Random sequential adsorption of partially oriented linear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math>-mers on a square lattice

Abstract

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 256. The 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 one-dimensional systems. In particular, the jamming threshold tends to the R\'enyi'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 ($k\ensuremath{\leqslant}4$), denser configurations are observed in disordered systems as compared to those of completely ordered systems. However, longer $k$-mers exhibit the opposite behavior.