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Unformatted text preview: IEEE Transactions on Dielectrics and Electrical Insulation Vol. 14, No. 2; April 2007 1070-9878/07/$25.00 © 2007 IEEE 287 Dielectric Permittivity Simulations of Layered Composites with Rough Interfacial Surfaces Jeffrey P. Calame Naval Research Laboratory Washington, DC 20375, USA and Morag Garven Science Applications International Corp. McLean, VA 22012, USA ABSTRACT 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 Index Terms - Dielectric materials, dielectric films, composite insulation, nonhomogeneous media, mixing laws, fractals, finite difference methods, ceramics. 1 I NTRODUCTION A CRITICAL issue in dielectric science is the prediction of the complex relative dielectric permittivity ( ε ′ − j ε ′′ ) of a composite based on the volume fractions of the constituents and their individual complex permittivity values. For simple, idealized geometries, well-known analytic dielectric mixing laws can be used [1, 2]. However, for more complicated (and hence more realistic) microstructural geometries, computer simulations of the composite permittivity using quasi- electrostatic finite difference or finite element methods are required [3-7]. The ultimate goal is the complete modeling of composite materials for capacitors and sensors at the microstructure level, including both mesoscale features (individual particles, layers, or ensembles of particles in a matrix) and the truly microscopic features (interfacial effects, coatings, local dipolar interactions in surface layers, etc.). Such a capability would allow experimental synthesis to be focused on the most promising microstructural approaches, without the need to physically test each idea. Within a specific class of microstructures, the computational capability would provide explicit guidance to synthesis efforts, for example allowing the intelligent selection of particle shapes, loading fractions, surface coatings, and hierarchical assembly...
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This note was uploaded on 06/08/2011 for the course ELECTRICAL 124 taught by Professor Ghjk during the Spring '11 term at Institute of Technology.
- Spring '11