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

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 $z\le (1-d)z_m$ 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 $k_{min}\le k\le k_{max}$ 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.

7 pages, 8 figures, 32 references

References in corpus (3)

• Percolation of linear $k$-mers on square lattice: from isotropic through partially ordered to completely aligned state
• Random sequential adsorption of partially oriented linear $k$-mers on square lattice
• Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattice

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• Influence of defects on the effective electrical conductivity of a monolayer produced by random sequential adsorption of linear $k$-mers onto a square lattice
• Two-dimensional systems of elongated particles: From diluted to dense
• Jamming and percolation of dimers in restricted-valence random sequential adsorption
• Generalized random sequential adsorption on Erdős-Rényi random graphs