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

Abstract

The percolation aspect of random sequential adsorption of extended objects on a triangular lattice is studied by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps on the lattice. Jamming coverage θ{jam}, percolation threshold θ{p}, and their ratio θ{p}/θ{jam} are determined for objects of various shapes and sizes. We find that the percolation threshold θ{p} may decrease or increase with the object size, depending on the local geometry of the objects. We demonstrate that for various objects of the same length, the threshold θ{p} of more compact shapes exceeds the θ{p} of elongated ones. In addition, we study polydisperse mixtures in which the size of line segments making up the mixture gradually increases with the number of components. It is found that the percolation threshold decreases, while the jamming coverage increases, with the number of components in the mixture.

Percolation and jamming of random sequential adsorption samples of large lineark-mers on a square lattice

“…We have generalized the results of [16] for the case of periodic boundary conditions in Appendix A and have proved that, in thermodynamic limit, percolation always occurs before jamming. 14 and L = 1 638 400 for k > 2 14 . For k ≤ 2 14 a single calculation was performed, for k > 2 14 two independent runs were carried out, and the mean values of pc and pj are shown.…”

“…Naturally, jamming and percolation produced by means of the RSA of k-mers has been studied on other kinds of substrates, e.g., on triangular lattices [14,15]. A non-monotonic size dependence of the percolation threshold and decrease of the jamming coverage have also been observed on such triangular lattices [15].…”

Impact of defects on percolation in random sequential adsorption of lineark-mers on square lattices

“…The jamming and percolation of k-mers on disordered (or heterogeneous) substrates with defects (or impurities) has attracted great attention [14,[16][17][18][19][20][21][22][23][24]. A lattice with defects is built by randomly selecting a fraction of insulating monomers [14,21,24] or k-mers [19,20] which are considered forbidden for the succeeding deposition of any objects.…”

“…The jamming limits p j for the deposition of kmers onto a one-dimensional line and a two-dimensional disordered square lattice were calculated using the Monte Carlo method [17]. Note that the total jamming coverage (i.e., the value of p j +d) decreased when the concentration of impurities d increased and reached a minimum which depended on k [17,18]. For the problem of k-mer deposition onto a square lattice, it has been established that, upon increasing d, the percolation threshold p c grows up to a maximum value p m c (d m ), and that there is no percolation above d m [14,21,22].…”

“…A lattice with defects is built by randomly selecting a fraction of insulating monomers [14,21,24] or k-mers [19,20] which are considered forbidden for the succeeding deposition of any objects. The jamming limits p j for the deposition of kmers onto a one-dimensional line and a two-dimensional disordered square lattice were calculated using the Monte Carlo method [17].…”