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

Susana Marín-Aguilar (), Fabrizio Camerin (), Stijn Ham, Andréa Feasson, Hanumantha Rao Vutukuri () and Marjolein Dijkstra ()
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Susana Marín-Aguilar: Utrecht University
Fabrizio Camerin: Utrecht University
Stijn Ham: University of Twente
Andréa Feasson: University of Twente
Hanumantha Rao Vutukuri: University of Twente
Marjolein Dijkstra: Utrecht University

Nature Communications, 2023, vol. 14, issue 1, 1-10

Abstract: Abstract 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.

Date: 2023
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DOI: 10.1038/s41467-023-43722-0

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