Influence of anisotropy on percolation and jamming of lineark-mers on square lattice with defects

Abstract

Using the Monte Carlo simulation, we study the percolation and jamming of oriented linear k-mers on a square lattice that contains defects. The point defects with a concentration, d, are placed randomly and uniformly on the substrate before deposition of the k-mers. The general case of unequal probabilities for orientation of depositing of k-mers along different directions of the lattice is analyzed. Two different relaxation models of deposition that preserve the predetermined order parameter s are used. In the relaxation random sequential adsorption (RRSA) model, the deposition of k-mers is distributed over different sites on the substrate. In the single cluster relaxation (RSC) model, the single cluster grows by the random accumulation of k-mers on the boundary of the cluster (Eden-like model). For both models, a suppression of growth of the infinite (percolation) cluster at some critical concentration of defects dc is observed. In the zero defect lattices, the jamming concentration pj (RRSA model) and the density of single clusters ps (RSC model) decrease with increasing length k-mers and with a decrease in the order parameter. For the RRSA model, the value of dc decreases for short k-mers (k < 16) as the value of s increases. For k = 16 and 32, the value of dc is almost independent of s. Moreover, for short k-mers, the percolation threshold is almost insensitive to the defect concentration for all values of s. For the RSC model, the growth of clusters with ellipse-like shapes is observed for non-zero values of s. The density of the clusters ps at the critical concentration of defects dc depends in a complex manner on the values of s and k. An interesting finding for disordered systems (s = 0) is that the value of ps tends towards zero in the limits of the very long k-mers, k → ∞ and very small critical concentrations dc → 0. In this case, the introduction of defects results in a suppression of k-mer stacking and in the formation of 'empty' or loose clusters with very low density. On the other hand, denser clusters are formed for ordered systems with ps ≈ 0.065 at s = 0.5 and ps ≈ 0.38 at s = 1.0.

Percolation and jamming of lineark-mers on a square lattice with defects: Effect of anisotropy

“…For the short k-mers (k 8), the percolation threshold, p c , is almost insensitive to the defect concentration, d, for any anisotropy, s [28] (e.g., see Fig. 8 for k = 2).…”