Abstract
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. Here we show that magic number clusters exist in a confined soft matter system with negligible interactions. Colloidal particles in an emulsion droplet spontaneously organize into a series of clusters with precisely defined shell structures. Crucially, free energy calculations demonstrate that colloidal clusters with magic numbers possess higher thermodynamic stability than those off magic numbers. A complex kinetic pathway is responsible for the efficiency of this system in finding its minimum free energy configuration. Targeting similar magic number states is a strategy towards unique configurations in finite self-organizing systems across the scales.
Highlights
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
Whereas the appearance and structure of atomic clusters are commonly explained by potential energy minimization, especially at low temperature[11], the formation of colloidal clusters is typically governed by several factors
We study the system sizedependent colloidal cluster formation in monodispersed droplets of an aqueous dispersion of polystyrene (PS) colloidal particles with different concentrations in a continuous oil phase produced by microfluidics (Supplementary Figure 1)
Summary
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. Phenomena that contribute to the development of colloidal clusters during a confined self-assembly process include the interaction of soft ligand shells[27], the presence of depletants[17], capillary forces acting on particles during the drying process[19], and entropy maximization[28]. The latter case is comparably easy to control in the experiment because it only requires weakly interacting colloids, which are described well via the simple hard sphere model[29,30]. Simulations and high-precision free energy calculations reproduce and explain the experimental observation
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