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

Abstract

Pattern formation occurring in a two-dimensional system of rod-like particles has been simulated using a lattice approach. The 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 different models of random sequential adsorption were used to produce an initial homogeneous and isotropic distribution of k-mers with different packing fraction values. 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, the kx- and ky-mers were considered as individual species. The system tended towards a well-organised nonequilibrium steady state in the form of diagonal stripes for relatively long k-mers (k ≥ 6) and moderate packing fractions (in the interval pdown < p < pup, where both the critical packing fractions pdown and pup were dependent on k).