The three-layered core model permittivity of polymer nano-composites in electrostatic field

Multi-layered core model of nanoparticle was supposed to have advantage in analyzing dielectric characteristic of polymer nano-composites by many researchers. However this model cannot be verified effectively from the view of mathematic. This paper focused on solving this problem. First the three-layered core physical model was built based on physical phenomenon and former research results, and then mathematical model was built by taking different densities into Maxwell Garnett Approximation (MGA). Permittivity of each layer was established by integrals mean value point of supposed three different functions in respective thickness. At last three-layered core mathematical model of diffusion system was built and the equivalent permittivity was calculated. The calculated results have a better coincidence with experimental result and all of this show that three-layer core model and arc-tangent function have a good description of character of interaction zone.