Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices

The effect of defects on the percolation of linear k-mers (particles occupying k adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The k-mers are deposited using a random sequential adsorption mechanism. Two models L-d and K-d are analyzed. In the L-d model it is assumed that the initial square lattice is nonideal and some fraction of sites d is occupied by nonconducting point defects (impurities). In the K-d model the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the k-mers d consists of defects, i.e., is nonconducting. The length of the k-mers k varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependences of the percolation threshold concentration of the conducting sites pc vs the concentration of defects d are analyzed for different values of k. Above some critical concentration of defects d(m), percolation is blocked in both models, even at the jamming concentration of k-mers. For long k-mers, the values of d(m) are well fitted by the functions d(m) proportional to k(m)(-alpha) - k(-alpha) (alpha = 1.28 +/- 0.01 and k(m) = 5900 +/- 500) and d(m) proportional to log(10)(k(m)/k) (k(m) = 4700 +/- 1000) for the L-d and K-d models, respectively. Thus, our estimation indicates that the percolation of k-mers on a square lattice is impossible even for a lattice without any defects if k greater than or similar to 6 x 10(3).