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

TL;DR

This study investigates the random sequential adsorption of straight rods on a cubic lattice, revealing new estimates for jamming coverage and its dependence on rod length, using a novel theoretical approach validated by simulations.

Contribution

Introduces a new theoretical scheme for analyzing RSA of rods on cubic lattices, providing more accurate jamming coverage estimates and insights into size-dependent behavior.

Findings

Jamming coverage for dimers is approximately 0.9184.

Jamming coverage decreases with increasing rod length.

The ratio of percolation threshold to jamming coverage decreases monotonically with rod length.

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 $k$.