Random walks in two-dimensional slab containing elongated obstacles

Source abstract

Abstract The constrained diffusion in two-dimensional slab containing elongated impenetrable obstacles (discorectangles) has been studied using the Monte-Carlo technique. The obstacles have aspect ratio ε = 1 − 10 , they were homogeneously distributed in systems with the surface coverage (concentration) φ . The diffusion processes of random walkers in a free space between obstacles were studied. At initial moment the random walkers were homogeneously distributed inside the slab and during the time they continuously extract in the external space outside the slab. The cases with different orientational ordering of obstacles inside the slab were considered. The study demonstrated the presence of significant dependence of diffusion coefficient versus surface coverage of obstacles φ , their aspect ratio ε and character of orientational ordering. For obstacles ideally oriented along the slab boundaries an increase of aspect ratio ε resulted in decrease of diffusion coefficient. It can be explained by formation of obstacle barriers for random walker movement. The similar effects were observed for randomly oriented obstacles. However, for elongated obstacles ideally oriented perpendicular to the slab boundaries the opposite effects were observed. It this case obstacles supported the diffusion flow from the slab and an increase of aspect ratio ε resulted in increase diffusion coefficient.