Field-dependent ionic conductivities from generalized fluctuation-dissipation relations

TL;DR

This paper develops a theoretical framework linking ionic conductivity to microscopic fluctuations, validated by simulations showing nonlinear conductivity behavior in different electrolytes under varying electric fields.

Contribution

It introduces a generalized fluctuation-dissipation relation for field-dependent ionic conductivities and a novel reweighting scheme for continuous field variation analysis.

Findings

Conductivity remains constant in strong electrolytes due to Gaussian current fluctuations.

In dilute electrolytes and molten salts, conductivity increases with applied field due to non-Gaussian fluctuations.

The nonlinear increase in conductivity is caused by suppression of ionic correlations at high fields.

Abstract

We derive a relationship for the electric field dependent ionic conductivity in terms of fluctuations of time integrated microscopic variables. We demonstrate this formalism with molecular dynamics simulations of solutions of differing ionic strength with implicit solvent conditions and molten salts. These calculations are aided by a novel nonequilibrium statistical reweighting scheme that allows for the conductivity to be computed as a continuous function of the applied field. In strong electrolytes, we find the fluctuations of the ionic current are Gaussian and subsequently the conductivity is constant with applied field. In weaker electrolytes and molten salts, we find the fluctuations of the ionic current are strongly non-Gaussian and the conductivity increases with applied field. This nonlinear behavior, known phenomenologically for dilute electrolytes as the Onsager-Wien effect, is general and results from the suppression of ionic correlations at large applied fields, as we elucidate through both dynamic and static correlations within nonequilibrium steady-states.