Precise estimation of surface-layer monomer counts in nanoparticles

A number of distinct physicochemical features of nanoparticles are derived from their high surface-to-volume ratio, including aspects of reactivity, energetics, and thermodynamic properties. Conventional geometric principles fall short of accurately describing the crucial feature of the number of surface monomers, even in ideal systems. In this study, employing structural analyses on both spherical and faceted surfaces, we introduce a precise and adaptable expression to estimate surface-layer monomer counts in nanoclusters. The efficacy of this expression is established across a number of systems, both particles with undefined geometric arrangements of the constituent particles and those with specific geometric structures. The applicability of the approach is demonstrated by comparison with numerical simulations of van der Waals systems, liquid water clusters, and by reproducing scaling laws observed in ligand-protected gold nanoparticles. Moreover, it points to a reassessment of the magnitude of the surface free energy, which is of obvious importance in nucleation theory.