Density-functional theory for attraction between like-charged plates

TL;DR

This paper develops a density-functional theory incorporating ion correlations to analyze the interaction between like-charged plates, revealing attraction at small separations and high surface charge densities.

Contribution

It introduces a novel density-functional approach that accounts for counterion correlations, extending beyond mean-field theories for charged surface interactions.

Findings

Attraction occurs at small plate separations.

Higher surface charge densities enhance attraction.

Results agree with simulations and integral equation theories.

Abstract

We study the interactions between two negatively charged macroscopic surfaces confining positive counterions. A density-functional approach is introduced which, besides the usual mean-field interactions, takes into account the correlations in the positions of counterions. The excess free energy is derived in the framework of the Debye-H{\"u}ckel theory of the one-component plasma, with the homogeneous density replaced by a weighted density. The minimization of the total free energy yields the density profile of the microions. The pressure is calculated and compared with the simulations and the results derived from integral equations theories. We find that the interaction between the two plates becomes attractive when their separation distance is sufficiently small and the surface charge density is larger than a threshold value.