The Electric Double Layer Structure Around Charged Spherical Interfaces

TL;DR

This paper presents an approximate analytical solution to the Poisson-Boltzmann equation for charged spherical interfaces, improving upon linearized solutions and defining its applicability based on system parameters.

Contribution

It introduces a simple approximate analytical method for the Poisson-Boltzmann equation specific to spherical geometries, with a clear regime of applicability.

Findings

The solution outperforms linearized solutions in accuracy.

Applicability depends on spherical radius and surface potential.

The method is formally simple and analytically derived.

Abstract

We derive a formally simple approximate analytical solution to the Poisson-Boltzmann equation for the spherical system via a geometric mapping. Its regime of applicability in the parameter space of the spherical radius and the surface potential is determined, and its superiority over the linearized solution is demonstrated.