Statistical Physics of the Two-Dimensional Coulomb Liquid with Ionic Hard-Core Size

TL;DR

This paper develops a self-consistent theoretical model for two-dimensional Coulomb liquids with finite ion size, accurately capturing thermodynamics and screening effects compared to simulations, especially at moderate densities.

Contribution

It introduces an improved self-consistent theory that accounts for non-uniform screening and ion size effects, enhancing predictions over continuum models.

Findings

Accurately describes thermodynamics of 2D electrolytes at moderate densities.

Improves upon continuum approaches by including ion size and non-uniform screening.

Underestimates ionic clustering at very low densities, near phase transition.

Abstract

A self-consistent theory of bulk electrolytes incorporating electrostatic and hard-core interactions on an equal level is applied to the two-dimensional Coulomb liquid with finite ion size. The ionic pair distributions, the structure factors, and the thermodynamic functions of the formalism are compared with extensive Monte-Carlo simulation results from the literature. At moderate salt densities, our computational approach can accurately describe the thermodynamics of two-dimensional solutions from weak to intermediate coupling strengths. The improved accuracy of the present theory with respect to continuum approaches stems mainly from its ability to account for the non-uniform screening of electrostatic interactions associated with the impenetrability of the charged hard disks by their ionic atmosphere. At low salt densities, the validity domain of our self-consistent framework underestimating the extent of ionic cluster formation drops below the critical coupling domain where the conductor-insulator transition of two-dimensional charged hard disks occurs. This indicates that approaching the low-temperature dielectric phase via the present formalism will require the extension of the underlying self-consistent approximation at least up to the next cumulant order.