Effective permittivity of composites with stratified particles

Abstract

The effective electromagnetic, thermal and mechanical properties ofheterogeneous media are commonly related to composition. Stratified compositesare entities that are important in physics and engineering and are a class ofcompounds actively investigated for their dielectric properties. Such systemsconsist of composite inclusions of multicomponent materials embedded in amatrix of a distinct material. The effects of the volume fraction, permittivityand thickness of the various constituents on the complex effectivepermittivity of the heterostructures, in the quasistatic approximation, arereported. We use an exact numerical technique for the evaluation of thedielectric characteristics of three-component composites, arranged in aregular simple cubic lattice, which is based on the field calculation packagePHI3D and a boundary integral equations solution scheme of Laplace's equation.`Exact' means that the correct properties are computed for the givenmicrostructure and choice of individual component properties because allinternal electric multipole interactions contributing to the polarization ofthe material medium are taken into account. The predictions of the Steeman andMaurer (dipolar) theory (Steeman P A M and Maurer F H J 1992 Colloid Polym.Sci. 270 1069) are compared with our numerical results whereappropriate. An important feature, suggested by the results presented forstratified spheres and spheroids, is that any approach based solely on thedipole approximation must fail to predict the effective permittivity ofdielectric heterostructures over the entire range of volume fraction ofinclusions. The results discussed give motivation for the development ofcareful experiments which can be used to test the numerical simulations and tofabricate synthetic composite materials in which new electromagneticproperties can be obtained from the combination of several materials.