Article
Dielectric Polarization in Random Media
Journal of Statistical Physics
(1984)
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 pointr1 to the external electric field at the pointr2 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*−ε0)(2ε*+ε0) /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.
Disciplines
Publication Date
April, 1984
DOI
10.1007/BF01017364
Publisher Statement
At the time of publication John Ramshaw was affiliated with the Los Alamos National Laboratory.
Citation Information
J. D. Ramshaw, "Dielectric Polarization in Random Media," J. Stat. Phys. 35, 49 (1984).