Impact of packing fraction on diffusion-driven pattern formation in a two-dimensional system of rod-like particles

Abstract

Pattern formation in a two-dimensional system of rod-like particles has been simulated using a lattice approach. Rod-like particles were modelled as linear k-mers of two mutually perpendicular orientations (kx-and ky-mers) on a square lattice with periodic boundary conditions (torus). Two kinds of random sequential adsorption model were used to produce the initial homogeneous and isotropic distribution of k-mers with different values of packing fraction. By means of the Monte Carlo technique, translational diffusion of the k-mers was simulated as a random walk, while rotational diffusion was ignored, so, kx-and ky-mers were considered as individual species. The system tends toward a well-organized nonequilibrium steady state in the form of diagonal stripes for the relatively long k-mer (k ≥ 6) and moderate packing densities (in the interval p down < p < pup, where both the critical packing fractions p down and pup are depended on k).