Frequency-Dependent Conductivity of Concentrated Electrolytes: A Stochastic Density Functional Theory

TL;DR

This paper develops a stochastic density functional theory to analyze the frequency-dependent conductivity of concentrated electrolytes, extending classical results to account for ion interactions at higher concentrations.

Contribution

It introduces a modified Coulomb potential into the DFT framework to accurately model concentrated electrolytes' conductivity behavior.

Findings

Recovers classical Debye-Falkenhagen result at low concentrations.

Extends the DF model to high concentrations with ion hard-core repulsion.

Discusses experimental challenges in observing the DF effect.

Abstract

The response of ionic solutions to time-varying electric fields, quantified by a frequency-dependent conductivity, is essential in many electrochemical applications. Yet, it constitutes a challenging problem due to the combined effect of Coulombic interactions, hydrodynamics, and thermal fluctuations. Here, we study the frequency-dependent conductivity of ionic solutions using a stochastic density functional theory. In the limit of small concentrations, we recover the classical Debye and Falkenhagen (DF) result, predicting an increase in conductivity with field frequency. At higher concentrations, we use a modified Coulomb interaction potential that accounts for the hard-core repulsion between the ions, which was recently employed in the zero-frequency case. Consequently, we extend the DF result to concentrated electrolytes. We discuss experimental and numerical studies and the complexity of observing the DF effect in such setups.