Saturated random packing built of arbitrary polygons under random sequential adsorption protocol

Abstract

Random packings and their properties are a popular and active field of research. Numerical algorithms that can efficiently generate them are useful tools in their study. This paper focuses on random packings produced according to the random sequential adsorption (RSA) protocol. Developing the idea presented in [G. Zhang, Phys. Rev. E 97, 043311 (2018)], where saturated random packings built of regular polygons were studied, we create an algorithm that generates strictly saturated packings built of any polygons. Then, the algorithm was used to determine the packing fractions for arbitrary triangles. The highest mean packing density, 0.552814 ± 0.000063, was observed for triangles of side lengths 0.63 : 1 : 1. Additionally, microstructural properties of such packings, kinetics of their growth as well as distributions of saturated packing fractions and the number of RSA iterations needed to reach saturation were analyzed.

Random sequential adsorption of rounded rectangles, isosceles and right triangles

“…The arm-to-base ratios for rounded isosceles triangles corresponding to local maxima of packing densities are approximately 1.87 and 0.66 for x = 1.4, r = 0.5 and x = 0.6, r = 0.3, respectively. Comparing these values with those reported for the densest RSA packings built of isosceles triangles (1.31, and 0.63) [23], we see that the smaller maximum is reached for almost the same but rounded triangle, while the global one is observed for a significantly more anisotropic shape. It confirms the reasoning that from the perspective of the densest RSA configurations, the optimal anisotropy is a result of the competition between a low value of the area blocked by a single object, described by the parameter B 2 , and a large elongation forcing neighboring figures to align in parallel.…”

“…The simulation ends where there are no voxels left, thus, the packing is saturated. A variant of this method for polygons was invented by Zhang [19] and improved further in [20] and the details about the voxel removal criterion can be found there. Although in its original version, this method was designed for the generation of saturated packings built of arbitrarily oriented polygons, its restriction to a single orientation is straightforward.…”

“…The highest mean density for RSA packings built of rectangles is 0.549632 (17), and it is reached for the shape with the width-to-height ratio around 1.49 [22], and for triangles it is 0.552814(63), where the side length ratio of an optimal shape is 1 : 1 : 0.63 [23]. The highest known RSA mean packing fraction among two-dimensional shapes was observed for ellipses 0.583999 (17) and was obtained for the figure with the semi-axes ratio of 1.84 [12].…”

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.…”

Random sequential adsorption on non-simply connected surfaces

“…Presently, this field of study seems to have several paradigms, one of them is the study of systems with dimensions greater than or equal to two, in two dimensions highlighting e.g. the works of Zhang [14], Cieśla [15] in the context of adsorption of hard polygons.…”