Effective permittivity of composites with stratified particles

The effective electromagnetic, thermal and mechanical properties of heterogeneous media are commonly related to composition. Stratified composites are entities that are important in physics and engineering and are a class of compounds actively investigated for their dielectric properties. Such systems consist of composite inclusions of multicomponent materials embedded in a matrix of a distinct material. The effects of the volume fraction, permittivity and thickness of the various constituents on the complex effective permittivity of the heterostructures, in the quasistatic approximation, are reported. We use an exact numerical technique for the evaluation of the dielectric characteristics of three-component composites, arranged in a regular simple cubic lattice, which is based on the field calculation package PHI3D and a boundary integral equations solution scheme of Laplace's equation. `Exact' means that the correct properties are computed for the given microstructure and choice of individual component properties because all internal electric multipole interactions contributing to the polarization of the material medium are taken into account. The predictions of the Steeman and Maurer (dipolar) theory (Steeman P A M and Maurer F H J 1992 Colloid Polym. Sci. 270 1069) are compared with our numerical results where appropriate. An important feature, suggested by the results presented for stratified spheres and spheroids, is that any approach based solely on the dipole approximation must fail to predict the effective permittivity of dielectric heterostructures over the entire range of volume fraction of inclusions. The results discussed give motivation for the development of careful experiments which can be used to test the numerical simulations and to fabricate synthetic composite materials in which new electromagnetic properties can be obtained from the combination of several materials.