With increasing particle number, entropy maximization has been identified as the driving force favoring the formation of icosahedral symmetry of spherical colloidal clusters 28, 39. Small numbers of nanoparticles and colloids pack into defined clusters with a wide variety of symmetries 17, 36, 37, 38. Temperature as the control variable for atomic cluster formation is then replaced by the packing fraction of the hard spheres 31, 32, 33, 34, 35. 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.
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. However, colloids can self-assemble into clusters by increasing short-range attraction 14, 15, 16, 17 or by applying geometric confinements 18, 19, 20, 21, 22, 23, 24, 25, 26. Colloids are initially stabilized against aggregation, which prevents them from aggregating in solution 12, 13. 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.
Atomic clusters therefore often possess complex geometries that differ from the typical face-centered cubic (FCC) bulk crystal structure 9, 10. This tendency provides a driving force to form clusters with closed, concentric shells, including the well-known Mackay icosahedra 8. Clusters with atom numbers that follow magic numbers show enhanced stability as a result of the maximized numbers of neighbors 5, 6, 7. Deviations from a pure statistical distribution of cluster sizes are also observed in the mass spectrum of small noble gas and metal clusters 3, 4.
#Magic engine 1.13 key series
Nucleons preferentially arrange into shells, which lead to the identification of the series of numbers that permit closed shells as magic numbers 1, 2. This first became apparent in the study of atomic nuclei. The structure of particle clusters is strongly affected by geometric constraints. Targeting similar magic number states is a strategy towards unique configurations in finite self-organizing systems across the scales.
#Magic engine 1.13 key free
A complex kinetic pathway is responsible for the efficiency of this system in finding its minimum free energy configuration.
Crucially, free energy calculations demonstrate that colloidal clusters with magic numbers possess higher thermodynamic stability than those off magic numbers. Colloidal particles in an emulsion droplet spontaneously organize into a series of clusters with precisely defined shell structures. Here we show that magic number clusters exist in a confined soft matter system with negligible interactions. To this point, magic number clusters have been exclusively found with attractive interactions as present between atoms. Certain numbers are termed ‘magic’ because they grant the system with closed shells and exceptional stability. 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.
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