Screened Coulomb interactions of general macroions with nonzero particle volume

TL;DR

This paper introduces a semi-analytical method to compute effective pair potentials for arbitrarily shaped macroions with volume, extending classical theories to complex geometries within linear screening and mean-field approximations.

Contribution

A novel semi-analytical framework mapping macroions to singular charge distributions for accurate potential calculations across diverse shapes.

Findings

Reproduces DLVO potential for charged spheres

Provides closed-form integrals for complex shapes like tori and ellipsoids

Accurate predictions for macroion phase behavior

Abstract

A semianalytical approach is developed to calculate the effective pair potential of rigid arbitrarily shaped macroions with a nonvanishing particle volume, valid within linear screening theory and the mean-field approximation. The essential ingredient for this framework is a mapping of the particle to a singular charge distribution with adjustable effective charge and shape parameters determined by the particle surface electrostatic potential. For charged spheres this method reproduces the well-known Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. Further exemplary benchmarks of the method for more complicated cases, like tori, triaxial ellipsoids, and additive torus-sphere mixtures, leads to accurate closed-form integral expressions for all particle separations and orientations. The findings are relevant for determining the phase behaviour of macroions with experiments and simulations for various particle shapes.