Quantifying selective solvent transport under an electric field in mixed-solvent electrolytes

Electrolytes in lithium-ion batteries comprise solvent mixtures, but analysis of ion transport is always based on treating the solvents as a single-entity. We combine electrophoretic NMR (eNMR) measurements and molecular dynamics (MD) simulations to quantify electric-field-induced transport in a concentrated solution containing LiPF6 salt dissolved in an ethylene carbonate/ethyl methyl carbonate (EC/EMC) mixture. The selective transport of EC relative to EMC is reflected in the difference between two transference numbers, defined as the fraction of current carried by cations relative to the velocity of each solvent species. This difference arises from the preferential solvation of cations by EC and its dynamic consequences. The simulations reveal the presence of a large variety of transient solvent-containing clusters which migrate at different velocities. Rigorous averaging over different solvation environments is essential for comparing simulated and measured transference numbers. Our study emphasizes the necessity of acknowledging the presence of four species in mixed-solvent electrolytes.

electrolyte could be resolved, allowing for the independent measurement of velocities of both species; the 7 Li and 19 F resonances unambiguously corresponded to Li + cations and TFSIanions, respectively. The eNMR instrumentation employed in this work is based upon the setup described previously, 1 and was supplied by P&L Scientific Instrument Service (www.plscientific.se; Lidingö, Sweden); details of our eNMR measurements have been previously reported in detail. 2 The electrolyte sample was loaded into the eNMR cell within an argon-filled glovebox. We used a convection-compensated double stimulated echo (DSTE) PFG-NMR sequence, 3 with electric field pulses of opposite polarity applied during the two halves of the sequence. [4][5][6] Typical applied voltages ranged from 5-15 V. Although a range of electric fields were applied, in this work all eNMR species velocities are reported relative to an applied electric field of 1 V/mm. For all experiments, the drift time Δ during which the electric field was applied was fixed at 100 ms. The recycle delay was set to 120 s, to allow for equilibration following the electric field pulses. The calibrated sample temperature was 30°C for all measurements. Calibration of the electric field was previously performed with a 10 mM solution of tetramethylammonium bromide (TMABr) in D2O (supplied by P&L Scientific) at 25°C. Analysis of eNMR phase shifts was performed as previously described 2 using an automated procedure comparing the "phase spectra" of the eNMR data.
Dependence of the extracted velocities on the applied magnetic field strength parameters was observed (Fig. S1), which likely reflects a distribution of velocities coupled with a distribution of self-diffusion coefficients; to obtain average species velocities that were not weighted by diffusivities, extrapolation of the velocity data to zero applied magnetic field was performed. Figure S1. Species velocities measured by electrophoretic NMR in the laboratory frame of reference, as a function of the magnitude of the product of the applied magnetic field gradient strength, |g|, and the applied magnetic field gradient length, δ. Velocities were measured at multiple electric field gradient strengths and scaled to 1 V/mm. Measurements reflect an average of positive and negative applied magnetic field gradient strengths. Linear extrapolation of the species velocities is depicted with dashed lines.
Conversion of the eNMR species velocities from the laboratory frame of reference to the moving electrode reference frame requires knowledge of the conductivity and partial molar volume of the electrolyte. 7 Experimental conductivity data on LiPF6:EC:EMC electrolytes were previously reported by Wang et al. 8 We interpolated this data, acquired at 30°C, to obtain the conductivity of the composition studied in this work (1 mol/L LiPF6; 1:1 volume ratio, EC:EMC), as shown in Fig. S2. Wang et al. 8 also reported concentration-dependent density data for LiPF6:EC:EMC electrolytes, which can be converted to partial molar volumes using where " ! is the partial molar volume of salt in the electrolyte, is the molar mass of the salt, is the density of the electrolyte, and is the molar concentration. We interpolated the previously reported density data acquired at 30°C to obtain the density as a function of concentration at the desired composition (1:1 volume ratio, EC:EMC), as shown in Fig. S3a. Using Eq. S1, " ! was calculated and found to be 0.0558 L/mol at a concentration of 1 mol/L LiPF6 (Fig. S3b).  Reference frame conversion was carried out by calculating the velocity of the electrodeelectrolyte interface, interface , in the laboratory frame of reference, using the equations previously derived in Halat et al. 7 , i.e., where ̅ -, ̅ 5 and ̅ . are the measured eNMR species velocities of the cation, anion, and solvent, -is the number of moles of cations into which a mole of salt dissociates (equal to 1 for a univalent salt), -is the cationic charge (equal to +1), is the conductivity, and ⁄ is the electric field, taken to be 1 V/mm as the reported species velocities have been normalized to this value. In using -S6-Eqs. S2 and S3, we assumed ̅ . to be the simple average of the measured velocities of the EC and EMC species. The experimental conductivity and partial molar volume were taken from Figs. S2 and S3; using the simulated partial molar volume (Fig. S4) had no effect on the calculated values within error. Table S1 shows the calculated values of interface , and the eNMR species velocities adjusted by this value, i.e., in the moving electrode reference frame. Within error, no difference was observed in the values calculated using Eq. S2 or Eq. S3.  Table S1. Calculated values of electrode-electrolyte interface, *+,-./01-, from equations Eq. S2 and Eq. S3, using the experimental conductivity and partial molar volume data depicted in Fig. S2 and S3, respectively. Species velocities converted to the moving electrode reference frame (i.e, adjusted by the calculated values of *+,-./01-) are also tabulated.

II. MD simulations
MD simulations were performed using the Gromacs package (version 5.1.4). 9 The bonds involving hydrogen atoms are constrained using the LINCS algorithm. 10 An NpT ensemble with velocity-rescale thermostat 11 and Berendsen barostat 12 was implemented at 303 K and 1 bar, respectively. A global cutoff of 1.2 nm is used for computing Lennard-Jones potential. The particle mesh Ewald (PME) method 13 was used to calculate the electrostatic interactions. Initially, the system was packed and energy minimized. Next, the system was cooled and heated by equilibrium simulations of 2 ns between (400 K, 1 bar) and (303 K, 1bar) for three cycles. This was followed by a short equilibrium simulation at 303 K and 1 bar for 10 ns. Finally, equilibrium system was performed for 800 ns.
LiPF6 salt and EC/ EMC solvent are modeled based on the OPLS-AA (optimized potentials for liquid simulations with all atom model) force field. 14,15 The Lennard-Jones potential and bonded interactions of all four species are obtained using LigParGen web server. 16 While the partial atomic charges for LiPF6 are directly available from OPLS-AA force field and widely used, the partial charges of EC and EMC are separately calculated using RESP method as mentioned in the main text. First, partial atomic charges of EC and EMC were first calculated via density functional theory (DFT) method with B3LYP/6-31G* basis sets using Gaussian package. 17 Then, the partial atomic charges were fitted using the RESP method via the Antechamber package. 18 The partial charges for all atomic species used in simulations are summarized in Fig. S5. Figure S5. Charges (in unit of e) for all atomic species LiPF6, EC, and EMC. Color codes for atoms: hydrogen in white, lithium in blue, carbon of EC in grey, carbon of EMC in green, oxygen in red, fluorine in yellow, and phosphorus in tan. -S8-

III. Obtaining transport coefficients
The transport coefficients are evaluated from the term equivalent to mean square displacement in Eqs. 3a and 3b in the main text. This term is defined as

IV. Determining the coordination number
The Li + coordination number is calculated based on radial distribution functions. Figure S7 shows the ( ) for carbonyl oxygen from EC, carbonyl oxygen from EMC, and phosphorus atom from PF6around Li + . The local of the valley outside of the primary peak is used as the cut-off distance to determine coordination number of EC, EMC, and PF6 -. To confirm the negligible anion solvation, we examine the radial distribution functions g( ) for both the cation and anion with the two solvents, as shown in Fig. S8. The cation-solvent interactions are represented by g( ) between Li + and carbonyl oxygens of EC and EMC; the anionsolvent interactions are represented by g( ) between F in PF6and hydrogen atoms in EC and EMC.
Note that only hydrogen atoms at the two ends of EMC are considered due to their positive atomic charges. It can be clearly seen that g( ) between the anion and the solvents is almost featureless, in stark contrast to the strong peaks in the case of the cation. This demonstrates a much weaker anion-solvent interaction than cation-solvent interaction, indicating that the anion solvation can be safely neglected in our analysis.

V. Cluster approximation
The velocity of cluster type carrying a net charge of : under an electric-field is : : / ; based on the Einstein relation, where : is the self-diffusion coefficient. Because the composition of a cluster type is not fixed, different : can exist for the same cluster type.
Considering this variability, the velocity of cluster type with composition is denoted as : < = : : . The velocity of species in cluster type is averaged through all possible compositions as 9,: = ∑ 9,: < : < < / ∑ 9,: < < , where 9,: < is the fraction of species in cluster type with composition . These velocities are normalized by the absolute velocity of anion under the same electric-field, which is equal to >?9 = @>7?> / ; . The normalized 9,: thus becomes < is the effective diameter of cluster type with composition . @>7?> / : < is then estimated by L @>7?> / : < M C/E , where is the molar mass. The contribution of velocities in each cluster type to species velocities ̅ 9 is given by 9,: 9,: , where 9,: is the fraction of species in cluster type as shown in Fig. S9.