Strong-Coupling Theory of Counter-ions at Charged Plates

TL;DR

This paper develops an analytical strong coupling theory for counter-ions near charged plates, providing a divergence-free expansion that aligns well with simulations and enhances understanding of like-charge attraction.

Contribution

It introduces a novel, divergence-free analytical expansion around the ground state for strongly coupled counter-ion systems near charged plates.

Findings

Excellent agreement with Monte-Carlo simulations

Clarifies the mechanism behind like-charge attraction

Provides a transparent physical framework for strong coupling regimes

Abstract

We present an analytical approach to the strong coupling regime of similarly and highly charged plates in the presence of counter-ions. The procedure is physically transparent and based on an exact expansion around the ground state formed by the two-dimensional Wigner crystal of counter-ions. The one plate problem is worked out, together with the two plates situation. Unlike previous approaches, the expansion is free of divergences, and is shown to be in excellent agreement with available data of Monte-Carlo simulations under strong Coulombic couplings. The present results shed light on the like-charge attraction regime.