Wigner-Crystal Formulation of Strong-Coupling Theory for Counter-ions Near Planar Charged Interfaces

TL;DR

This paper introduces a Wigner-crystal-based analytical approach for strong electrostatic coupling near charged interfaces, providing accurate predictions that align well with simulations and explaining phenomena like like-charge attraction.

Contribution

It develops a novel Wigner-crystal-based strong-coupling theory that improves upon previous virial approaches and clarifies counter-ion mediated interactions.

Findings

Excellent agreement with Monte-Carlo data.

Improved accuracy over virial strong-coupling estimates.

Clarifies mechanisms behind like-charge attraction.

Abstract

We present a new analytical approach to the strong electrostatic coupling regime (SC), that can be achieved equivalently at low temperatures, high charges, low dielectric permittivity etc. Two geometries are analyzed in detail: one charged wall first, and then, two parallel walls at small distances, that can be likely or oppositely charged. In all cases, one type of mobile counter-ions only is present, and ensures electroneutrality (salt free case). The method is based on a systematic expansion around the ground state formed by the two-dimensional Wigner crystal(s) of counter-ions at the plate(s). The leading SC order stems from a single-particle theory, and coincides with the virial SC approach that has been much studied in the last 10 years. The first correction has the functional form of the virial SC prediction, but the prefactor is different. The present theory is free of divergences and the obtained results, both for symmetrically and asymmetrically charged plates, are in excellent agreement with available data of Monte-Carlo simulations under strong and intermediate Coulombic couplings. All results obtained represent relevant improvements over the virial SC estimates. The present SC theory starting from the Wigner crystal and therefore coined Wigner SC, sheds light on anomalous phenomena like the counter-ion mediated like-charge attraction, and the opposite-charge repulsion.