Jammed systems of oriented needles always percolate on square lattices

Abstract

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.

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Cited by in corpus (9)

• Percolation and jamming of random sequential adsorption samples of large linear $k$-mers on a square lattice
• Jamming and percolation of $k^3$-mers on simple cubic lattices
• Random sequential adsorption on Euclidean, fractal and random lattices
• Jamming and percolation of $k^2$-mers on simple cubic lattices
• Two-dimensional systems of elongated particles: From diluted to dense
• Jamming and percolation of dimers in restricted-valence random sequential adsorption
• Percolation of aligned rigid rods on two-dimensional triangular lattices
• Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and nematic deposition/removal
• Jammed systems of oriented dimers always percolate on hypercubic lattices