Order and disorder in the microstructure of dielectrically nonlinear heterogeneous materials

The paper deals with the electrical characterisation of dispersions of pseudo-oriented ellipsoids of revolution. We are thus dealing with mixtures of inclusions of arbitrary eccentricity and arbitrary non-random orientational distributions. The analysis ranges from parallel spheroidal inclusions to completely random oriented inclusions. A unified theory covers all the orientational distributions between the random and parallel cases. Each ellipsoidal inclusion is made from an isotropic nonlinear dielectric material described by means of the so-called Kerr nonlinear relation. The electrical averaging inside the composite material is carried out by means of explicit results. We obtain closed form expressions for the macroscopic or equivalent dielectric properties of the overall composite materials. This study affirms that the nonlinear electrical behaviour of such a dispersion of pseudo-oriented particles is completely defined by two specific order parameters, which depends on the given angular distribution. The theory may be applied to characterise media with different shapes of the inclusions (i.e. spheres, cylinders or planar inhomogeneities) yielding a set of procedures describing several composite materials of great technological interest.