Predicting effective permittivity of composites containing conductive inclusions at microwave frequencies

We predict the effective dielectric properties at microwave frequencies of composites containing various volume loadings of high conductivity (stainless steel or iron) spheres or flakes by adapting the semi-empirical method developed by McLachlan. Rather than the typical approach of fixing A (A = 1/vc – 1, where vc is percolation threshold) for a given inclusion shape, we consider it as an unknown and fix one of the geometric exponents. We observe that A varies linearly with the inverse of volume loading with a higher slope for flakes than spheres. The exponent is consistently higher for spheres than flakes and for iron than stainless steel. We achieve good agreement between measured and calculated permittivity over a wide range of volume loadings, inclusion shapes, and materials from 3 to 20 GHz.