Computing Counterion Densities at Intermediate Coupling

TL;DR

This paper develops a unified approach to compute counterion densities near charged surfaces across all coupling regimes by combining mean-field theory with a modified strong-coupling expansion, revealing nonperturbative effects.

Contribution

It introduces a novel decomposition of Coulomb interactions and a finite strong-coupling expansion to accurately model counterion densities at intermediate coupling.

Findings

Counterion density profiles are accurately computed across all coupling strengths.

Nonperturbative lateral correlation effects significantly modify the density at intermediate coupling.

The method bridges the gap between weak and strong coupling theories.

Abstract

By decomposing the Coulomb interaction into a long distance component appropriate for mean-field theory, and a nonmean-field short distance component, we compute the counterion density near a charged surface for all values of the counterion coupling parameter. A modified strong-coupling expansion that is manifestly finite at all coupling strengths is used to treat the short distance component. We find a nonperturbative correction related to the lateral counterion correlations that modifies the density at intermediate coupling.