Modeling of high-k dielectric nanocomposites

In this paper, based on recent research on BaTiO 3 (BT) nanoparticles, BT/P(VDF-HFP) nanocomposites, frequency-dependent dielectric properties of such a material system with high energy density have been investigated as functions of the volume fraction of the nanoparticles at room temperature by several theoretical models. For single domain and single crystals of BT, a Debye type of dissipation and soft mode theory have been adopted to obtain a more precise frequency-dependent dielectric spectrum of BT. For nanodielectric composites, among the others, Wiener Rule, Lichtenecker model, Maxwell–Wagner model, Yamada, and modified Kerner model were applied to evaluate the frequency-dependent dielectric spectrum of nanocomposites. A simple rule of mixture for the dielectric loss tangent was obtained using Lichtenecker logarithmic rule. The results from theoretical calculations are compared with the experimental data. For the dielectric constant, Lichtenecker model, Maxwell–Wagner model, and Yamada model show reasonable agreements with the experimental data up to 50 % volume fraction of the nanoparticles. At the higher volume fraction of the nanoparticles, the experimental data show a decreasing trend of the dielectric constant of the composites due to an increase in porosity of the system. In this case, a three-phase model (nanoparticles/pores/matrix) was developed to predict dielectric properties of the system at higher volume fraction of the nanoparticles (up to 80 %). The results showed reasonable agreements for a wide range of frequency. This theoretical study provides an essential information on dielectric properties of polymer-based BT nanocomposites with a wide frequency range instead of the trial-and-error strategy of experiments and can be used for designing high energy density dielectric materials in the future.