Diffusion in a two-species two-dimensional system has been simulated using a lattice approach. Rodlike particles were considered as linear k-mers of two mutually perpendicular orientations (k x -and k y -mers) on a square lattice. These k xand k y -mers were treated as species of two kinds. A random sequential adsorption model was used to produce an initial homogeneous distribution of k-mers. The concentration of k-mers, p, was varied in the range from 0.1 to the jamming concentration, p j . By means of the Monte Carlo technique, translational diffusion of the k-mers was simulated as a random walk, while rotational diffusion was ignored. We demonstrated that the diffusion coefficients are strongly anisotropic and nonlinearly concentration-dependent. For sufficiently large concentrations (packing densities) and k ≥ 6, the system tends toward a well-organized steady state. Boundary conditions predetermine the final state of the system. When periodic boundary conditions are applied along both directions of the square lattice, the system tends to a steady state in the form of diagonal stripes. The formation of stripe domains takes longer time the larger the lattice size, and is observed only for concentrations above a particular critical value. When insulating (zero flux) boundary conditions are applied along both directions of the square lattice, each kind of k-mer tries to completely occupy a half of the lattice divided by a diagonal, e.g., k x -mers locate in the upper left corner, while the k y -mers are situated in the lower right corner ("yin-yang" pattern). From time to time, regions built of k x -and k y -mers exchange their locations through irregular patterns. When mixed boundary conditions are used (periodic boundary conditions are applied along one direction whereas insulating boundary conditions are applied along the other one), the system still tends to form the stripes, but they are unstable and change their spatial orientation.

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Using the Monte Carlo simulation, we study the percolation and jamming of oriented linear kmers 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.

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.