Double Statistical Distribution of Conductivity and Aspect Ratio of Inclusions in Dielectric Mixtures at Microwave Frequencies

An analytical model of a composite dielectric presented in this paper is the extension of Maxwell Garnett formulation. It takes into account the simultaneous statistical (Gaussian) distribution of conductivity and aspect ratio of inclusions. The inclusions are randomly oriented elongated conducting spheroids at concentrations below the percolation threshold. The formulation presented herein is limited to microwave frequencies. However, taking subtle frequency-dependent effects that play important part at optical frequencies into account is straightforward. Some results of computations of microwave complex effective permittivity of composites with different input parameters have been obtained using analytical and numerical integration in Maple 10 software. It is shown how the parameters of the distribution laws - mean values and standard deviations of aspect ratio and conductivity - affect the resultant complex effective permittivity. The results of computations demonstrate that the most important factors affecting frequency characteristics of microwave effective permittivity are the mean values of the aspect ratio and conductivity. As for the standard deviations of aspect ratio and conductivity, their effects are the most noticeable in the transition between the static and optical limits of the Debye characteristic for the effective permittivity. There is almost no effect in the static and optic regions of the Debye curves