Entropic Trapping of Hard Spheres in Spherical Confinement

TL;DR

This study uses simulations and free energy calculations to show how entropic forces cause large spheres to migrate and trap at the vertices of icosahedral clusters formed by hard spheres in spherical confinement.

Contribution

It demonstrates that entropic forces can drive large particles to specific cluster sites, leading to perfect icosahedral structures, and quantifies this process with free energy analysis.

Findings

Large spheres migrate to cluster surface due to entropic forces.

Addition of twelve large spheres forms a perfect icosahedral frame.

Free energy calculations confirm trapping at vertices with multiple kBT.

Abstract

Monodisperse spherical colloidal particles confined within emulsion droplets can crystallize into icosahedral clusters. Experimentally it was observed that a few large colloidal particles added as defects preferentially migrate to the vertices of the icoshedral clusters. To understand this structure formation phenomenon, we simulate the confined self-assembly of hard spheres in the presence of a small number of larger particles. The results demonstrate that large spheres are significantly influenced by concentric shells of small spheres near the crystallization transition. Entropic forces drive the large spheres to the cluster surface, where they settle into free energy minima at the icosahedron vertices. Notably, the addition of twelve large spheres results in the formation of a perfect icosahedral frame. Free energy calculations via umbrella sampling are used to quantify this process and show that both the migration to the cluster surface and the trapping at the vertices with trapping strength of multiple $k_\text{B}T$ results from free energy minimization. Moreover, our study reveals that the crystallization pathway and dynamics of large spheres are consistent across different systems, suggesting robustness of entropic trapping.