Numerical analysis of complex dielectric mixture formulae

Abstract

As a continuation of our earlier work (Ref. [9]) the complex (frequency dependent) dielectric behaviour of some mixture formulae are studied numerically. These include matrix-inclusion type formulae (as the Wagner-Sillars or the Bruggeman-Boyle equations), mean-field statistical mixture formulae (as the Böttcher-Hsu equation) and symmetrical integral formulae (as the Looyenga equation). The frequency dependent dielectric properties are first calculated for a model system at various particle shapes, field orientations and volume fractions. After this, the validity of these equations is checked on typical sets of experimental data. For low loss powders, the Böttcher and Looyenga equations are suggested; for emulsions, suspensions and filled polymers, the matrix-inclusion type formulae give acceptable results in most cases, while for metal-insulator composites mean-field statistical mixture formulae have to be used, as they are capable of describing the percolation phenomenon.