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.

In this study, the solid-vapor equilibrium and the quasi liquid layer (QLL) of ice Ih exposing the basal and primary prismatic faces were explored by means of grand canonical molecular dynamics simulations with the monatomic mW potential. For this model, the solid-vapor equilibrium was found to follow the Clausius-Clapeyron relation in the range examined, from 250 to 270 K, with a Δ H of 50 kJ/mol in excellent agreement with the experimental value. The phase diagram of the mW model was constructed for the low pressure region around the triple point. The analysis of the crystallization dynamics during condensation and evaporation revealed that, for the basal face, both processes are highly activated, and in particular cubic ice is formed during condensation, producing stacking-disordered ice. The basal and primary prismatic surfaces of ice Ih were investigated at different temperatures and at their corresponding equilibrium vapor pressures. Our results show that the region known as QLL can be interpreted as the outermost layers of the solid where a partial melting takes place. Solid islands in the nanometer length scale are surrounded by interconnected liquid areas, generating a bidimensional nanophase segregation that spans throughout the entire width of the outermost layer even at 250 K. Two approaches were adopted to quantify the QLL and discussed in light of their ability to reflect this nanophase segregation phenomena. Our results in the μVT ensemble were compared with NPT and NVT simulations for two system sizes. No significant differences were found between the results as a consequence of model system size or of the working ensemble. Nevertheless, certain advantages of performing μVT simulations in order to reproduce the experimental situation are highlighted. On the one hand, the QLL thickness measured out of equilibrium might be affected because of crystallization being slower than condensation. On the other, preliminary simulations of AFM indentation experiments show that the tip can induce capillary condensation over the ice surface, enlarging the apparent QLL.