A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem

S Marin-Aguilar and F Camerin and S van der Ham and A Feasson and HR Vutukuri and M Dijkstra, NATURE COMMUNICATIONS, 14, 7896 (2023).

DOI: 10.1038/s41467-023-43722-0

It is commonly believed that the most efficient way to pack a finite number of equal-sized spheres is by arranging them tightly in a cluster. However, mathematicians have conjectured that a linear arrangement may actually result in the densest packing. Here, our combined experimental and simulation study provides a physical realization of the finite sphere packing problem by studying arrangements of colloids in a flaccid lipid vesicle. We map out a state diagram displaying linear, planar, and cluster conformations of spheres, as well as bistable states which alternate between cluster-plate and plate-linear conformations due to membrane fluctuations. Finally, by systematically analyzing truncated polyhedral packings, we identify clusters of 56 <= N <= 70 number of spheres, excluding N = 57 and 63, that pack more efficiently than linear arrangements. Packing a finite number of spheres in a compact cluster does not always result in the densest packing. Here, the authors provide a physical realization of the finite sphere packing problem by enclosing colloids in a flaccid lipid vesicle and mapping out a state diagram that displays linear, planar, and cluster conformations of spheres, as well as bistable states that alternate between cluster-plate and plate-linear conformations.

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