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

TL;DR

This study investigates how the orientation and length of linear particles affect the jamming threshold in a square lattice, revealing different behaviors for ordered and disordered systems across various $k$-mer lengths.

Contribution

It provides new simulation data on partially oriented $k$-mers, bridging the gap between ordered and disordered RSA models and analyzing the impact of orientation on jamming configurations.

Findings

Jamming threshold approaches R{\'e}nyi's Parking Constant for large $k$ in ordered systems.

Disordered systems show denser configurations for small $k$, while longer $k$-mers form less dense arrangements.

Jamming configurations consist of oriented blocks and voids, with their proportions depending on the order parameter and $k$-mer length.

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 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.