Anomalous Multipole Expansion: Charge Regulation of Patchy, Inhomogeneously Charged Spherical Particles

TL;DR

This paper investigates how charge regulation affects the multipole moments of patchy, inhomogeneously charged spherical particles, revealing a mixing mechanism that alters their electrostatic properties.

Contribution

It introduces a novel analysis of charge regulation in inhomogeneously charged spheres, showing how it causes multipole mixing via capacitance-dependent response functions.

Findings

Charge regulation induces multipole mixing in spherical particles.

Significant changes in multipole moments due to charge regulation.

Charge regulation introduces an anomalous feature in molecular electrostatics.

Abstract

Charge regulation is an important aspect of electrostatics in biological and colloidal systems, where the charges are generally not fixed, but depend on the environmental variables. Here, we analyze the charge regulation mechanism in patchy, inhomogeneously charged spherical particles, such as globular proteins, colloids, or viruses. Together with the multipole expansion of inhomogeneously charged spherical surfaces, the charge regulation mechanism on the level of linear approximation is shown to lead to a mixing between different multipole moments depending on their capacitance -- the response function of the charge distribution with respect to the electrostatic potential. This presents an additional anomalous feature of molecular electrostatics in the presence of ionic screening. We demonstrate the influence of charge regulation on several examples of inhomogeneously charged spherical particles, showing that it leads to significant changes in their multipole moments.