The tailored design of nanoparticles becomes more important with the advancement of heterogeneous catalysis and materials science. The formation of nanoparticles in catalysts with a specific geometry of the active site becomes necessary to improve activity and selectivity in catalysis. Here we have used physical sphere-in-contact models of various nanoparticles with hexagonal, square and trigonal geometries on flat close-packed surfaces to understand how the distribution of (100) and (111) sites changes as a function of nanoparticle (NP) size in a simplified model of nanoparticle supported metals. The results from this approach clearly show that in 2-layer NPs that have a hexagonal base have 2–3 times more (100) sites than the square and trigonal base NPs as a function of the number of atoms in the NP. In 3D isotropic NPs, this phenomenon is even more pronounced than the 2-layer NPs. We derive equations that estimate the number of (100), (111), the number of atoms and the aspect ratio as a function of n. These equations are important in tailoring the properties of NPs supported on close-packed metal surfaces, which may find applications in materials science, nanotechnology and catalysis.
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