Effective nonlinear coefficient of strongly nonlinear spherical dielectric composites

Abstract

This research is an extension of the work of Yu and Yuen (1996) in studying the electric field response of strongly nonlinear dielectric composites by using the decoupling technique. These composites consist of spherical strongly nonlinear dielectric inclusions randomly embedded in different strongly nonlinear dielectric host media. The effective medium theory (EMT) is applied for theoretical modeling and bounds of the effective nonlinear coefficient (chi) of the composite are determined for arbitrary inclusion packing fractions. The results show the lower and upper bounds which the gap increases with increasing the contrast between the nonlinear coefficients of the inclusion and host medium. If the composite has material of higher nonlinear coefficient being the host medium instead of the inclusions, the higher chi is obtained for the composite of the same packing fractions. Our results of chi based on the EMT are more general than those of Yu and Yuen which are valid only at low inclusion packing fraction limit. The EMT results agree very well with the results of Yu and Yuen at inclusion packing fractions less than 0.1. Moreover, we also apply the simple variational method to calculate chi in order to confirm all decoupling technique results. It is found that the decoupling technique results are less than those obtained by using the variational method, satisfying the theoretical prediction of Yu, Hui and Lee (1996)