Renormalized Surface Charge Density for a Strongly Charged Plate in Asymmetric Electrolytes: Asymptotic Exact Results in Poisson Boltzmann Theory

TL;DR

This paper derives asymptotic expressions for the renormalized surface charge density of a strongly charged plate in asymmetric electrolytes using Poisson-Boltzmann theory, providing systematic near and far field analysis.

Contribution

It introduces a method of asymptotic matching to analytically determine the renormalized surface charge density in asymmetric electrolytes within Poisson-Boltzmann theory.

Findings

Asymptotic series for renormalized surface charge density derived

Near and far field behaviors systematically analyzed

Provides explicit formulas for strongly charged plates in asymmetric electrolytes

Abstract

The Poisson-Boltzmann equation for a strongly charged plate inside a generic charge-asymmetric electrolyte is solved using the method of asymptotic matching. Both near field and far field asymptotic behaviors of the potential are systematically analyzed. Using these expansions, the renormalized surface charge density is obtained as an asymptotic series in terms of the bare surface charge density.