Electric-Field-Induced Spatially Dynamic Heterogeneity of Solvent Motion and Cation Transference in Electrolytes

While electric fields primarily result in migration of charged species in electrolytic solutions, the solutions are dynamically heterogeneous. Solvent molecules within the solvation shells of the cation will be dragged by the field while free solvent molecules will not. We combine electrophoretic NMR measurements of ion and solvent velocities under applied electric fields with molecular dynamics simulations to interrogate different solvation motifs in a model liquid electrolyte. Measured values of the cation transference number ($t_{+}^0$) agree quantitatively with simulation-based predictions over a range of electrolyte concentrations. Solvent-cation interactions strongly influence the concentration-dependent behavior of $t_{+}^0$. We identify a critical concentration at which most of the solvent molecules lie within solvation shells of the cations. The dynamic heterogeneity of solvent molecules is minimized at this concentration where $t_{+}^0$ is approximately equal to zero.

Figure 1

(a) Average species velocities in $\mathrm{LiTFSI}/\text{tetraglyme}$ electrolytes ($r=[{\mathrm{Li}}^{+}]/[\mathrm{O}]$) measured by ${}^7\mathrm{Li}$, ${}^1\mathrm{H}$, and ${}^{19}\mathrm{F}$ electrophoretic NMR (eNMR) at $30°\mathrm{C}$: cation (blue), solvent (black) and anion (red). To highlight the smaller values of $v_0$ and $v_{+}$, a separate vertical axis is plotted for these velocities compared to that for $v_{-}$. (See Fig. S4 [45] for data plotted on same axis.) Velocities are in the lab frame of reference. All velocities reflect an applied electric field of $1\mathrm{V}/\mathrm{mm}$; measurements were performed at a range of electric fields and velocities were scaled to $1\mathrm{V}/\mathrm{mm}$. (b) Representative ${\mathrm{MSD}}^{\prime }$ as defined in Eq. (6) calculated from MD simulations, for $r=0.048$ (upper traces) and $r=0.08$ (lower traces), corresponding to Onsager transport coefficients $L^{++}$ (top), $L^{--}$ (middle) and $L^{+-}$ (bottom), which are extracted from the diffusive regime, i.e., the indicated timescale over which the slope equals one in the log-log scale. (c) Ionic conductivity from independent electrochemical and eNMR experiments (filled diamonds and open circles, respectively, which are nearly coincident), and predicted from MD simulations (filled squares).

Figure 2

Transference numbers in the solvent reference frame ($t_{+}^0$) determined from eNMR (open symbols) and MD (filled symbols), using Eqs. (2) and (5), respectively. The critical salt concentration, $r_c=0.08$, is indicated with a dashed line.

Figure 3

(a) Average number of tetraglyme molecules (TEG, circles) and anions (${\mathrm{TFSI}}^{-}$, triangles) in the coordination shell of each ${\mathrm{Li}}^{+}$ cation, obtained from MD. A tetraglyme molecule or ${\mathrm{TFSI}}^{-}$ anion is determined to coordinate ${\mathrm{Li}}^{+}$ if one of its oxygen atoms lies within 0.3 nm of ${\mathrm{Li}}^{+}$. The insets, representative snapshots from simulations, depict the two-chain motif that dominates at low salt concentrations (left) and the one–chain motif that appears for $r>r_c$ (right); Li is shown in dark blue, C is shown in cyan and O in red; within ${\mathrm{TFSI}}^{-}$, all atoms are shown in yellow except O in red. (b) Fraction of tetraglyme within the two-chain (open circles) and one-chain (open triangles) motifs, determined from MD. Solvent velocity measured by eNMR (filled squares) is overlaid using the right vertical axis, highlighting similar trends.

Figure 4

Quantification of dynamic heterogeneity by estimating the drift velocity of only those solvent molecules that are in the solvation shell of the ${\mathrm{Li}}^{+}$ cation. (a) Depiction of solvation motifs and free chains. In our model, only solvent molecules in the two-chain motif are dragged with the migrating cation (rightward arrow). The depicted electrodes are schematic. (b) MD snapshot of representative tetraglyme molecules (colored chains) and cations (spheres) at $r_c=0.08$. The solvation motifs are highlighted using the same color scheme in (a). (c) Comparison of calculated shell velocity $v_{\text{shell}}$ using Eq. (7) with measured cation velocity $v_{+}$ from eNMR. Error bars for $v_{\text{shell}}$ reflect propagation of error in $v_0$ and $f_2$; both parameters approach zero as $r$ tends to zero, resulting in large error bars. Velocities assume an applied electric field of $1\mathrm{V}/\mathrm{mm}$.