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

In a preceding paper, Šćepanović et al. [J.R. Šćepanović, I. Lončarević, Lj. Budinski-Petković, Z.M. Jakšić, 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 ρ p ∗ of more compact shapes exceeds the ρ p ∗ of elongated ones. At the lower densities of ρ p ∗ , 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 ρ p ∗ , 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 ρ c above the percolation threshold ρ p ∗ . In the case of k -mers, the critical density ρ c cannot be distinguished from the closest packing limit ρ C P L ⪅ 1 . For other objects, the critical density ρ c is usually below the jamming limit ρ j a m .