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 polymers for high-density capacitors, polymer carbon black mixtures for automotive tires and current limiters in circuit protection. These multiscale systems lead to challenging problems of connecting microstructural features (shape, spatial arrangement and size distribution of inclusions) to macroscopic materials response (permittivity, conductivity). In this paper, we briefly discuss an ab initio computational electrostatics approach, based either on the use of the field calculation package FLUX3D (or FLUX2D) and a conventional finite elements method, or the use of the field calculation package PHI3D and the resolution of boundary integral equations, for calculating the effective permittivity of two-component dielectric heterostructures. Numerical results concerning inclusions of permittivity ε1 with various geometrical shapes periodically arranged in a host matrix of permittivity ε2 are provided. Next we discuss these results in terms of phenomenological mixing laws, analytical theory and connectedness. During the pursuit of these activities, several interesting phenomena were discovered that will stimulate further investigation.