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 p_c 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∝k_m^-α-k^-α (α =1.28 ±0.01 and k_m=5900 ±500 ) and d_m∝log1₀(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 ⪆6 ×10³ .