A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 38036561.
- Also identified by DOI 10.1038/s41467-023-43722-0 and PMC identifier 10689752.
- Licence recorded as CC BY.
- The licence permits redistribution, so the abstract is shown in full and the full text is available from the publisher.
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.