Mesoscopic theory for a double layer capacitance in concentrated ionic systems

TL;DR

This paper develops a mesoscopic theory to analyze how oscillatory charge density decay affects double-layer capacitance in concentrated ionic solutions and ionic liquids, emphasizing Coulomb and steric forces.

Contribution

It introduces a simple formula linking charge oscillations to capacitance, providing a reference for understanding ionic system behaviors.

Findings

Charge oscillations influence the effective electrode-ions distance.

A rescaling factor depends on the oscillation period.

The formula applies to high-density ions and low voltages.

Abstract

Effect of an oscillatory decay of the charge density in concentrated ionic solutions and ionic liquids on the double-layer capacitance is studied in a framework of a mesoscopic theory. Only Coulomb and steric forces between the ions that are present in all ionic systems are taken into account. We show that the charge oscillations lead to a rescaled distance between the electrode and the virtual monolayer of counterions in the Helmholtz capacitance, and the scaling factor depends on the period of the charge oscillations. Our very simple formula for large density of ions and small voltage can serve as a reference point for the double layer capacitance in concentrated ionic solutions and ionic liquids, and can help to disentangle the universal and specific contributions to the capacitance in particular systems.