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^*

^*Corresponding author for this work

University of Twente

Research output: Contribution to journal › Article › Academic › 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
Number of pages	10
Journal	Nature Communications
Volume	14
Issue number	1
DOIs	https://doi.org/10.1038/s41467-023-43722-0
Publication status	Published - 30 Nov 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).

Funding

S.M.-A., F.C., and M.D. thank Gerardo Campos-Villalobos and Rodolfo Subert for early contributions to this work and for useful discussions. H.R.V. and S.v.d.H. thank Frieder Mugele and Mireille Claessens for kindly providing access to confocal and fluorescence microscopes. S.M.-A., F.C. and M.D. acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant agreement No. ERC-2019-ADG 884902, SoftML). S.M.-A. and M.D. acknowledge funding from the Netherlands Center for Multiscale Catalytic Energy Conversion (MCEC). F.C. and M.D. acknowledge funding from the World Premiere International (WPI) Research Center Initiative of the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT).

Funders	Funder number
Frieder Mugele and Mireille Claessens
MCEC
Netherlands Center for Multiscale Catalytic Energy Conversion
World Premiere International
Horizon 2020 Framework Programme	ERC-2019-ADG 884902
European Research Council
Ministry of Education, Culture, Sports, Science and Technology

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Cite this

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

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