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

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 and metal–metal 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’s permittivity are relatively modest but not insignificant, these effects being pronounced by anisotropy when all dimers are identically oriented.

Acknowledgements

TGM acknowledges the support of EPSRC grant EP/M018075/1. AL thanks the Charles Godfrey Binder Endowment at Penn State for ongoing support of his research activities.

Notes

No potential conflict of interest was reported by the authors.