Charge regulation and ionic screening of patchy surfaces

TL;DR

This paper investigates how charge regulation and ionic screening affect patchy surfaces using non-linear Poisson-Boltzmann theory, revealing how patch size and separation influence surface charge densities.

Contribution

It introduces a mode expansion method for efficient non-linear Poisson-Boltzmann calculations and develops an analytical model for average surface charge density on patchy surfaces.

Findings

Smaller patches charge to higher densities when well separated.

The analytical model accurately predicts surface charge densities.

Patch size and separation significantly influence charge regulation behavior.

Abstract

The properties of surfaces with charge-regulated patches are studied using non-linear Poisson-Boltzmann theory. Using a mode expansion to solve the non-linear problem efficiently, we reveal the charging behaviour of Debye-length sized patches. We find that patches charge up to higher charge densities if their size is relatively small and if the patches are well separated. The numerical results are used to construct a basic analytical model which predicts the average surface charge density on surfaces with patchy chargeable groups.