How Laplace pressure reshapes local structure: Voronoi analysis of water and argon droplets

Abstract

Curvature induces pressure differences across liquid–vapor interfaces and introduces corrections to surface tension that are described by classical thermodynamics in the macroscopic limit via the Tolman length. At the nanoscale, however, deviations from this behavior are difficult to interpret due to the nonlocal character of the stress tensor and the ambiguity in defining bulk phases. We address this by applying Voronoi tessellation to nanodroplets of argon and water to examine how curvature alters the local molecular structure. Unlike conventional density profiles—smeared out by capillary fluctuations—the Voronoi analysis yields a quasi-local geometric observable that can resolve curvature-induced changes in packing even near the molecular liquid surface. We find that inhomogeneity effects extend deep into the droplet interior. Using a simple classic thermodynamic framework to remap the droplet molecular volumes onto those of the flat interface, we find a collapse onto a single trend, suggesting that there are no specific curvature-induced changes beyond those implied by macroscopic thermodynamics. Remarkably, this collapse holds even for droplets smaller than those where classical approaches fail to extract a consistent Tolman length using local pressure tensor definitions.