Comparison of electrical mixture rules for composites

Firstly the basic theoretical methods of calculating the dielectric properties of heterogeneous mixtures are discussed. These are the mean field and effective medium theories and integral methods. Formulae are presented for systems containing parallel oriented ellipsoids and for randomly oriented ellipsoidal systems. Theoretical formulae are divided into two sub-groups: symmetric equations for statistical mixtures and asymmetric equations for matrix-inclusion type composites. In the former case only the relative amount of the components is important, in the second case phase inversion results in a change of the dielectric properties.Formulae are compared numerically using spherical and spheroidal systems with sharply different components (permittivity ratio is 1 100). In the case of asymmetric formulae the effect of phase inversion is studied as well. Percolation behaviour predicted by the equations is demonstrated and discussed. Functional shapes are compared in relation to the theoretical differences.Finally, experimental data are compared with the theoretical results, advantages and drawbacks of the various formulae are discussed. For spherical systems the simplest mean field formula yields somewhat worse values than effective medium or integral equations. The Looyenga equation does not work very well if the permittivity difference is high. For nonspherical systems the fit is better in general, even the simplest formula works satisfactorily. The shape independence predicted by the Looyenga theory for randomly oriented ellipsoids is in conflict with experimental data.