Modeling the Interphase of a Polymer-based Nanodielectric

A three-phase theoretical model is proposed that is suitable for describing the effective permittivity of polymer-matrix composites containing spherical nanoparticles. The model accounts for the presence of an interphase region, which surrounds each nanosphere, whose permittivity is allowed to be different from that of the matrix polymer. The nanoparticles themselves are approximated as hard (non-overlapping) spheres, whereas the interphase regions of neighboring nanoparticles are permitted to overlap. The volume fraction of the interphase region is computed by assuming that the nanoparticles are arranged on the nodes of a simple-cubic lattice. The effective permittivity of the composite is subsequently computed via three-phase Wiener bounds. As an example application of the model, permittivity data measured on a silicon/bisphenol E cyanate ester nanodielectric and a low-density polyethylene/ alumina nanodielectric are shown to lie outside the range of the two-phase Wiener bounds yet lie within the range of the three-phase Wiener bounds with appropriate choice of interphase permittivity and thickness.