Percolation threshold for Bruggeman composites

Using a simple phenomenological approach, we calculate the percolation threshold for Bruggeman composites having microgeometry of two kinds. Both kinds of composites consist of spheroids whose shape follows the Beta distribution. At the same time, the first one is a mixture of spheroids equally oriented along their revolution axis. In this case the percolation threshold is shown to be the same as for an assembly of equally oriented identical spheroids whose shape corresponds to the most probable shape of the distribution. For such composites the percolation threshold can vary between 0 and 1. The second one is a random mixture of the spheroids. In this case the percolation threshold is expressed in terms of the Gauss hypergeometric function; it is shown to vary between 0 and 1/3. The derived analytical results are supplemented with numerical calculations carried out for different values of the Beta distribution parameters.