Dielectric relaxation in dielectric mixtures: Application of the finite element method and its comparison with dielectric mixture formulas

Abstract

In this article, the frequency dependent dielectric properties, ε(ω), of an “ideal” binary composite structure were investigated by using the finite element method in the frequency domain. The material properties of the phases, i.e., dielectric permittivity, ε, and direct-current conductivity, σ, were assumed to be frequency independent. Moreover, the inclusion phase was more conductive than the matrix phase. The inclusions were infinitely long unidirectional cylinders which could be assumed to be hard disks in two dimensions in the direction perpendicular to the cylinder direction. Three different inclusion concentration levels were considered, e.g., low, intermediate, and high. The calculated dielectric relaxations were compared with those of the dielectric mixture formulas in the literature and it was found that there were no significant differences between the formulas and the numerical solutions at low inclusion concentration. Furthermore, the obtained responses were curve fitted by the addition of the Cole–Cole empirical expression and the ohmic losses by using a complex nonlinear least squares algorithm in order to explain the plausible physical origin of the Cole–Cole type dielectric relaxation. The dielectric relaxations were Debye-like when the concentration of the inclusions were low. For intermediate and high concentrations, the responses obtained from the numerical simulations deviated from that of the Debye one, whose curve fittings with the Cole–Cole empirical expression were inadequate.