Permittivity of lossy heterostructures: effect of shape anisotropy

The complex values of the permittivity of two-component lossy (deterministi c) heterostructures, composed of inclusions of permittivity epsilon(1) embe dded in a host matrix of permittivity epsilon(2), are rigorously evaluated with the use of the field calculation package PHI3D and the resolution of b oundary integral equations. Numerical results are provided concerning spher ical and rod-like inclusions with various radius-to-length ratios, of finit e conductivity, periodically arranged in a simple-cubic lattice configurati on. For illustrative purposes, a single set of permittivities is investigat ed: epsilon(1) = 80 - i10(2) and epsilon(2) = 2 - i0. The conduction thresh old volume concentration is strongly dependent on the shape of the inclusio ns. Increasing the radius-to-length ratio by one order of magnitude has the effect of shifting the conduction threshold upwards by two decades. The ex ponents which determine how the real and imaginary parts of the effective p ermittivity scale with the distance from the conduction threshold are deter mined and are compared with the scaling predictions of the percolation theo ry for infinite three-dimensional (random) lattices of insulator-normal met al composite systems and the self-consistent effective-medium approximation . We also found that the data concerning the imaginary part of the effectiv e permittivity collapse on a single scaling plot over the range of aspect r atio investigated. The effect of the orientation of the rod-like inclusions is further studied. We observed that the conduction transition is shifted towards higher concentrations as the angle between the rod axis and the dir ection of the applied electric field increases.