Dielectric relaxation in distributed dielectric layers

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Abstract
The Maxwell–Wagner theory of interfacial polarization was extended to the layer system in which the layer properties are distributed continuously. The equation was derived to transform the distribution of relaxation times into that of layer properties. Each layer was characterized by the thickness and by the time constant which is defined as the ratio of permittivity to conductivity for the layer. The distribution of layer properties which yields the relaxation of the Cole–Cole type was calculated to show the applicability of the transformation thus derived. The calculation in the Cole–Cole type clarified that the system consists of two types of layers, i.e., the one of narrow distribution with a longer time constant than the characteristic relaxation time of the Cole–Cole type and the other of broad distribution with a shorter time constant. It was proved that the system considered here did not yield the Davidson–Cole type dielectric relaxation. Model experiments were carried out and proved the theory appropriate.