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

Susana Marín-Aguilar; Fabrizio Camerin; Stijn van der Ham; Andréa Feasson; Hanumantha Rao Vutukuri; Marjolein Dijkstra

doi:10.1038/s41467-023-43722-0

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

Susana Marín-Aguilar, Fabrizio Camerin, Stijn van der Ham, Andréa Feasson, Hanumantha Rao Vutukuri, Marjolein Dijkstra

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	7896
Journal	Nature Communications
Volume	14
Issue number	1
DOIs	https://doi.org/10.1038/s41467-023-43722-0
Publication status	Published - 2023 Dec
Externally published	Yes

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title = "A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem",

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.",

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AU - Marín-Aguilar, Susana

AU - Camerin, Fabrizio

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AU - Feasson, Andréa

AU - Vutukuri, Hanumantha Rao

AU - Dijkstra, Marjolein

PY - 2023/12

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N2 - 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.

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

Abstract

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