Complex permittivity based on equivalent circuit model for polymer/metal composite. Frequency dependence of permittivity as function of concentration

Abstract

The frequency dependence of the complex permittivity of a binary composite system in which metal particles were randomly dispersed in a polymer was formulated for a wide range of particle concentrations (5 to 50%vol) by using a simple equivalent circuit model. A composite containing a small amount of particles has a unit structure in which polymer separates the metal particles. This indicates one type of channel for electric-flux running from one particle to the next one via the polymer. The complex permittivity /spl epsiv//spl dot//sub c/, of this composite was found to be proportional to the complex permittivity /spl epsiv//spl dot//sub p/ of the polymer, independent of frequency /spl epsiv//spl dot//sub c/=k/spl epsiv//spl dot//sub p/, where coefficient k increases with the particle concentration. In contrast, a composite containing a large amount of particles has a unit structure in which the metal particles directly touch. This indicates two types of channels running from particle to particle: one via the polymer and one via the particle boundaries. The complex permittivity /spl epsiv//spl dot//sub c/, of this composite is expressed as the sum of two terms: /spl epsiv//spl dot//sub c/=k/sub 1//spl epsiv//spl dot//sub p/+F/sub 2/(f), where k/sub 1/ increases with the particle concentration and F/spl dot//sub 2/(f) decreases with the frequency. Both formulas were verified experimentally by analyzing the relationship between composite permittivity /spl epsiv//spl dot//sub c/, and polymer permittivity /spl epsiv//spl dot//sub p/.