Percolation of polyatomic species with the presence of impurities

Abstract

In this paper, the percolation of (a) linear segments of size k and (b) k-mers of different structures and forms deposited on a square lattice contaminated with previously adsorbed impurities have been studied. The contaminated or diluted lattice is built by randomly selecting a fraction of the elements of the lattice (either bonds or sites) which are considered forbidden for deposition. Results are obtained by extensive use of finite size scaling theory. Thus, in order to test the universality of the phase transition occurring in the system, the numerical values of the critical exponents were determined. The characteristic parameters of the percolation problem are dependent not only on the form and structure of the k-mers but also on the properties of the lattice where they are deposited. A phase diagram separating a percolating from a nonpercolating region is determined as a function of the parameters of the problem. A comparison between random site and random bond percolation in the presence of impurities on the lattice is presented.