Effective dielectric properties of composite materials: The dependence on the particle size distribution

We have carried out numerical simulations on the effective transport properties of composites consisting of well separated conductive spherical inclusions in an insulating matrix. The simulations show that the effective permittivity depends markedly on the size distribution of the inclusions. Results are presented in a broad range of filling factors and degrees of polydispersity. For a simple cubic lattice of identical spheres the calculated values agree exactly with the analytical solution. The Maxwell-Garnett model has shown to describe well the case of randomly distributed uniformly sized inclusions independently of the concentration, even at filling factors up to 30%. With increasing degree of polydispersity the permittivity rises towards a limiting value close to the Bruggeman result.