Field-driven Ion Pairing Dynamics in Concentrated Electrolytes

TL;DR

The paper addresses nonlinear transport in concentrated electrolytes driven far from equilibrium, where traditional continuum theories fail. It uses nonequilibrium molecular dynamics for 0.5 M LiPF6 in acetonitrile and water, together with a transition-path-theory–based rate framework and a dynamical free-ion population proxy derived from the mean backward committor, to extract field-dependent association and dissociation rates. Key findings show stronger field-induced dissociation and conductivity enhancement in acetonitrile than in water, and that Onsager's theory overestimates the nonlinear response due to solvent-mediated pathways and dielectric decrement; explicit solvent dynamics are essential to correctly describe the kinetics. The work provides a molecular interpretation of nonlinear electrolyte transport, demonstrates a general framework for extracting nonequilibrium reaction kinetics from trajectory ensembles, and offers guidance for extending such analyses to other condensed-phase processes.

Abstract

We investigate ion pairing dynamics in electrolytes driven far from equilibrium using molecular simulations and nonequilibrium rate theory. Focusing on 0.5 M $\mathrm{LiPF_6}$ in water and acetonitrile under uniform electric fields, we compute transition path theory observables including reactive fluxes and mean first-passage times of ion pairing. Moreover, we introduce a dynamical proxy of free-ion population, where its field-induced change is strongly correlated with the nonlinear enhancement of conductivity, yielding an increase of $40 \ \%$ at 50 mV/Å in acetonitrile, compared to less than $10 \ \%$ in aqueous electrolytes. Further kinetic analysis elucidates that Onsager's classical theory substantially overestimates field-induced enhancement of ion pair dissociation in molecular electrolytes. This discrepancy arises from solvent-mediated dynamical pathways and field-induced dielectric decrement that suppress ion pair dissociation within explicit solvents, highlighting that a faithful description of molecular details is essential. Our results provide a molecular interpretation of nonlinear electrolyte transport beyond continuum theories and establish a general framework for quantifying nonequilibrium reaction kinetics in condensed phase systems.

Figures (4)

• Figure 1: Molecular dynamics simulation snapshots of $\mathrm{0.5 \ M}$$\mathrm{LiPF_6}$ in (a) acetonitrile and (b) water. Black and yellow spheres represent $\mathrm{Li^+}$ and $\mathrm{PF_6^-}$, respectively. (c) Probability distribution function of the cluster-based nearest-counterion distance. Colors progress from light to dark with increasing field strength from $0$ to $50$$\mathrm{mV / \AA}$. Dashed lines indicate locations of domain boundaries. (d) $\mathrm{Li^+}$-solvent radial distribution functions with the same color gradient scale in c.
• Figure 2: (a) Relative percent change of the molar conductivity of electrolytes with applied field (filled symbols) and free-ion population (empty symbols). The values at zero field are $\lambda(0) = 66.5 \pm \ 1.9 \ \mathrm{S \ cm^2 \ mol^{-1}}$, $\lambda(0)= 78.4 \pm \ 2.6 \ \mathrm{S \ cm^2 \ mol^{-1}}$, $\langle q_- \rangle_0 = 0.401 \pm \ 0.002$ and $\langle q_- \rangle_0 = 0.585 \pm \ 0.004$ for acetonitrile (orange color) and water (blue color), respectively. (b) Relative dielectric constant in parallel direction to the electric field. Dashed lines indicate the zero field limits.
• Figure 3: (a) Field-induced dissociation and (b) association rate enhancements of the $\mathrm{LiPF_6}$ in acetonitrile (square) and water (circle) in log-scale. The rate constants at zero field for acetonitrile are $k_{\mathrm{d}}(0) = 12.7 \ \pm \ 0.1 \ \mathrm{ns}^{-1}$ and $k_{\mathrm{a}}(0) = 18.9 \ \pm \ 0.1 \ \mathrm{ns}^{-1}$, and those for water are $k_{\mathrm{d}}(0) = 36.2 \ \pm \ 0.4 \ \mathrm{ns}^{-1}$ and $k_{\mathrm{a}}(0) = 25.6 \ \pm \ 0.3 \ \mathrm{ns}^{-1}$. Colored dashed lines show a linear fit and black dashed line indicates zero field value.
• Figure 4: The hitting probability distribution at boundaries (inner boundary for black and outer boundary for red) for the dissociation events for (a) explicit acetonitrile system and (b) implicit solvent system. The field strength is $50 \ \mathrm{mV / \AA}$ for both systems, pointing the right direction. Insets show representative reactive trajectories.