Theoretical Study of Nanocomposite Permittivity with a Tunable Clustering of Inclusions

Abstract

AbstractA new analytical model is proposed for the nanocomposite permittivity εeff in mean‐field approach using integrated coefficients for the inclusion clustering and matrix reaction effects. Predictions for εeff are in a satisfactory agreement with the Lichtenecker and Bruggeman mixing rules, depending on whether the reaction field is ignored or incorporated into the theory. The observed differences between the Maxwell–Garnett, Lichtenecker, and Bruggeman results are interpreted in terms of the fraction of the stored dipolar energy they take into account. A novel analytical expression for the average dipolar field in the film shows a U‐shaped dependence on the filler packing fraction η, with an absolute maximum at = 1/e. New analytical expressions derived for the average dipolar energy and dipole–dipole interaction energy in the nanocomposite depend on the cluster orientation parameter γ, and take into account the film boundary effects. It is found that the enhancement of εeff at higher γ is associated with an increase in the inclusion dipole moment in the oriented clusters resulting from dipole–dipole correlations, which inflate the energy stored inside the inclusions.