A review of the current state of understanding of dielectric mixture properties, and approaches to use numerical calculations for their modeling are presented. It is shown that interfacial polarization can yield different non-Debye dielectric responses depending on the properties of the constituents, their concentrations and geometrical arrangements. Future challenges on the subject are also discussed.

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.

In this article, the frequency dependent dielectric properties ε(ω) of ordered and disordered two-dimensional binary composite structures were investigated and compared. The ordered structures were composed of hard disk inclusions in a matrix phase, and the inclusions were distributed on lattice sites. The disordered structures were, on the other hand, composed of 16 × 16 square networks (crossword puzzle-like structures), and the phases were assigned randomly to each square. The material parameters of the phases were assumed to be frequency independent (ε and σ being constant). Numerical calculations were performed using the finite element method in the frequency domain. We have found that the dielectric relaxation character of the structures, which were due to the interfacial (or Maxwell–Wagner–Sillars) polarization, changed drastically depending on the conductivity ratio of the phases and topology of the structures. Application of a recently developed dielectric data analysis method have resulted additional information about the dielectric relaxations in the considered structures. The regular lattice structures with a less conductive matrix phase than the inclusions’ (match composite), σ1<σ2, show a symmetric distribution of relaxation times, narrower than those with σ1>σ2 (reciprocal composite) when ε1 in both cases were lower than ε2. The generated random structures have, on the other hand, resulted in symmetrical relaxations (of Cole–Cole type) for match composites and asymmetrical relaxations of Davidson–Cole type for reciprocal composites in two dimensions. Therefore, depending on the ratio of the conductivities and permittivities of the phases, the interfacial polarization can be interpreted differently. The obtained relaxation time distributions have revealed that the relaxations were broad, and unlike the responses of the empirical formulas, there existed one maximum and one minimum, or two cutoff, time constants for the dielectric relaxation in dielectric mixtures. Comparison of the data to the Wiener and Hashin–Shtrikman bounds has indicated that the latter one was not valid for the triangular lattice and random structures. Finally, our simulations have also yielded similar dielectric responses as an analytical formula proposed for brine-saturated rock mixtures when σ1<σ2, when the constituent with the lowest ε is also the least conductive, match composite.