Application of Bruggeman and Maxwell Garnett homogenization formalisms to random composite materials containing dimers

TL;DR

This paper develops and compares Bruggeman and Maxwell Garnett homogenization formalisms for random composite materials with dimers, analyzing their permittivity estimates under various orientations and compositions.

Contribution

It introduces homogenization formalisms that account for dimer coupling and orientation, extending existing models for composite permittivity estimation.

Findings

Close agreement between the two formalisms for dielectric--dielectric dimers.

Broad agreement for metal--dielectric dimers with low volume fractions.

Dimer orientation and coupling effects influence permittivity estimates modestly.

Abstract

The homogenization of a composite material comprising three isotropic dielectric materials was investigated. The component materials were randomly distributed as spherical particles, with the particles of two of the component materials being coupled to form dimers. The Bruggeman and Maxwell Garnett formalisms were developed to estimate the permittivity dyadic of the homogenized composite material (HCM), under the quasi-electrostatic approximation. Both randomly oriented and identically oriented dimers were accommodated; in the former case the HCM is isotropic, whereas in the latter case the HCM is uniaxial. Representative numerical results for composite materials containing dielectric--dielectric dimers demonstrate close agreement between the estimates delivered by the Bruggeman and Maxwell Garnett formalisms. For composite materials containing metal--dielectric dimers with moderate degrees of dissipation, the estimates of the two formalisms are in broad agreement, provided that the dimer volume fractions are relatively low. In general, the effects of intradimer coupling on the estimates of the HCM permittivity are relatively modest but not insignificant, these effects being exacerbated by anisotropy when all dimers are identically oriented.