Spectral density representation of dielectric mixtures

Abstract

Dielectric relaxation has attracted lot of interest since the days of J.C. Maxwell. Although relaxation in pure, single materials is a puzzling topic, relaxation in mixtures has its own perplexing sides. However, with the help of spectral density representation, one has the possibility to separate contributions of the constituents and the geometrical composition of the mixture phases. Here, we will present the theory of dielectric mixtures with the spectral density representation. It will be shown that depending on the dielectric properties and geometrical description of the constituents different effective permittivity can be obtained for a chosen pair of mixture components—binary mixtures. The tools presented here can be used to better understand the dielectric properties of materials. The numerical implementations presented for immittance data can be used for various physical properties of heterogeneous materials. For mixtures, they provide great value in (i) designing the permittivity of a mixture composed of substances with known permittivities and geometrical composition (for device and insulation applications), (ii) calculating the permittivity of the second component of a two-component mixture when the permittivities of the mixture and the first component are known (for material and system characterization), and (iii) estimating the morphology of a two-component mixture when the permittivities of the mixture and each of the components are known (for microstructure and structure/property relationships).