Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Several studies have recently conjectured that in the RSA of rectangular needles, or k-mers, on a square lattice the percolation is impossible if the needles are sufficiently long (k of order of several thousand). We refute these claims and present a strict proof that in any jammed configuration of nonoverlapping, fixed-length, horizontal or vertical needles on a square lattice, all clusters are percolating clusters.
@article{arxiv.1706.02550,
title = {Jammed systems of oriented needles always percolate on square lattices},
author = {Grzegorz Kondrat and Zbigniew Koza and Piotr Brzeski},
journal= {arXiv preprint arXiv:1706.02550},
year = {2017}
}