Non-Debye dielectric relaxation in binary dielectric mixtures (50-50): Randomness and regularity in mixture topology

Abstract

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), σ 1 <σ 2 , show a symmetric distribution of relaxation times, narrower than those with σ 1 >σ 2 (reciprocal composite) when ε 1 in both cases were lower than ε 2 . 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 σ 1 <σ 2 , when the constituent with the lowest ε is also the least conductive, match composite.