Dependence of the percolation threshold on the size of the percolating species

Abstract

Site and bond percolation of k-mers of different structures and forms deposited on 2-D regular lattices is studied. In addition, the percolation threshold for percolating k-mers on a Bethe lattice is analytically obtained. By using finite-size scaling theory, the analysis of the results is performed in order to determine the behavior of the percolation threshold which exhibits an exponential decrease with the k-mer size. Characteristic parameters of that function are dependent not only on the form and structure of k-mers but also on the properties of the lattice where they are deposited. An expression for the percolation threshold as a function of the parameters of the problem is proposed and discussed.