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This work simulates the self-assembly of hard spheres within spherical confinement, introducing larger particles to mimic defects observed in colloidal crystallization experiments. Simulations reveal that entropic forces drive the larger spheres to the surface of the forming icosahedral clusters, specifically trapping them at the vertices. Free energy calculations using umbrella sampling confirm that this trapping, with a strength of multiple k_{B}T, results from free energy minimization, suggesting a robust mechanism for directing particle assembly.
Entropic forces can be harnessed to precisely direct the self-assembly of colloidal structures, trapping larger "defect" particles at specific locations within icosahedral clusters.
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 icosahedral 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_{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.