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

In this article, the frequency dependent dielectric properties, epsilon(ome ga), of an "ideal" binary composite structure were investigated by using th e finite element method in the frequency domain. The material properties of the phases, i.e., dielectric permittivity, epsilon, and direct-current con ductivity, sigma, were assumed to be frequency independent. Moreover, the i nclusion phase was more conductive than the matrix phase. The inclusions we re infinitely long unidirectional cylinders which could be assumed to be ha rd disks in two dimensions in the direction perpendicular to the cylinder d irection. Three different inclusion concentration levels were considered, e .g., low, intermediate, and high. The calculated dielectric relaxations wer e compared with those of the dielectric mixture formulas in the literature and it was found that there were no significant differences between the for mulas and the numerical solutions at low inclusion concentration. Furthermo re, the obtained responses were curve fitted by the addition of the Cole-Co le empirical expression and the ohmic losses by using a complex nonlinear l east 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 intermedi ate and high concentrations, the responses obtained from the numerical simu lations deviated from that of the Debye one, whose curve fittings with the Cole-Cole empirical expression were inadequate. (C) 2001 American Institute of Physics.