Dielectric properties of periodic heterostructures: A computational electrostatics approach

The dielectric properties of heterogeneous materials for various condensed- matter systems are important for several technologies, e.g. impregnated pol ymers for high-density capacitors, polymer carbon black mixtures for automo tive tires and current limiters in circuit protection. These multiscale sys tems lead to challenging problems of connecting microstructural features (s hape, spatial arrangement and size distribution of inclusions) to macroscop ic materials response (permittivity, conductivity). In this paper, we brief ly discuss an ab initio computational electrostatics approach, based either on the use of the field calculation package FLUX3D (or FLUX2D) and a conve ntional finite elements method, or the use of the field calculation package PHI3D and the resolution of boundary integral equations, for calculating t he effective permittivity of two-component dielectric heterostructuues. Num erical results concerning inclusions of permittivity epsilon(1) with variou s geometrical shapes periodically arranged in a host matrix of permittivity epsilon(2) are provided. Next we discuss these results in terms of phenome nological mixing laws, analytical theory and connectedness. During the purs uit of these activities, several interesting phenomena were discovered that will stimulate further investigation.