Irreversible deposition of directed self-avoiding random walks on a square lattice

Abstract

Random sequential adsorption of directed self-avoiding random walks of various lengths on a square lattice is studied by Monte Carlo simulations. Before each run through the system n random walks are made at random and they are deposited with equal probability. At the late stage of deposition, the approach to the jamming coverage is exponential for all the lengths of random walks and all numbers of components in the mixtures. The deposition rate increases with n and reaches a saturation value for high enough values of n. The jamming coverage asymptotically approaches the value for large number of components in the mixture, when n increases, and decreases exponentially with the length of random walks.