Confined Coulomb systems with absorbing boundaries: the two-dimensional two-component plasma

TL;DR

This paper analyzes a two-dimensional Coulomb gas confined in a disk and annulus with absorbing boundaries, deriving explicit formulas for thermodynamic properties and revealing boundary-induced stability and charge screening effects.

Contribution

It provides exact analytic expressions for the grand potential, pressure, and density profiles of the confined Coulomb system with absorbing boundaries, highlighting stability mechanisms.

Findings

System is unstable without adsorbing boundaries.

Attractive boundaries stabilize the system via surface tension.

Density profiles show boundary screening layers.

Abstract

Using a solvable model, the two-dimensional two-component plasma, we study a Coulomb gas confined in a disk and in an annulus with boundaries that can adsorb some of the negative particles of the system. We obtain explicit analytic expressions for the grand potential, the pressure and the density profiles of the system. By studying the behavior of the disjoining pressure we find that without the adsorbing boundaries the system is naturally unstable, while with attractive boundaries the system is stable because of a positive contribution from the surface tension to the disjoining pressure. The results for the density profiles show the formation of a positive layer near the boundary that screens the adsorbed negative particles, a typical behavior in charged systems. We also compute the adsorbed charge on the boundary and show that it satisfies a certain number of relations, in particular an electro-neutrality sum rule.