Pair-cluster theory for the dielectric constant of composite media

By considering the embedding of nearest-neighbor grains of a random composite in an "effective medium," a pair-cluster theory for the dielectric constant of composites is formulated in which the interactions between pairs of nearest-neighbor grains are explicitly taken into account. Compared to the well-known effective-medium theory, the new theory displays similar dc behavior but predicts different optical dielectric constants. A comparison of the two theories shows in particular that the absence of optical dielectric anomaly in the effective-medium theory is attributable to the neglect of nearest-neighbor interactions. Differences between the optical characteristics of the Maxwell-Garnett theory and the pair-cluster theory are also pointed out and discussed in relation to the underlying microstructures.