Breakdown of Magic Numbers in Spherical Confinement.

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 relationships in finite clusters across different scales. However, as the system size increases, the significance of magic numbers diminishes, and the precise system size at which magic number phenomena disappear remains uncertain.

Early-stage bifurcation of crystallization in a sphere.

Bifurcations in kinetic pathways decide the evolution of a system. An example is crystallization, in which the thermodynamically stable polymorph may not form due to kinetic hindrance. Here, we use confined self-assembly to investigate the interplay of thermodynamics and kinetics in the crystallization pathways of finite clusters.

Coloration in Supraparticles Assembled from Polyhedral Metal-Organic Framework Particles.

Supraparticles are spherical colloidal crystals prepared by confined self-assembly processes. A particularly appealing property of these microscale structures is the structural color arising from interference of light with their building blocks. Here, we assemble supraparticles with high structural order that exhibit coloration from uniform, polyhedral metal-organic framework (MOF) particles.

Free Energy Landscape of Colloidal Clusters in Spherical Confinement.

The structure of finite self-assembling systems depends sensitively on the number of constituent building blocks. Recently, it was demonstrated that hard sphere-like colloidal particles show a magic number effect when confined in emulsion droplets. Geometric construction rules permit a few dozen magic numbers that correspond to a discrete series of completely filled concentric icosahedral shells.

Magic number colloidal clusters as minimum free energy structures.

Clusters in systems as diverse as metal atoms, virus proteins, noble gases, and nucleons have properties that depend sensitively on the number of constituent particles. Certain numbers are termed 'magic' because they grant the system with closed shells and exceptional stability. To this point, magic number clusters have been exclusively found with attractive interactions as present between atoms.