Variational field theory of macroscopic forces in Coulomb fluids

TL;DR

This paper develops a variational field theory framework to account for electrostatic correlations in Coulomb fluids, deriving a stress tensor and disjoining pressure expressions for confined electrolytes, advancing beyond mean-field models.

Contribution

It introduces a covariant variational approach that incorporates ion correlations into the stress tensor and disjoining pressure calculations for Coulomb fluids in confined geometries.

Findings

Derived a total stress tensor including electrostatic correlations.

Established a general expression for disjoining pressure in slit-like pores.

Provided an asymptotic formula for disjoining pressure with conductive walls.

Abstract

Based on the variational field theory framework, we extend our previous mean-field formalism, taking into account the electrostatic correlations of the ions. We employ a general covariant approach and derive a total stress tensor that considers the electrostatic correlations of ions. This is accomplished through an additional term that depends on the autocorrelation function of local electric field fluctuations. Utilizing the derived total stress tensor and applying the mechanical equilibrium condition, we establish a general expression for the disjoining pressure of the Coulomb fluids, confined in a pore with a slit-like geometry. Using this equation, we derive an asymptotic expression for the disjoining pressure in a slit-like pore with non-electrified conductive walls. Present theory is the basis for future modeling of the mechanical stresses that occur in electrode pores with conductive charged walls, immersed in liquid phase electrolytes beyond the mean-field theory.