Vapor pressure of water nanodroplets

Classical thermodynamics is assumed to be valid up to a certain length-scale, below which the discontinuous nature of matter becomes manifest. In particular, this must be the case for the description of the vapor pressure based on the Kelvin equation. However, the legitimacy of this equation in the nanoscopic regime can not be simply established, because the determination of the vapor pressure of very small droplets poses a challenge both for experiments and simulations. In this article we make use of a grand canonical screening approach recently proposed to compute the vapor pressures of finite systems from molecular dynamics simulations. This scheme is applied to water droplets, to show that the applicability of the Kelvin equation extends to unexpectedly small lengths, of only 1 nm, where the inhomogeneities in the density of matter occur within spatial lengths of the same order of magnitude as the size of the object. While in principle this appears to violate the main assumptions underlying thermodynamics, the density profiles reveal, however, that structures of this size are still homogeneous in the nanosecond time-scale. Only when the inhomogeneity in the density persists through the temporal average, as it is the case for clusters of 40 particles or less, do the macroscopic thermodynamics and the molecular descriptions depart from each other.