Boundary Effects in the One Dimensional Coulomb Gas

TL;DR

This paper analyzes a one-dimensional Coulomb gas model with boundary effects, revealing how surface interactions influence finite size systems and disjoining pressure, with implications for colloids and soap films.

Contribution

It provides an exact solution to the 1D Coulomb gas with boundary interactions, comparing results with Poisson-Boltzmann theory and exploring finite size and charge regulation effects.

Findings

Surface presence affects physics in finite systems.

Disjoining pressure can be positive or negative depending on separation.

Exact results align with experimental and three-dimensional calculations.

Abstract

We use the functional integral technique of Edwards and Lenard to solve the statistical mechanics of a one dimensional Coulomb gas with boundary interactions leading to surface charging. The theory examined is a one dimensional model for a soap film. Finite size effects and the phenomenon of charge regulation are studied. We also discuss the pressure of disjunction for such a film. Even in the absence of boundary potentials we find that the presence of a surface affects the physics in finite systems. In general we find that in the presence of a boundary potential the long distance disjoining pressure is positive but may become negative at closer interplane separations. This is in accordance with the attractive forces seen at close separations in colloidal and soap film experiments and with three dimensional calculations beyond mean field. Finally our exact results are compared with the predictions of the corresponding Poisson-Boltzmann theory which is often used in the context of colloidal and thin liquid film systems.