Percolation in irreversible deposition on a triangular lattice: effects of anisotropy

Abstract

The percolation properties in anisotropic irreversible deposition of extended objects are studied by Monte Carlo simulations on a triangular lattice. Depositing objects of various shapes and sizes are made by directed self-avoiding walks on the lattice. Anisotropy is introduced by imposing unequal probabilities for placing the objects along different directions of the lattice. The degree of the anisotropy is characterized by the order parameter p determining the probability for deposition in the chosen (horizontal) direction. For each of the other two directions adsorption occurs with probability . It is found that the percolation threshold increases with the degree of anisotropy, having the maximum values for fully oriented objects. Percolation properties of the elongated shapes, such as k-mers, are more affected by the presence of anisotropy than the compact ones. Percolation in anisotropic deposition was also studied for a lattice with point-like defects. For elongated shapes a slight decrease of the percolation threshold with the impurity concentration d can be observed. However, for these shapes, significantly increases with the degree of anisotropy. In the case when depositing objects are triangles, results are qualitatively different. The percolation threshold decreases with d, but is not affected by the presence of anisotropy.

Percolation in random sequential adsorption of polydisperse mixtures of extended objects on a triangular lattice

“…For most real percolating systems, some important physical properties depend on the detailed geometry of the substrate and on the shape and size of the adsorbed particles. Consequently, more general percolation problems can be formulated by including irreversible random deposition of extended objects occupying more than one site on the lattice [18][19][20][21][22][23]. In random sequential adsorption (RSA) processes particles are randomly, sequentially and irreversibly deposited on an initially empty substrate or lattice with the restriction that they must not overlap with previously added objects [24][25][26][27].…”