Precise algorithm to generate random sequential adsorption of hard polygons at saturation

Abstract

Random sequential adsorption (RSA) is a time-dependent packing process, in which particles of certain shapes are randomly and sequentially placed into an empty space without overlap. In the infinite-time limit, the density approaches a "saturation" limit. Although this limit has attracted particular research interest, the majority of past studies could only probe this limit by extrapolation. We have previously found an algorithm to reach this limit using finite computational time for spherical particles and could thus determine the saturation density of spheres with high accuracy. In this paper, we generalize this algorithm to generate saturated RSA packings of two-dimensional polygons. We also calculate the saturation density for regular polygons of three to ten sides and obtain results that are consistent with previous, extrapolation-based studies.

Kinetics of random sequential adsorption of two-dimensional shapes on a one-dimensional line

“…In contrast to more popular random close packings, where neighboring particles are in touch, the RSA packings have well-defined mean packing fraction, which is an additional asset for numerical and theoretical studies [4,5]. However, only for some specific two-dimensional shapes, there exist algoritms, which generates saturated RSA packings [6][7][8][9][10][11] and estimation of the mean saturated packing fraction is straightforward. In general case, the knowledge about packing growth kinetics is needed because above described RSA protocol does not give any * michal.ciesla@uj.edu.pl † konrad.p.kozubek@gmail.com ‡ pkua.log@gmail.com § a.baule@qmul.ac.uk hint when packing become saturated and no other particle can be added to it.…”

Effective modelling of adsorption monolayers built of complex molecules

“…The algorithm is based on tracing regions where it is possible to place another molecule. A similar approach was applied previously for disks [19,20,21], as well as anisotropic shapes [24,25,23]. At the beginning, the molecule can be placed anywhere, so the region for molecule placement is equal to the whole packing surface.…”

“…These problems have already been solved for spherically symmetric molecules [19,20,21] and oriented rectangles [22]. Recently, it has been shown how to effectively produce RSA packings built of rectangles [23], polygons [24], ellipses, and spherocylinders [25]. Although it allows to model quite many types of adsorption monolayers these shapes do not cover the whole possible spectrum of complex molecules.…”

Random sequential adsorption of partially ordered discorectangles onto a continuous plane

“…The RSA simulations for disks gave a jamming coverage ϕ j = 0.547 ± 0.002 [29,30]. 2D saturated RSA packings of unoriented ellipses [31], squares [32], rectangles [33,34], discorectangles [35], polygons [36,37], sphere dimers, sphere polymers and other shapes [38][39][40] have been investigated. For all the studied problems, cusp-like maximums of jamming coverage at some aspect ratios (ε ≈ 1.7 − 1.9) were observed.…”