Random sequential adsorption of partially oriented linear $k$-mers on square lattice

Details Random sequential adsorption of partially oriented linear $k$-mers on square lattice Random sequential adsorption of partially oriented linear $k$-mers on square lattice

2011-09-15

arxiv.org/abs/1109.3271v1

Physical Review E 84, 061603 (2011)

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 12 figures

Scientific paper

10.1103/PhysRevE.84.061603

Jamming phenomena on a square lattice are investigated for two different models of anisotropic random sequential adsorption (RSA) of linear $k$-mers (particles occupying $k$ adjacent adsorption sites along a line). The length of a $k$-mer varies from 2 to 128. Effect of $k$-mer alignment on the jamming threshold is examined. For completely ordered systems where all the $k$-mers are aligned along one direction (e.g., vertical), the obtained simulation data are very close to the known analytical results for 1d systems. In particular, the jamming threshold tends to the R{\'e}nyi's Parking Constant for large $k$. In the other extreme case, when $k$-mers are fully disordered, our results correspond to the published results for short $k$-mers. It was observed that for partially oriented systems the jamming configurations consist of the blocks of vertically and horizontally oriented $k$-mers ($v$- and $h$-blocks, respectively) and large voids between them. The relative areas of different blocks and voids depend on the order parameter $s$, $k$-mer length and type of the model. For small $k$-mers ($k\leqslant 4$), denser configurations are observed in disordered systems as compared to those of completely ordered systems. However, longer $k$-mers exhibit the opposite behavior.

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