Symmetry effects in electrostatic interactions between two arbitrarily charged spherical shells in the Debye-H\"uckel approximation

TL;DR

This paper derives a general electrostatic interaction energy formula for two charged spherical shells with symmetric patchy charge distributions in the Debye-Hückel approximation, revealing how symmetry and patch size influence attraction and repulsion.

Contribution

It introduces a comprehensive model for electrostatic interactions considering arbitrary charge distributions with specific symmetries, extending previous simpler models.

Findings

Charge inhomogeneities reduce repulsion between particles.

Sufficient orientational variation can induce attraction.

Larger patches and lower symmetry increase attractive interactions.

Abstract

Inhomogeneous charge distributions have important repercussions on electrostatic interactions in systems of charged particles but are often difficult to examine theoretically. We investigate how electrostatic interactions are influenced by patchy charge distributions exhibiting certain point group symmetries. We derive a general form of the electrostatic interaction energy of two permeable, arbitrarily charged spherical shells in the Debye-H\"uckel approximation and apply it to the case of particles with icosahedral, octahedral, and tetrahedral inhomogeneous charge distributions. We analyze in detail how charge distribution symmetry modifies the interaction energy and find that local charge inhomogeneities reduce the repulsion of two overall equally charged particles, while sufficient orientational variation in the charge distribution can turn the minimum interaction energy into an attraction. Additionally we show that larger patches and thus lower symmetries and wave numbers result in bigger attraction given the same variation.