Exact polarization energy for clusters of contacting dielectrics

TL;DR

This paper introduces a regularization method to accurately compute the polarization energy in clusters of dielectric particles, addressing divergence issues at contact points and revealing how permittivity influences cluster stability.

Contribution

A novel regularization scheme that isolates the logarithmic singularity in polarization energy calculations for dielectric clusters, enabling exact cohesive energy determination.

Findings

Polarization energy stabilizes open configurations at high permittivity.

Polarization energy stabilizes compact configurations at low permittivity.

Singularity strength is logarithmic in separation and permittivity.

Abstract

The induced surface charges appear to diverge when dielectric particles form close contacts. Resolving this singularity numerically is prohibitively expensive because high spatial resolution is needed. We show that the strength of this singularity is logarithmic in both inter-particle separation and dielectric permittivity. A regularization scheme is proposed to isolate this singularity, and to calculate the exact cohesive energy for clusters of contacting dielectric particles. The results indicate that polarization energy stabilizes clusters of open configurations when permittivity is high, in agreement with the behavior of conducting particles, but stabilizes the compact configurations when permittivity is low.