Theoretical Study of Nanocomposite Permittivity with a Tunable Clustering of Inclusions. Issue 5 (4th March 2020) - Allahyarov, Elshad
Abstract: A 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 ⟨ E ⃗ μ ⟩ in the film shows a U‐shaped dependence on the filler packing fraction η, with an absolute maximum at η m = 1/ e . New analytical expressions derived for the average dipolar energy u m μ and dipole–dipole interaction energy u m μ μ 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 μ p in the oriented clusters resulting from dipole–dipole correlations, which inflate the energy u p stored inside the inclusions. Abstract : A new mean‐field theory is presented for nanocomposite permittivity that takes into account inclusion clustering effects. An integrated approach for the matrix reaction field and the cumulative field of the neighboring dipoles makes it possible to test the validity of various mixing rules against theoretical predictions. The observed differences between the mixing rules are interpreted in terms of the fraction of the stored dipolar energy they take into account. For the case of a homogeneous inclusion distribution, the Bruggeman mixing rule results are the closest to theoretical predictions.