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 Ld and Kd are analyzed. In the Ld 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 Kd 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 dₘ, percolation is blocked in both models, even at the jamming concentration of k-mers. For long k-mers, the values of dₘ are well fitted by the functions dₘ∝kₘ^-α-k^-α (α=1.28±0.01 and kₘ=5900±500) and dₘ∝log₁₀(kₘ/k) (kₘ=4700±1000) for the Ld and Kd 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.