ANALYTIC APPROACH TO THE INTERFACIAL POLARIZATION OF HETEROGENEOUS SYSTEMS

We have obtained an analytical solution of Maxwell's equations for a d ielectric system of spherical particles in a medium. The system is pla ced between two parallel electrode plates, subject to a low-frequency alternating potential, and the solution is obtained from the correspon ding boundary-value problem for the Green function. All the multipole moments and the electric field are expressed in terms of the applied p otential at the electrodes and a matrix which depends on the system co nfiguration. The effective dielectric function is then obtained as an average over the whole sample. For disordered systems, we solve exactl y the case of two-particle distributions with short-range correlations and find that the form of the distribution plays a crucial role. In p articular, we prove that for spherically symmetric two-particle distri butions all multipole moments except dipoles are exactly zero, and the Maxwell-Garnett result, or, equivalently, the Clausius-Mossotti relat ion for spherical particles, is valid regardless of the particle conce ntration. Within the two-particle distribution, corrections to the Max well-Garnett result can only derive from nonsphericity in the distribu tion: in such a case, higher multipole moments are generally nonzero a nd may strongly affect the effective dielectric function. We provide t he explicit expressions for all the multipole moments and the effectiv e dielectric function, which can be computed straightforwardly for any given distribution. We show that an iterative unsymmetrical procedure proposed originally by Bruggeman is inconsistent with our results.