Analytic approach to the interfacial polarization of heterogeneous systems

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Abstract
We have obtained an analytical solution of Maxwell’s equations for a dielectric system of spherical particles in a medium. The system is placed between two parallel electrode plates, subject to a low-frequency alternating potential, and the solution is obtained from the corresponding boundary-value problem for the Green function. All the multipole moments and the electric field are expressed in terms of the applied potential at the electrodes and a matrix which depends on the system configuration. The effective dielectric function is then obtained as an average over the whole sample. For disordered systems, we solve exactly the case of two-particle distributions with short-range correlations and find that the form of the distribution plays a crucial role. In particular, we prove that for spherically symmetric two-particle distributions all multipole moments except dipoles are exactly zero, and the Maxwell-Garnett result, or, equivalently, the Clausius-Mossotti relation for spherical particles, is valid regardless of the particle concentration. Within the two-particle distribution, corrections to the Maxwell-Garnett result can only derive from nonsphericity in the distribution: in such a case, higher multipole moments are generally nonzero and may strongly affect the effective dielectric function. We provide the explicit expressions for all the multipole moments and the effective 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.