Counterion Condensation and Fluctuation-Induced Attraction

TL;DR

This paper investigates electrostatic interactions between charged plates with counterions beyond mean-field theory, revealing fluctuation-driven attraction, possible first-order binding transitions, and the significance of counterion condensation.

Contribution

It introduces a fluctuation-based counterion condensation model to analyze interactions beyond Poisson-Boltzmann theory, highlighting new attraction mechanisms and phase transitions.

Findings

Fluctuation-induced attraction can dominate at large distances for high surface charges.

A first-order binding transition can occur at short distances depending on ion valency.

The model predicts significant effects of counterion condensation on electrostatic interactions.

Abstract

We consider an overall neutral system consisting of two similarly charged plates and their oppositely charged counterions and analyze the electrostatic interaction between the two surfaces beyond the mean-field Poisson-Boltzmann approximation. Our physical picture is based on the fluctuation-driven counterion condensation model, in which a fraction of the counterions is allowed to ``condense'' onto the charged plates. In addition, an expression for the pressure is derived, which includes fluctuation contributions of the whole system. We find that for sufficiently high surface charges, the distance at which the attraction, arising from charge fluctuations, starts to dominate can be large compared to the Gouy-Chapmann length. We also demonstrate that depending on the valency, the system may exhibit a novel first-order binding transition at short distances.