Dielectric polarization in random media

Abstract

The theory of dielectric polarization in random media is systematically formulated in terms of response kernels. The primary response kernel K(12) governs the mean dielectric response at the pointr ₁ to the external electric field at the pointr ₂ in an infinite system. The inverse of K(12) is denoted by L(12); it is simpler and more fundamental than K(12) itself. Rigorous expressions are obtained for the effective dielectric constantε ^* in terms of L(12) and K(12). The latter expression involves the Onsager-Kirkwood function (ε ^*−ε ₀)(2ε ^*+ε ₀) /ε₀ε^* (where ε₀ is an arbitrary reference value), and appears to be new to the random medium context. A wide variety of series representations forε ^* are generated by means of general perturbation expansions for K(12) and L(12). A discussion is given of certain pitfalls in the theory, most of which are related to the fact that the response kernels are long ranged. It is shown how the dielectric behavior of nonpolar molecular fluids may be treated as a special case of the general theory. The present results forε ^* apply equally well to other effective phenomenological coefficients of the same generic type, such as thermal and electrical conductivity, magnetic susceptibility, and diffusion coefficients.