Permittivity of lossy heterostructures: effect of shape anisotropy

The complex values of the permittivity of two-component lossy (deterministic) heterostructures, composed of inclusions of permittivity ε 1 embedded in a host matrix of permittivity ε 2 , are rigorously evaluated with the use of the field calculation package PHI3D and the resolution of boundary integral equations. Numerical results are provided concerning spherical and rod-like inclusions with various radius-to-length ratios, of finite conductivity, periodically arranged in a simple-cubic lattice configuration. For illustrative purposes, a single set of permittivities is investigated: ε 1 = 80-i10 2 and ε 2 = 2-i0. The conduction threshold volume concentration is strongly dependent on the shape of the inclusions. Increasing the radius-to-length ratio by one order of magnitude has the effect of shifting the conduction threshold upwards by two decades. The exponents which determine how the real and imaginary parts of the effective permittivity scale with the distance from the conduction threshold are determined and are compared with the scaling predictions of the percolation theory for infinite three-dimensional (random) lattices of insulator-normal metal composite systems and the self-consistent effective-medium approximation. We also found that the data concerning the imaginary part of the effective permittivity collapse on a single scaling plot over the range of aspect ratio 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 direction of the applied electric field increases.