Strong-coupling theory of counterions between symmetrically charged walls: from crystal to fluid phases

TL;DR

This paper develops a strong-coupling theoretical framework for counterions between charged walls, accurately describing both crystal and fluid phases and extending analytical equations of state for such systems.

Contribution

It introduces a harmonic expansion around bilayer positions and a correlation hole concept to model counterion behavior across coupling regimes.

Findings

Analytical density profiles match Monte Carlo simulations.

Pressure calculations agree with numerical data for various distances.

The theory extends the validity of analytical models for charged interfaces.

Abstract

We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance $d$. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner Strong-Coupling expansion. Analytical results for the particle density profile and the pressure are in good agreement with numerical Monte Carlo data, for small as well as intermediate values of $d$ comparable with the Wigner lattice spacing. While the strong-coupling theory is extended to the fluid regime by using the concept of a correlation hole, the Wigner calculations appear trustworthy for all electrostatic couplings investigated. Our results significantly extend the range of accuracy of analytical equations of state for strongly interacting charged planar interfaces.