Percolation and jamming in random sequential adsorption of linear k-mers on square lattices with the presence of impurities

Abstract

Percolation and jamming of linear k-mers (particles occupying k adjacent sites) on two-dimensional square lattices with impurities have been studied by numerical simulations and finite-size scaling analysis. The model offers a simplified representation of the problem of percolation in amorphous solids, where the presence of defects in the system is simulated by introducing a fraction of imperfect bonds ρ, which are considered forbidden for deposition.The dependence of percolation and jamming thresholds on the concentration of defects was investigated for dierent values of k, ranging from 2 to 64. Theresults obtained show that: for each fixed value of k, percolation can occur when ρ is smaller than a certain value ρ*_k; and in the range 0<ρ<ρ*_k, the percolation threshold is practically independent of the fraction of defects. The behavior of ρ*_k as a function of k indicates that the percolation of linear k-mers on square lattices is impossible even for an ideal lattice if k ⪆ 5500. Critical exponents were also calculated to show that the universality class corresponding to ordinary percolation is preserved.