Dielectric permittivity simulation of random irregularly shaped particle composites and approximation using modified dielectric mixing laws

Abstract

Finite difference quasielectrostatic modeling is used to predict the dielectric permittivity of composites consisting of irregular particles in a background matrix. Representations of particles having undulating surfaces described by sums of harmonic functions are created on the computer and subsequently packed into a three-dimensional cellular model space. Composite dielectric permittivities as a function of volumetric filling fraction and particle undulation amplitude were simulated using constituent permittivities similar to the low-field behavior of barium titanium oxide (particles) and polyvinylidene fluoride-trifluoroethylene-chlorofluoroethylene (terpolymer matrix). An increase in particle roughness (undulation amplitude) causes a more rapid increase in composite permittivity than that predicted by random spherical particle simulations. The dielectric behavior of irregular particle composites is also simulated over a wide range of ratios of particle permittivity to matrix permittivity, where both permittivities are purely real. An empirical mixing law, which is a modification of the Hanai equation with an exponent 1/μ instead of 1/3, is investigated and found to be in excellent agreement with the simulations. Additional empirical expressions that provide approximate values of μ in terms of the particle undulation amplitude and the ratio of constituent permittivities are developed. Together, the empirical expressions are potentially useful as a predictive mixing law for irregular particle systems.