Random sequential adsorption of rounded rectangles, isosceles and right triangles

Abstract

We have studied random sequential adsorption (RSA) of three classes of polygons with rounded corners: rectangles, isosceles triangles and orthogonal triangles. Using the algorithm that allows generating strictly saturated random packing, we have systematically determined the mean saturated packing fraction for RSA configurations built by these shapes. The main aim was to find out the figure that forms the densest random configuration. Although for rounded rectangles the packing fractions were lower than for discorectangles, the densities reached for some rounded isosceles and right triangles exceed the highest known two-dimensional packing fraction for configurations built of unoriented monodispersive objects. The microstructural properties of several packings were discussed in terms of the two-point density autocorrelation function.

Optimal shapes of disk assembly in saturated random packings

“…17 We also report the densest known SRP density of 0.5921 AE 0.0006 in the family of COD (n = 5), whose shape bears significant resemblance with the optimal shape given by the family of rounded isosceles triangles. 68 For the minimal SRP density, similar configurations and dependence of f min s on n to CTD can be found for ITD and COD. As expected, for COD, no overlapping pairs are presented and the species just degenerates into CTD, while the size dispersity in constituent disks contributes to a lower packing efficiency of unclosed ring-like shapes.…”

“…17 We also report the densest known SRP density of 0.5921 ± 0.0006 in the family of COD ( n = 5), whose shape bears significant resemblance with the optimal shape given by the family of rounded isosceles triangles. 68…”

“…The maximal SRP density in 2D was reported for ellipses with a density of around 0.58405, 18 and the recent result of rounded isosceles triangles yielded an even higher value of f s of B0.600619. 68 Accordingly, one aim of this study is to find the optimal particle shape via the disk assembly model which gives a higher SRP density than previously found. However, it is infeasible to traverse a category of shapes in locating the global maxima of saturated packing density f s , thus making the above evolutionary strategies a promising new research scheme for material design.…”

“…The maximal f s is reported here as 0.6025 AE 0.0003, much higher than those of ellipses (B0.58405) and spherocylinders in 2D (B0.58281), 18 and is comparable to the highest value of rounded isosceles triangles around 0.600619. 68 We begin this paper by introducing the ''blueprint'' method and the genotype representation concerned with the disk assembly model in Section 2. This is followed by detailed elaborations of the packing generation protocol, e.g., the RSA process and GA methods.…”

“…The maximal ϕ s is reported here as 0.6025 ± 0.0003, much higher than those of ellipses (∼0.58405) and spherocylinders in 2D (∼0.58281), 18 and is comparable to the highest value of rounded isosceles triangles around 0.600619. 68…”