A van der Waals free energy in electrolytes revisited

TL;DR

This paper rederives the van der Waals free energy for a three-electrolyte system between parallel planes using linear response theory and Maxwell stress tensor, providing an alternative approach to previous methods.

Contribution

It introduces a new derivation method for van der Waals free energy in electrolytes, differing from the traditional approach in Dispersion Forces by Mahanty and Ninham.

Findings

Revised free energy expression for electrolytes system

Application of linear response theory to dispersion forces

Use of electrostatic Maxwell stress tensor in derivation

Abstract

A system of three electrolytes separated by two parallel planes is considered. Each region is described by a dielectric constant and a Coulomb fluid in the Debye-H\"uckel regime. In their book Dispersion Forces, Mahanty and Ninham have given the van der Waals free energy of this system. We rederive this free energy by a different method, using linear response theory and the electrostatic Maxwell stress tensor for obtaining the dispersion force.