Temporal response of the conductivity of electrolytes

TL;DR

This paper investigates how electrolyte conductivity responds over time to sudden changes in an external electric field, revealing different relaxation behaviors when the field is turned on versus off, influenced by non-linear effects.

Contribution

The study introduces a stochastic density functional theory approach to analyze transient ionic correlations and current responses under arbitrary electric field changes.

Findings

Current decays exponentially when the field is switched off.

Current relaxes algebraically when the field is switched on.

Non-linear effects cause different transient behaviors in the two cases.

Abstract

We study the temporal response of the electric current in an electrolyte under a sudden switch on or switch off of an external electric field of arbitrary magnitude. We use Stochastic Density Functional Theory including hydrodynamic interactions to express the current as a function of the ionic correlations. Assuming small density fluctuations, we linearize the field theory to compute the correlations in the transient regime. We first show that the correlations do not follow the same trajectory when the field is switched on or switched off. Accordingly, the behavior of the current differs in the two cases: it decays exponentially when the field is switched off, but it relaxes algebraically to its stationnary value when the field is switched on. This difference is a non-linear effect since an exponential relaxation is recovered in both cases in the weak field limit.