Breakdown of Magic Numbers in Spherical Confinement

TL;DR

This paper investigates how magic numbers, which are specific system sizes with low free energy configurations, break down in larger colloidal clusters under spherical confinement, revealing a transition to football-shaped structures.

Contribution

It introduces a sphere packing model explaining the disappearance of magic numbers beyond a critical system size in confined colloidal clusters.

Findings

Magic number configurations are stable in small clusters with icosahedral symmetry.

Beyond a critical size, closed surface shells no longer form, reducing free energy minima.

Large clusters form football-shaped structures with lower-coordinated facets.

Abstract

Magic numbers in finite particle systems correspond to specific system sizes that allow configurations with low free energy, often exhibiting closed surface shells to maximize the number of nearest neighbors. Since their discovery in atomic nuclei, magic numbers have been essential for understanding the number-structure-property relationship in finite clusters across different scales. However, as system size increases, the significance of magic numbers diminishes, and the precise system size at which magic number phenomena disappear remains uncertain. In this study, we investigate colloidal clusters formed through confined self-assembly. Small magic number clusters display icosahedral symmetry with closed surface shells, corresponding to pronounced free energy minima. Our findings reveal that beyond a critical system size, closed surface shells disappear, and free energy minima become less pronounced. Instead, we observe a distinct type of colloidal cluster, termed football cluster, which retains icosahedral symmetry but features lower-coordinated facets disconnected by terraces. A sphere packing model demonstrates that forming closed surface shells becomes impossible beyond a critical system size, explaining the breakdown of magic numbers in large confined systems.