Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction

TL;DR

This paper introduces an efficient image charge method for calculating polarization potentials in dielectric systems, revealing how size, charge asymmetry, and interfaces influence electrostatic interactions, including like-charge attraction.

Contribution

The paper develops a rapid, convergent image charge algorithm with coarse-graining for 3D Poisson's equation in dielectric interfaces, enabling detailed interaction studies.

Findings

Like charges can attract due to size and charge asymmetry.

Interaction force depends on interface curvature and can be non-monotonic.

The method reduces computational complexity by an order of magnitude.

Abstract

Electrostatic polarization is important in many nano-/micro-scale physical systems such as colloidal suspensions, biopolymers, and nanomaterials assembly. The calculation of polarization potential requires an efficient algorithm for solving 3D Poisson's equation. We have developed a useful image charge method to rapid evaluation of the Green's function of the Poisson's equation in the presence of spherical dielectric discontinuities. This paper presents an extensive study of this method by giving an convergence analysis and developing a coarse-graining algorithm. The use of the coarse graining could reduce the number of image charges to around a dozen, by 1-2 orders of magnitude. We use the algorithm to investigate the interaction force between likely charged spheres in different dielectric environments. We find the size and charge asymmetry leads to an attraction between like charges, in agreement with existing results. Furthermore, we study three-body interaction and find in the presence of an external interface, the interaction force depends on the curvature of the interface, and behavior a non-monotonic electrostatic force.