Structural and Dynamical Crossovers in Dense Electrolytes

TL;DR

This study uses molecular dynamics to dissect how dense electrolytes reorganize structurally and transportively as salt concentration grows, comparing explicit-space-filling solvents with implicit-solvent models. It identifies a screening crossover that is highly sensitive to ion–solvent coupling: explicit solvents shift from a charge-dominated dilute regime to a density-dominated concentrated regime, while implicit solvents show a transition between two charge-dominated regimes. Dynamical crossovers in ion self-diffusion and ion-pair lifetimes accompany the structural changes and are tied to short-range ion–counterion free-energy landscapes, manifesting as sharp, discontinuous changes rather than smooth transitions; percolation of ionic clusters does not tightly couple to these crossovers. A diffusion-corrected ion-pair lifetime, $\tau_{\text{pair}}/\tau_{\text{diff}}$, emerges as a unifying descriptor linking structure and dynamics across solvent models, providing a practical framework for comparing dense electrolytes and guiding future, more chemically detailed investigations.

Abstract

Electrostatic interactions fundamentally govern the structure and transport of electrolytes. In concentrated electrolytes, however, electrostatic and steric correlations, together with ion-solvent coupling, give rise to complex behavior, such as underscreening, that remains challenging to explain despite extensive theoretical effort. Using molecular dynamics simulations of primitive electrolytes with and without space-filling solvent particles, we elucidate the structural and dynamical crossovers and their connection that emerge with increasing salt concentration. Explicit-solvent electrolytes exhibit a screening transition from a charge-dominated dilute regime to a density-dominated concentrated regime, accompanied by dynamical crossovers in ion self-diffusion and ion-pair lifetimes. These dynamical crossovers display a marked discontinuity, unlike the smoother variation of the screening crossover, which originates from short-range ion-counterion structures. Despite the pronounced growth of ionic clusters, their percolation transition does not appear to be directly coupled to the onset of these crossovers. Both structural and dynamical behaviors are found to depend sensitively on ion-solvent coupling: implicit-solvent electrolytes exhibit a screening transition between two charge-dominated regimes, accompanied by qualitatively distinct dynamical behavior. Finally, we demonstrate that the diffusion-corrected ion-pair lifetime provides a consistent descriptor linking ionic structure and dynamics across electrolyte systems.

Figures (6)

• Figure 1: Space-filling solvent effects. (A) Dependence of solvent concentration ($c_{\mathrm{solv}}$) and salt concentration ($c_{\mathrm{salt}}$) on the number of salt pairs $N_{\mathrm{salt}}$, with the number of solvent particles fixed at $N_{\mathrm{solv}} = 5000$. (B) Solvent–solvent radial distribution function $g_{SS}(r)$ for LJ electrolytes and (C) for WCA electrolytes. In both cases, the results collapse onto a single curve across all $c_{\mathrm{salt}}$. Insets show the distinct decay behavior of $g_{SS}(r)$, with black solid lines indicating decay lengths $\lambda_s=1~\sigma$ and $\sigma/2$, respectively. In this work, “LJ” and “WCA” refer to electrolytes with and without Lennard–Jones attractive interactions (Eq. \ref{['eq:lj']}), corresponding to cutoff distances of $r_c = 2.5~\sigma$ and $1.122~\sigma$, respectively.
• Figure 2: Crossover in structural correlations of explicit-solvent electrolytes. (A) Charge–charge correlation functions, $\ln(|r \cdot h_{ZZ}(r)|)$, for LJ electrolytes with $\varepsilon_s = 0.2$, and (B) the corresponding results for WCA electrolytes. (C) Decay length $\lambda_Z$ of $h_{ZZ}(r)$ as a function of $a/\lambda_D$, where $a$ is the ion size and $\lambda_D$ is the Debye screening length (Eq. \ref{['eq:debye']}). Black dash–dot ($\alpha = 2$) and dashed ($\alpha = 1.5$) lines serve as visual guides to the scaling behavior described in Eq. \ref{['eq:scaling']}. (D) Density–density correlation functions, $\ln(|r \cdot h_{NN}(r)|)$, for LJ electrolytes with $\varepsilon_s = 0.2$, and (E) the corresponding results for WCA electrolytes. (F) Ratio of decay lengths, $\lambda_Z/\lambda_N$, as a function of $a/\lambda_D$. The black dashed horizontal line indicates $\lambda_Z/\lambda_N = 1$. The inset shows a magnified view of the transition region. In panels (A–B, D–E), $c_{\mathrm{salt}}$ increases with the color changing from purple to green to red. Panels (C) and (F) present results across all explicit-solvent systems examined in this study, with the colors and markers consistent with those in Fig. \ref{['fig:solvent']}. Structural correlation functions and their corresponding fitting results for the other systems are provided in the SM SI.
• Figure 3: Percolation transition of ionic clusters in explicit-solvent electrolytes. (A) Evolution of ionic clusters with salt concentration $c_{\mathrm{salt}}$. The composition of each cluster is defined by the number pair ($n_+$, $n_-$). (B) Size distribution $P(s)$ (Eq. \ref{['eq:cluster']}) of ionic clusters with $s = n_+ + n_-$. $c_{\mathrm{salt}}$ increases with the color changing from purple to green to red. The black dotted line indicates the power-law decay at the percolation threshold, $c_{\mathrm{gel}}\approx0.063~\sigma^{-3}$, $P(s)\sim s^{-1.85}$. Panels (A) and (B) show results for explicit-solvent LJ electrolytes with $\varepsilon_s = 0.2$. (C) Dependence of the exponential decay length $\xi_s$, extracted from $P(s)$, on salt concentration $c_{\mathrm{salt}}$ across all explicit-solvent electrolytes. In panel (C), the colors and markers are consistent with those in Fig. \ref{['fig:solvent']}.
• Figure 4: Crossovers in ion dynamics and their structural origins as a function of the ratio $a/\lambda_D$ across all electrolytes examined. (A, D) Diffusion relaxation time, $\tau_{\mathrm{Diff}}$. (B, E) Mean ion-pair lifetime, $\tau_{\mathrm{pair}}$. (C, F) Free-energy barrier for ion-counterion dissociation, $\beta\Delta F$. Panels (A–C) on the top row correspond to explicit-solvent models, while panels (D–F) on the bottom row correspond to implicit-solvent models. In panels (A-B) and (D-E), the left and right axes represent results for LJ (filled markers) and WCA (open markers), respectively. For the LJ electrolytes, the colors and markers are consistent with those in Fig. \ref{['fig:solvent']}, and the black counterparts correspond to the WCA electrolytes.
• Figure 5: Crossover in structural correlations of implicit-solvent electrolytes. (A) Decay length $\lambda_Z$ of $h_{ZZ}(r)$ as a function of $a/\lambda_D$, where $a$ is the ion size and $\lambda_D$ is the Debye screening length (Eq. \ref{['eq:debye']}). Black dash–dot ($\alpha=2$) and dashed ($\alpha=1.5$) lines serve as visual guides for the scaling behavior described in Eq. \ref{['eq:scaling']}. (B) Ratio of decay lengths $\lambda_Z/\lambda_N$ as a function of $a/\lambda_D$. Black dashed horizontal line indicates $\lambda_Z/\lambda_N=1$. The inset shows a magnified view of the transition region. (C) The growth and percolation of ionic clusters with salt concentration $c_{\mathrm{salt}}$, characterized by the exponential decay length $\xi_s$ extracted from $P(s)$ (Eq. \ref{['eq:cluster']}). The colors and markers are consistent with those in Fig. \ref{['fig:msd']}(D-F). Structural correlation functions and their corresponding fitting results for the implicit-solvent systems are provided in the SM SI.