Toward a Quantitative Theory of Ultrasmall Liquid Droplets and Vapor—Liquid Nucleation

Abstract

Thermodynamic properties of small systems can be drastically different from those corresponding to their macroscopic counterparts due to the surface and fluctuation effects. While the equations of state for macroscopic systems are well advanced, quantitative predictions of the structural and thermodynamic properties of small systems from a molecular perspective remain a daunting challenge. This article illustrates applications of a nonmean-field density functional theory to two types of ultrasmall liquid droplets: one is stabilized in a container of finite size and the other is unstable as appeared during vapor—liquid nucleation. For small systems of simple fluids represented by the Lennard-Jones model, theoretical predictions are compared with results from molecular simulations for the microscopic structure, the droplet size, and the free energy of formation over a broad range of conditions. The numerical agreement of theory with simulation data is comparable to that for the corresponding macroscopic systems. While the Tolman length, a correlation of curvature on surface tension, is negligible at least for small droplets of simple fluids, the vapor—liquid interfacial tension declines with the droplet size approximately proportional to the Gaussian curvature. Surprisingly, the Laplace equation for pressure change across a curved surface remains accurate even for a liquid droplet with the radius only a few times the molecular diameter.