Random sequential adsorption of straight rigid rods on a simple cubic lattice

Abstract

Random sequential adsorption of straight rigid rods of length $k$ ($k$-mers) on a simple cubic lattice has been studied by numerical simulations and finite-size scaling analysis. The calculations were performed by using a new theoretical scheme, whose accuracy was verified by comparison with rigorous analytical data. The results, obtained for \textit{k} ranging from 2 to 64, revealed that (i) in the case of dimers ($k=2$), the jamming coverage is ${\theta }_j=0.918388(16)$. Our estimate of ${\theta }_j$ differs significantly from the previously reported value of ${\theta }_j=0.799(2)$ [Y. Y. Tarasevich and V. A. Cherkasova, Eur. Phys. J. B \textbf{60}, 97 (2007)]; (ii) ${\theta }_j$ exhibits a decreasing function when it is plotted in terms of the $k$-mer size, being ${\theta }_j(\infty )=0.4045(19)$ the value of the limit coverage for large $k$'s; and (iii) the ratio between percolation threshold and jamming coverage shows a non-universal behavior, monotonically decreasing with increasing $k$.

6 pages, 4 figures