Concerning Maximal Packing Arrangements of Binary Disk Mixtures Pdf | View in browser
O. U. Uche
Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA
F. H. Stillinger
Available online 2 July 2004. Physica A 342, 428-446 (2004).
The determination of the maximal packing arrangements of two-dimensional, binary hard disks of radii RS and RL (with RSRL) for sufficiently small RS amounts to finding the optimal arrangement of the small disks within a tricusp: the nonconvex cavity between three close-packed large disks. We present a particle-growth Monte Carlo algorithm for the generation of geometric packings of equi-sized hard disks within such a tricusp. The first 19 members of an infinite sequence of maximal density structures thus produced are reported. In addition, the Monte Carlo algorithm is applied to the geometric packing of disks within a flat-sided equilateral triangle and compared to published results for that packing problem. We perform an analysis of geometric properties of the packings, e.g. packing fractions and symmetries of structures confined to both containers. Interestingly, we find a non-monotonic increase in the packing fraction with increasing number of disks packed within both the flat-sided triangle and tricusp. It is important to note that for disk packings within a flat-sided equilateral triangle, this non-monotonic behavior of the packing fraction had not been reported in previously published works.
Author Keywords: Maximal packings; Binary hard-disk mixtures; Polydispersity; Rattlers; Tricusp; Packing fraction