Dielectric permittivity simulations of layered composites with rough interfacial surfaces

Finite difference quasi-electrostatic simulations are used to predict the interfacial dielectric permittivity of a rough-surfaced contact zone between two distinct materials in a layered composite. Fractional Brownian surfaces, which have fractal geometry, are used to represent the rough interfaces in a model space. The interfacial simulations are combined with a macroscopic analytic model for planar dielectric layers, which allows the calculation of composite permittivity for a layered composite with an arbitrary ratio of surface roughness-to-layer thickness and arbitrary volumetric filling fractions of the constituents. Examples are given for a ceramic-polymer system, and the effects of alternate ratios of constituent dielectric permittivities and changes in surface fractal character are also explored. Compared to the behavior of composites with perfectly flat interfaces, the rough-surfaced composite exhibits a significantly earlier increase in permittivity as a function of the volumetric filling fraction of the higher permittivity material. The behavior with extremely rough surfaces tends towards the predictions of the effective medium approximation