First-principles approach to dielectric response of graded spherical particles

TL;DR

This paper presents a first-principles method to determine the dielectric response of graded spherical particles, validated against exact solutions and applicable to various physical systems.

Contribution

The authors developed a first-principles approach to compute the dielectric response of graded spherical particles and validated it against exact solutions and the differential effective dipole approximation.

Findings

Excellent agreement between the first-principles approach and the differential effective dipole approximation.

The approach is applicable to dielectric, conductivity, and elastic systems.

Validated with exact solutions for specific dielectric profiles.

Abstract

We have studied the effective response of composites of spherical particles each having a dielectric profile which varies along the radius of the particles. We developed a first-principles approach to compute the dipole moment of the individual spherical particle and hence the effective dielectric response of a dilute suspension. The approach has been applied to two model dielectric profiles, for which exact solutions are available. Moreover, we used the exact results to validate the results from the differential effective dipole approximation, recently developed to treat graded spherical particles of an arbitrary dielectric profile. Excellent agreement between the two approaches were obtained. While the focus of this work has been on dielectric responses, the approach is equally applicable to analogous systems such as the conductivity and elastic problems.