provided results which are in better agreement with the experimental analyses previously reported.¹ Fig. 1a shows a snapshot of the simulation box for the n = 10 composition (i.e., the simulation box captured at a particular time during the equilibrium run period). To more fully access the information contained within this simulation (i.e., to scrutinize the computed solution structure), visualization of the solvates and their distribution is necessary. To this end, the snapshots (at select time intervals during the equilibrium portion of the simulations) were modified by coloring the AN molecules light gray if they were > 2.70 Å from the Li⁺ cations (i.e., uncoordinated and not in close proximity) and the solvent molecules and ions were unwrapped/periodic boundary conditions were applied so as not to divide the anions and solvates across the periodic box boundaries (Fig. 1b). The individual uncoordinated anions and solvates were then extracted from the dissected simulation box snapshot and assembled into a visual list (Fig. 2). A number of notable features are evident:

• (a)  
  this particular simulation snapshot contains 13 uncoordinated BF₄⁻ anions (out of 64), but only 11 fully solvated Li⁺ cations;
• (b)  
  aggregate solvates with either excess Li⁺ cations or excess anions are present, but there are more of the former as is evident by the larger number of uncoordinated anions than fully solvated Li⁺ cations;
• (c)  
  in addition to contact ion pair solvates (12 of these), several of the aggregate solvates also contain equal numbers of anions and Li⁺ cations (and thus are electrically neutral for the lifetime of these solvates);
• (d)  
  the BF₄⁻ anions coordinated to three Li⁺ cations serve as central linkage sites for the larger aggregates;
• (e)  
  nearly all of the Li⁺ cations have 4-fold coordination to anions and/or solvent molecules;⁵
• (f)  
  very few of the BF₄⁻ anions have bidentate coordination (i.e., two fluorine atoms from the same anion coordinated to a single Li⁺ cation) and none of them have tridentate coordination (i.e., three fluorine atoms from the same anion coordinated to a single Li⁺ cation); and
• (g)  
  many of the aggregate solvates contain anions coordinated to a single Li⁺ cation with the cations, however, coordinated to multiple anions—thus these former anions would result in a spectral signature (Raman and/or FTIR spectroscopy) identical to that for contact ion pair solvates when conducting an anion spectroscopic vibrational band analysis to determine the solution ionic association interactions even though the anions are actually part of larger aggregate solvates.

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Fig. 2 can be compared with the data obtained from the (AN)_n-LiX (n = 10; X = ClO₄⁻, TFSI⁻ and PF₆⁻) electrolyte simulations previously reported.^1–3 Figs. 3 and 4 consist of similar plots for the (AN)_n-LiX (n = 10) electrolytes with the LiCF₃SO₃ and LiCF₃CO₂ salts, respectively (plots for the n = 30 simulations are provided in the Supporting Information). The electrolytes with LiCF₃SO₃ (Fig. 3) are considerably more associated than the comparable electrolytes with LiBF₄ (less uncoordinated anions, less fully solvated Li⁺ cations, more aggregates) which, in turn, are more associated than the electrolytes with LiClO₄, LiTFSI and LiPF₆. This difference is even more evident for the electrolytes with LiCF₃CO₂ (Fig. 4), which is in accord with the largest binding energy observed for the (Li⁺CF₃CO₂⁻)_m complexes in the QC calculations. Notably, the latter simulations contain no uncoordinated CF₃CO₂⁻ anions and very few CF₃CO₂⁻ anions coordinated to a single Li⁺ cation as contact ion pairs, even for the n = 30 composition. The snapshot of the n = 10 mixture (Fig. 4), however, does contain 8 fully solvated Li⁺ cations (out of 64). These cations become available for full solvation due to the coordination of the remaining cations within aggregate solvates which contain a greater number of CF₃CO₂⁻ anions.

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Given that the (AN)_n-LiX electrolyte mixtures with LiCF₃SO₃ and LiCF₃CO₂ are more highly associated than comparable mixtures with salts such as LiClO₄ or LiPF₆, it is instructive to examine the differences between these electrolytes. The modes of CF₃SO₃⁻...Li⁺ cation coordination in the liquid solvates (MD simulations) closely resemble the interactions noted for the BF₄⁻...Li⁺ cation coordination (Figs. 2 and 3) (as well as for ClO₄⁻ and PF₆⁻ anions).^1–3 It is the extent of this coordination which differs for the different anions resulting in differences in the ionic association and thus overall solution structure. Specifically, all of these anions tend to be coordinated to zero-three Li⁺ cations with each coordinated anion oxygen (or fluorine) atom forming a single coordinate bond to a single Li⁺ cation using a single electron lone-pair. This Li⁺ cation coordination from the MD simulations is in excellent agreement with the coordination found in solvate crystalline structures with LiCF₃SO₃, LiBF₄, LiClO₄ and LiPF₆.^12–36 None of these crystalline solvate structures, even for highly aggregated solvates, have single donor atoms from the anions coordinated to two Li⁺ cations. Note that the crystal structures for the neat LiCF₃SO₃ and LiClO₄ salts do, however, have single anion oxygen atoms coordinated to two Li⁺ cations.^37–39

This single anion donor atom...Li⁺ cation coordination is not what is found, however, in the MD simulations of the electrolytes with LiCF₃CO₂. The simulations instead indicate that the CF₃CO₂⁻ anions are nearly always coordinated to two or three Li⁺ cations, even for the dilute compositions (see Supporting Information), and thus are usually present as aggregate solvates (Fig. 4). The aggregate solvates with the CF₃CO₂⁻ anions, however, differ from those formed with other anions, such as CF₃SO₃⁻, BF₄⁻, ClO₄⁻ and PF₆⁻, due to the tight clustering of ions which results from the coordination of the anions to multiple Li⁺ cations through the use of several of the electron lone-pairs on the CF₃CO₂⁻ anion oxygen atoms. Crystalline solvate structures—i.e., (G2)_1/3:LiCF₃SO₃ and (G4)_2/5:LiCF₃CO₂ with diglyme and tetraglyme, respectively—also have CF₃CO₂⁻ anions coordinated to two, three and even four Li⁺ cations using the available electron lone-pairs (Fig. 5).^24,25 These structures therefore strongly supports the MD simulation results (Fig. 4). Some differences, however, are found between the coordination in the MD simulations and the solvate crystal structures. For example, some of the CF₃CO₂⁻ anions in the simulations are coordinated to three Li⁺ cations with one of the Li⁺ cations having bidentate coordination by two of the oxygen atoms. Such coordination is not found in the two known solvate crystal structures, but it may be present within liquid electrolytes.

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As noted above for the mixtures with BF₄⁻ anions, scrutiny of the solvates in Figs. 2–4 indicates that the vast majority of the Li⁺ cations have a coordination number of 4—irregardless of the anion present—due to both solvent and anion coordination. Thus, although the (AN)_n-LiCF₃CO₂ electrolytes have a very low degree of solvation (<1.5 AN molecules per Li⁺ cation on average over a wide concentration range) as determined from both experimental¹ and computational (Table V) analyses, highly concentrated liquid electrolytes (>5 M) can be prepared at room temperature due to the extensive anion coordination.¹ In fact, some of the Li⁺ cations within the solvates are unsolvated (i.e., the cations are coordinated solely by four CF₃CO₂⁻ anions) (Fig. 4).

The snapshots of the MD simulations (e.g., Fig. 1) do not provide any insight into the dynamics of the solvent and anion exchange in the Li⁺ cation coordination shells. One way in which this can be visualized is shown in Fig. 6. A similar plot was provided in an earlier publication which showed both the AN solvent and BF₄⁻ anion coordination to a specified Li⁺ cation from the previous (AN)_n-LiBF₄ simulations (many additional plots were also provided in the Supporting Information for varying electrolytes).³ Typical AN solvent residence times (i.e., time coordinated to a specified Li⁺ cation) from the simulations for the (AN)_n-LiX (n = 10) mixtures at 60°C were 75–80 ps for the mixtures with LiBF₄, LiClO₄ and LiPF₆. Significant differences were noted, however, for the residence times of the anions (i.e., individual anion...Li⁺ cation coordination bonds). A direct comparison of this is shown in Fig. 6 (note that the x-axis has been scaled up by an order of magnitude relative to the previously reported plots—i.e., 10,000 ps instead of 1000 ps). For each of the different electrolytes, the plot data consists of the anion residence times for the different anions within a single specified Li⁺ cation's coordination shell over the 10,000 ps time period. For example, for the electrolyte with the LiBF₄ salt, 29 different BF₄⁻ anions are coordinated to the specified Li⁺ cation over 10,000 ps of the electrolyte simulation run. A dot is marked on the plot if a particular anion is coordinated for at least 40 ps during the 100 ps intervals. This Li⁺ cation is initially coordinated to three BF₄⁻ anions (and, presumably, one AN solvent molecule). At the beginning of the time period scrutinized, the first anion remains coordinated for ∼300 ps. The second anion remains coordinated for ∼100 ps, while the third anion remains coordinated for ∼400 ps. A fourth BF₄⁻ anion coordinates this Li⁺ cation around this time period, but for <40 ps so no dot is shown in the figure. This same anion then later recoordinates the same Li⁺ cation at a time of 5100 ps (this is attributed to the limited number (64) of anions present in and size of the simulation box). This particular Li⁺ cation in the LiBF₄ electrolyte transitions back and forth between an aggregated state and coordination to a single anion (i.e., contact ion pair), with only brief periods when it is uncoordinated to BF₄⁻ anions (i.e., fully solvated). In contrast, Fig. 6 indicates that the specified Li⁺ cation in the LiPF₆ simulation is typically either fully solvated or exists as short-lived contact ion pairs. The cation in the LiClO₄ simulation behaves similarly, but the contact ion pairs are longer lived and some aggregation occurs as well. The cation in the LiCF₃SO₃ simulation exists as long-lived contact ion pairs or aggregates. In fact, for 1000 ps or so near the beginning of the time period reported in Fig. 6, the Li⁺ cation is coordinated to four CF₃SO₃⁻ anions (and presumably uncoordinated by AN solvent molecules). This, coordination only by anions is uncommon in the LiCF₃SO₃ simulations, but coordinated to three anions is more frequently observed (Figs. 3, S7–S11, S21 and S22). The Li⁺ cation noted in Fig. 6 for the LiCF₃CO₂ simulation, however, is coordinated to three or four anions for much of the observed simulation period, although at one point it rapidly sheds all of the coordinated anions and for 1300 ps or so it becomes fully solvated. The on-off-on coordination for the same CF₃CO₂⁻ anions in Fig. 6 is understandable given that the anions are bonded to multiple Li⁺ cations in tight ion clusters. When a coordination bond is broken with a Li⁺ cation, the anion remains located in close proximity enabling it to readily become recoordinated again. The solvates consisting of aggregated clusters of ions in the (AN)_n-LiCF₃CO₂ electrolytes are thus expected to be quite long-lived, although it is evident that exchanges of the solvent molecules and ions do occur (Figs. S12–S14 and S23).

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Fig. 7 summarizes the solvent and anion residence times (on average) for coordination to the Li⁺ cations as a function of the salt concentration obtained from the MD simulations. The solvent residence times are in good agreement with the values previously obtained for (AN)_n-LiX electrolytes with other salts.³ For the most concentrated (n = 2) mixtures, most of the Li⁺ cations are extensively coordinated by anions. The long residence times of the anions (relative to the AN solvent molecules) and extensive polymeric aggregation of the ions perhaps restricts the ability of the solvent molecules to disengage from the coordinated Li⁺ cations and reorient (to be replaced by other solvent molecules or anions). Instead, the solvent molecules may break the coordination bond, but then shortly thereafter reform the bond resulting in the very long effective residence times noted.

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Additional insight into the mechanism(s) of the Li⁺ cation mobility is obtained by calculating the distance that a Li⁺ cations travels in one Li⁺-anion residence time period, as shown in Table S1. In the dilute (AN)_n-LiCF₃CO₂ (n = 30) electrolyte, the Li⁺ cations travel (on average) > 100 Å before they exchange anions indicating that the Li⁺ cations within the aggregrate solvates move significant distances as either neutral or charged complexes and that these aggregates, and the few fully solvated Li⁺ cations, are therefore the dominant species present for charge transfer. As the salt concentration increases, however, the Li⁺ cations move up to 5 times shorter distances (< 20 Å) before exchanging anions indicating that an anion exchange mechanism becomes more important for more concentrated mixtures in which the aggregated solvates are in closer proximity to one another. In the dilute (AN)_n-LiBF₄ and (AN)_n-LiCF₃SO₃ (n = 30) electrolytes, however, the Li⁺ cations move 5 and 3 times shorter distances with anions, respectively, than occurs for the (AN)_n-LiCF₃CO₂ electrolytes. Nevertheless, in the dilute (AN)_n-LiBF₄ (n = 30) electrolyte, the Li⁺ cations move 20 Å (on average) before they exchange anions, which is the size of a few solvent molecules suggesting that motion with anions is still dominant in this concentration regime.

The data in Figs. 6 and 7 are only indicative of the anion residence times within the coordination spheres of the given cations. These figures provides no direct information about the types of solvates present—information which is instead obtained from the simulation snapshots (Figs. 2–4). The residence times of the anions are well correlated with the ionic association strength of the anions which increases in the order:^1–3

As noted above, with increasing ionic association strength, the anions also tend to remain coordinated longer to the Li⁺ cations. This is quite significant as it indicates that the contact ion pair and aggregate solvates in the (AN)_n-LiPF₆ electrolytes have short lifetimes before the Li⁺ cations become fully solvated or transform into another form of solvate structure. In contrast, the aggregate solvates in the (AN)_n-LiCF₃CO₂ electrolytes are long-lived, although they evolve and change in structure over time. Fig. 8 summarizes the total number of anions coordinated to the 64 different Li⁺ cations in the simulation boxes over the 10,000 ps simulation run period for each (AN)_n-LiX electrolyte (e.g., 1 of the Li⁺ cations is coordinated to a total of 4 CF₃CO₂⁻ anions, 10 are each coordinated to a total of 5 CF₃CO₂⁻ anions, etc.). A direct correlation is found between the ionic association strength of the anions and the total number of coordinated anions. The Li⁺ cations in the electrolytes with the more associated salts are coordinated to the fewest number of different anions. The exception to this trend is the LiPF₆ electrolyte (Fig. 8)—the probable explanation for the lower numbers of anions for the LiPF₆ mixture, relative to the LiClO₄ and LiBF₄ mixtures, is that the PF₆⁻ anion is very weakly coordinating so less coordination occurs overall. Thus, the total number of anions coordinated to a given Li⁺ cation is a function of both the length of time in which the anions remain coordinated and the tendency of the anions to form coordinate bonds to the Li⁺ cations.

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One additional important aspect of this study pertains to electrolyte-electrode interactions. Generally, when a Li⁺ cation intercalates into or is plated onto an electrode or solid-electrolyte interphase,⁴⁰ desolvation occurs. Based upon the information noted above, however, the shedding of the coordinated species is expected to be much slower if anions are part of the cation's coordination shell, although the polarized electrode surface may influence these dynamics. Thus, the ionic association state of the electrolyte (solution structure) likely impacts battery performance as a key determinant of both the ionic conductivity^3,4 (and diffusion) and the electrode intercalation/plating kinetics (with the associated cell impedance).

The degree of ion uncorrelated motion (α_d), sometimes called ionicity, determined from the simulations is shown in Fig. 9. In accord with the Li⁺ cation solvation numbers, α_d is the largest for the (AN)_n-LiBF₄ electrolyte, followed by the (AN)_n-LiCF₃SO₃ and -LiCF₃CO₂ electrolytes. It is instructive, however, to compare the fraction of fully solvated Li⁺ cations (i.e., labeled SSIP) shown in Fig. 9 with the behavior of α_d. While the fraction of fully solvated Li⁺ cations for the simulations with LiBF₄ and LiCF₃SO₃ drops monotonically, changes in α_d with concentration are less pronounced. Large error bars (∼0.1) are expected, however, for α_d for the n = 5 and 2 mixtures due to the slow ion dynamics in this range for the simulations with LiCF₃SO₃ and LiCF₃CO₂. Thus, the significant variance of α_d for these salt concentrations is likely to be exaggerated. Interestingly, α_d for the simulation with LiCF₃CO₂ shows an initial drop from 0.23 to 0.10 and then stays constant afterwards, while the fraction of fully solvated Li⁺ cations (SSIP) shows a similarly weak concentration dependence indicating that the LiCF₃CO₂ electrolyte is heavily aggregated over the wide concentration range studied.

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The viscosity values (Tables III–V) were extracted from MD simulations using the Einstein relation, as described in the Supporting Information. The calculated viscosity of the electrolytes with LiCF₃CO₂ is lower than the viscosity of those with LiCF₃SO₃ due to the significantly higher fraction of uncoordinated AN solvent molecules in the former, while the smaller size of the BF₄⁻ anions, relative to the CF₃SO₃⁻ anions, may perhaps explain the comparable or lower viscosity values for electrolytes with LiBF₄ as compared to those with LiCF₃SO₃.

To further examine the relationship between the structural and transport properties, solvent and ion self-diffusion coefficient (D) and ionic conductivity (κ) values were also extracted from the MD simulations using the Einstein relations. For the AN solvent molecules, the highest diffusion coefficients (Fig. 9 and Table S1) are for the dilute electrolytes with LiCF₃CO₂. This likely reflects the greater fraction of uncoordinated solvent molecules in these electrolytes relative to those with LiCF₃SO₃ and LiBF₄. The solvent diffusion coefficients decrease with increasing salt concentration as a greater fraction of the solvent becomes coordinated to the Li⁺ cations. For the calculated ion diffusion coefficients, the BF₄⁻ anions have higher values than the Li⁺ cations for the dilute electrolytes (<1 M or n = 30 and 20) (Fig. 9), but the diffusion coefficients become closely correlated for the more concentrated LiBF₄ electrolytes perhaps due to increased aggregation of the ions. This is supported by the similar anion and Li⁺ cation diffusion coefficients for the LiCF₃SO₃ and LiCF₃CO₂ simulations (Fig. 9).

The experimental analysis of the AN solvent Raman vibrational bands indicated that the (AN)_n-LiCF₃CO₂ mixtures have average solvation numbers of close to 1 over a wide composition range, even for the very dilute solutions.¹ An examination of the MD simulation snapshot results for the (AN)_n-LiCF₃CO₂ (n = 10) mixture shown in Fig. 4 finds that 91 AN molecules are coordinated to the 64 Li⁺ cations giving an average solvation number of about 1.42. Over the course of the entire equilibrium run, however, the solvation number is 1.35 (Table V). The solvation numbers from the MD simulations for the LiCF₃CO₂ mixtures over the entire concentration range studied only vary from 1.42–1.12 (Table V). These results are in excellent agreement with the experimental data.¹ The corresponding solvation numbers from the MD simulations for the (AN)_n-LiBF₄ and -LiCF₃SO₃ (n = 10) mixtures shown in Figs. 2 and 3 are 2.80 and 2.42 (2.59 and 2.34, respectively, for the entire simulations—Tables III and IV). The calculated values for the (revised) LiBF₄ mixtures are also in excellent agreement with the experimental data, while no experimental data is available for (AN)_n-LiCF₃SO₃ mixtures.¹ The phase diagram for the (AN)_n-LiCF₃CO₂ mixtures indicates that bulk (uncoordinated) AN can be crystallized from the dilute mixtures, but a small amount can even be crystallized for the n = 2 composition (with no crystalline solvates forming).¹ This is readily understandable from the low extent of solvation and extensive CF₃CO₂⁻...Li⁺ cation coordination found in these mixtures (Fig. 4).

Experimental values for the viscosity and ionic conductivity of the (AN)_n-LiX mixtures with LiPF₆, LiClO₄, LiBF₄ and LiCF₃CO₂ were previously reported.³ The lower viscosity values for the mixtures with LiCF₃CO₂ (relative to the other electrolytes)³ are explained by the solvate structure distribution (shown in Figs. 4 and S14–S17) and anion residence time (Fig. 6) information since this demonstrates that much of the solvent in the mixtures remains uncoordinated. Similarly, the low values for the ionic conductivity³ for the electrolytes with LiCF₃CO₂ are explained by the presence of large, long-lived aggregate solvates (Fig. 6) with only a few fully solvated Li⁺ cations and no uncoordinated anions present (Fig. 4).