The study of dielectric heterostructures has been advancing at a rapid pace. Much of the interest in these materials stems from the fact that their physical properties can be systematically tuned by variation of the size and shape of the constituents. Here we report on extensive computer simulations of the effective permittivity of dielectric periodic (deterministic) heterostructures, having monosized hard core inclusions of anisotropic shape (rod, ellipsoid) embedded in an otherwise homogeneous and isotropic matrix. The real and imaginary parts of the permittivity, in the quasistatic limit, are rigorously evaluated with the use of the PHI3D field calculation package and the resolution of boundary integral equations. In this article, we show that the effective permittivity has critical properties near a conduction threshold. The conduction threshold concentration can be significantly modified by the size, shape, and spatial arrangement of the constituents. More specifically, it obeys a square law dependence as a function of the aspect ratio, i.e., the ratio of the smaller dimension to the larger dimension in both the rodlike and ellipsoidal inclusions. The data exhibit a scaling behavior and can all be collapsed onto a single master curve, indicative of a remarkable universality in the conductivity property. The critical exponents which determine how the real and imaginary parts of the effective permittivity scale with the distance from the conduction threshold are determined. Our results are compared with the scaling prediction of the standard percolation theory for infinite three-dimensional random lattices of insulator-normal metal composite systems. We also observed that the conduction transition is shifted towards higher concentrations as the angle between the symmetry axis and the direction of the applied electric field increases. Increasing the contrast ratio, between the permittivity and the conductivity of the background medium and the inclusions, results in dramatic changes of the complex effective permittivity, depending on the geometry of the inclusions. The scale-dependent properties and the mechanism which govern criticality are related to the actual area of contacts between the inclusions. (C) 2000 American Institute of Physics. [S0021-8979(00)07723-9].

Composite composites are entities that are important in physics and engineering and are a class of compounds actively investigated for their dielectric properties. Such systems consist of composite inclusions multicomponent materials embedded in a matrix of a distinct material. The effects of volume fraction, permittivity, shape and thickness of the various constituents on the complex permittivity, in the quasistatic approximation, of the heterostructures are reported. We use an ab initio numerical technique for the evaluation of the dielectric characteristics of composite composites, arranged in a regular simple cubic lattice, which is based on the field calculation package PHI3D and the resolution of boundary integral equations. This method is exact in the sense that all internal electric multipole interactions are taken into account. Typical results presented for spheres and ellipsoids indicate that any approach based solely on the dipole approximation must fail to predict the effective permittivity of dielectric heterostructures.

An ab initio numerical simulation model has been used to compute the complex effective dielectric constant of a two-component lossy composite material, in the quasistatic limit. A computational algorithm with a conventional finite element formulation solves Laplace’s equation for a spatially heterogeneous medium, using the field calculation package FLUX3D. In this way, different three-dimensional topological arrangements of the components were considered. The composite material consists of dense spheres of uniform size that are arranged in simple, body-centered, and face-centered cubic lattices. The accuracy of the method is checked by comparing with results previously presented in the literature. Detailed predictions provide a comparison with percolation theory when the imaginary part of the relative permittivity of the spheres is very large. A comparison with McLachlan’s generalized effective medium equation [D. S. McLachlan, J. Phys. C 20, 865 (1987)] is further provided over a wide range of conditions. From these calculations one can conclude that there are significant discrepancies between the ab initio evaluated values of the effective permittivity and those obtained on the basis of McLachlan’s analysis. On the one hand, the numerical method demonstrated here shows that the real part of the effective permittivity, obtained from ab initio results, can be significantly different from that predicted on the basis of McLachlan’s equation when the imaginary part of the permittivity of the inclusion is very large compared to its real part. On the other hand, these computational results capture the trends in the percolation threshold variation with cubic lattice packing. We measured the exponents s and t which determine how the real and imaginary parts of the permittivity scales with the distance from the percolation threshold. This behavior is most probably due to the drastic differences in the basic assumptions existing between McLachlan’s modeling and our numerical approach. In particular, this analysis makes it clear that any approach based only on the dipole approximation must fail to correctly describe the complex effective dielectric constant, over the entire range of volume fraction of spherical inclusions.

The complex values of the permittivity of two-component lossy heterostructures, composed of inclusions of permittivity /spl epsiv//sub 1/ embedded in a host matrix of permittivity /spl epsiv//sub 2/, are rigorously evaluated with use of the finite element method and the code FLUX3D. Numerical results concerning spherical and rodlike inclusions with various radius-to-length ratios, of finite conductivity, periodically arranged in a simple cubic lattice configuration are provided. For illustrative purpose, a single set of permittivities was investigated: /spl epsiv//sub 1/=80-i10/sup 6/ and /spl epsiv//sub 2/=2-i0. The percolation threshold volume concentration is strongly dependent on the inclusion shape. Increasing the radius-to-length ratio by one order of magnitude has the effect of shifting upwards the percolation threshold by two decades. The exponents which determine how the real and imaginary parts of the effective permittivity scale with the distance from the percolation threshold are determined and are compared with the scaling predictions of percolation theory for infinite three-dimensional lattices of insulator-normal metal composite systems.

An ab initio numerical simulation model has been used to compute the complex effective dielectric constant of a two-component lossy composite material, in the quasistatic limit. A computational algorithm with a conventional finite element formulation solves Laplace's equation for a spatially heterogeneous medium, using the field calculation package FLUX3D. In this way, different three-dimensional topological arrangements of the components were considered. The composite material consists of dense spheres of uniform size that are arranged in simple, body-centered and face centered cubic lattices. A comparison with McLachlan's generalized effective medium equation is further provided over a wide range of conditions