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Updated: Jul 9, 2025

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures
Published on: May 20, 2014
A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem
Susana Marín-Aguilar1, Fabrizio Camerin2,3, Stijn van der Ham4
1Soft Condensed Matter & Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, Utrecht, 3584 CC, Utrecht, The Netherlands. s.marinaguilar@uu.nl.
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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