Relaxation properties in a diffusive model of extended objects on a triangular lattice

In a preceding paper, Scepanovic et al. [J.R. Scepanovic, I. Loncarevic, Lj. Budinski-Petkovic, Z.M. Jaksic, S.B. Vrhovac, Phys. Rev. E 84 (2011) 031109. http://dx.doi.org/10.1103/PhysRevE.84.031109] studied the diffusive motion of k-mers on the planar triangular lattice. Among other features of this system, we observed that the suppression of rotational motion results in a subdiffusive dynamics on intermediate length and time scales. We also confirmed that systems of this kind generally exhibit heterogeneous dynamics. Here we extend this analysis to objects of various shapes that can be made by self-avoiding random walks on a triangular lattice. We start by studying the percolation properties of random sequential adsorption of extended objects on a triangular lattice. We find that for various objects of the same length, the threshold ρp∗ of more compact shapes exceeds the ρp∗ of elongated ones. At the lower densities of ρp∗, the long-time decay of the self-intermediate scattering function (SISF) is characterized by the Kohlrausch–Williams–Watts law. It is found that near the percolation threshold ρp∗, the decay of SISF to zero occurs via the power-law for sufficiently low wave-vectors. Our results establish that power-law divergence of the relaxation time τ as a function of density ρ occurs at a shape-dependent critical density ρc above the percolation threshold ρp∗. In the case of k-mers, the critical density ρc cannot be distinguished from the closest packing limit ρCPL⪅1. For other objects, the critical density ρc is usually below the jamming limit ρjam.