Anomalous Effects of "Guest" Charges Immersed in Electrolyte: Exact 2D Results

TL;DR

This paper derives exact formulas for guest charge interactions in a 2D electrolyte, revealing anomalous effects like charge inversion and effective attraction between like charges, based on integrable sine-Gordon theory.

Contribution

It provides the first exact analytical results for guest charge effects in a 2D Coulomb gas using sine-Gordon integrability, revealing novel anomalous electrostatic phenomena.

Findings

Demonstrates charge inversion near highly-charged particles.

Shows effective attraction between like-charged guest particles.

Confirms the validity of the renormalized charge concept across stability conditions.

Abstract

We study physical situations when one or two "guest" arbitrarily-charged particles are immersed in the bulk of a classical electrolyte modelled by a Coulomb gas of positive/negative unit point-like charges, the whole system being in thermal equilibrium. The models are treated as two-dimensional with logarithmic pairwise interactions among charged constituents; the (dimensionless) inverse temperature $\beta$ is considered to be smaller than 2 in order to ensure the stability of the electrolyte against the collapse of positive-negative pairs of charges. Based on recent progress in the integrable (1+1)-dimensional sine-Gordon theory, exact formulas are derived for the chemical potential of one guest charge and for the asymptotic large-distance behavior of the effective interaction between two guest charges. The exact results imply, under certain circumstances, anomalous effects such as an effective attraction (repulsion) between like-charged (oppositely-charged) guest particles and the charge inversion in the electrolyte vicinity of a highly-charged guest particle. The adequacy of the concept of renormalized charge is confirmed in the whole stability region of inverse temperatures and the related saturation phenomenon is revised.