English

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

Soft Condensed Matter 2023-06-26 v1

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 realization of the finite sphere packing problem by studying non-close-packed 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 56N7056\leq N \leq 70 spheres, excluding N=57N=57 and 63, that pack more efficiently than linear arrangements.

Keywords

Cite

@article{arxiv.2306.13377,
  title  = {A colloidal viewpoint on the finite sphere packing problem: the sausage catastrophe},
  author = {Susana Marín-Aguilar and Fabrizio Camerin and Stijn van der Ham and Andréa Feasson and Hanumantha Rao Vutukuri and Marjolein Dijkstra},
  journal= {arXiv preprint arXiv:2306.13377},
  year   = {2023}
}