Structure-property relationship in dielectric mixtures: application of the spectral density theory

This paper presents numerical simulations performed on dielectric properties of two-dimensional binary composites. The influence of structural differences and intrinsic electrical properties of constituents on the composite's overall electrical properties is investigated. The structural differences are resolved by fitting the dielectric data with an empirical formula and by the spectral density representation approach. At low concentrations of inclusions (concentrations lower than the percolation threshold), the spectral density functions are delta-sequences, which corresponds to the predictions of the general Maxwell-Garnett (MG) mixture formula. At high concentrations of inclusions (close to the percolation threshold) systems exhibit non-Debye-type dielectric dispersions, and the spectral density functions differ from each other and that predicted by the MG expression. The analysis of the dielectric dispersions with an empirical formula also brings out the structural differences between the considered geometries, however, the information is not qualitative. The empirical formula can only be used to compare structures. The spectral representation method on the other hand is a concrete way of characterizing the structures of the dielectric mixtures. Therefore, as in other spectroscopic techniques, a look-up table might be useful to classify/characterize structures of composite materials. This can be achieved by generating dielectric data for known structures by using ab initio calculations, as presented and emphasized in this study. The numerical technique presented here is not based on any a priori assumption methods.