Contents I. Introduction
A critical issue in dielectric science is the prediction of the complex relative dielectric permittivity 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 strategies. Finally, computational techniques provide a means of understanding experimental results on existing and new materials.
