Effective conductivity of composites of graded spherical particles

TL;DR

This paper develops a first-principles method to accurately compute the effective electrical conductivity of composites made of graded spherical particles with arbitrary conductivity profiles, validating the method with exact solutions.

Contribution

It introduces a rigorous proof for the differential effective multipole moment approximation (DEMMA) and shows that the differential effective dipole approximation (DEDA) is a special case, enhancing modeling accuracy.

Findings

DEDA and DEMMA are exact for graded spherical particles.

The method applies to arbitrary conductivity profiles.

Validation with exactly solvable profiles confirms accuracy.

Abstract

We have employed the first-principles approach to compute the effective response of composites of graded spherical particles of arbitrary conductivity profiles. We solve the boundary-value problem for the polarizability of the graded particles and obtain the dipole moment as well as the multipole moments. We provide a rigorous proof of an {\em ad hoc} approximate method based on the differential effective multipole moment approximation (DEMMA) in which the differential effective dipole approximation (DEDA) is a special case. The method will be applied to an exactly solvable graded profile. We show that DEDA and DEMMA are indeed exact for graded spherical particles.