ELECTRICAL RESPONSE OF HETEROGENEOUS SYSTEMS OF CLUSTERED INCLUSIONS

An exact formalism to calculate the multipole moments, electric field, and the effective dielectric function of a heterogeneous system of clustered spherical particles is presented. The formalism is derived from a boundary-value problem corresponding to the typical low-frequency experimental configuration of a system placed between two parallel electrode plates. The formalism is then suited to cluster distributions, neglecting fluctuations. When the correlations among cluster pairs are short range and spherically symmetric, the results are remarkably simple: only the dipole moments of the other clusters and the images contribute to the local field acting on each cluster, and the effective dielectric function has the Clausius-Mossotti form, with cluster polarizabilities directly related to the cluster configurations. We study as an illustrative example systems containing particle chains along the direction of the applied field. We find that if the conductivity of the particles is much larger than that of the host material, the multipole moments and the effective dielectric function are greatly enhanced, whereas in the opposite case the effect of chaining is negligible.