Permittivity of lossy composite materials

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 nb 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. (C) 1998 American Institute of Physics.