Effective dielectric response of dispersions of graded particles

TL;DR

This paper presents a new theoretical approach to accurately predict the effective dielectric permittivity of dispersions containing graded particles, accounting for many-particle effects in concentrated systems.

Contribution

It introduces a novel solution based on the compact group approach and Hashin-Shtrikman theorem that incorporates many-particle effects in dielectric dispersions.

Findings

The theory recovers existing analytical and simulation results for hard dielectric spheres.

It effectively describes the dielectric response of polymer-ceramic composites with core-shell particles.

Possible generalizations of the model are discussed.

Abstract

Based upon our compact group approach and the Hashin-Shtrikman variational theorem, we propose a new solution, which effectively incorporates many-particle effects in concentrated systems, to the problem of the effective quasistatic permittivity of dispersions of graded dielectric particles. After the theory is shown to recover existing analytical results and simulation data for dispersions of hard dielectric spheres with power-law permittivity profiles, we use it to describe the effective dielectric response of nonconducting polymer-ceramic composites modeled as dispersions of dielectric core-shell particles. Possible generalizations of the results are specified.