Jamming and percolation in generalized models of random sequential adsorption of linear $k$-mers on a square lattice

TL;DR

This study investigates how defects and contact restrictions affect jamming and percolation in models of random sequential adsorption of linear particles on a square lattice, revealing critical dependencies on particle length and defect concentration.

Contribution

It introduces two generalized RSA models incorporating defects and contact restrictions, analyzing their impact on percolation thresholds and jamming limits through Monte Carlo simulations.

Findings

Defects inhibit percolation for long $k$-mers even at low concentrations.

Percolation occurs only within a specific $k$ range depending on contact restrictions.

The maximum $k$ for percolation decreases with increasing forbidden contact fraction, following a logarithmic relation.

Abstract

The jamming and percolation for two generalized models of random sequential adsorption (RSA) of linear $k$-mers (particles occupying $k$ adjacent sites) on a square lattice are studied by means of Monte Carlo simulation. The classical random sequential adsorption (RSA) model assumes the absence of overlapping of the new incoming particle with the previously deposited ones. The first model LK$_d$ is a generalized variant of the RSA model for both $k$-mers and a lattice with defects. Some of the occupying $k$ adjacent sites are considered as insulating and some of the lattice sites are occupied by defects (impurities). For this model even a small concentration of defects can inhibit percolation for relatively long $k$-mers. The second model is the cooperative sequential adsorption (CSA) one, where, for each new $k$-mer, only a restricted number of lateral contacts $z$ with previously deposited $k$-mers is allowed. Deposition occurs in the case when $z\leq (1-d)z_m$ where $z_m=2(k+1)$ is the maximum numbers of the contacts of $k$-mer, and $d$ is the fraction of forbidden NN contacts. Percolation is observed only at some interval $k_{min}\leq k\leq k_{max}$ where the values $k_{min}$ and $k_{max}$ depend upon the fraction of forbidden contacts $d$. The value $k_{max}$ decreases as $d$ increases. A logarithmic dependence of the type $\log(k_{max})=a+bd$, where $a=-4.03 \pm 0.22$, $b=4.93 \pm 0.57 $, is obtained.