Performance of some nucleation theories with a nonsharp droplet-vapor interface

Investigating the significance of zero-point motion in small molecular clusters of sulphuric acid and water

The nucleation of particles from trace gases in the atmosphere is an important source of cloud condensation nuclei, and these are vital for the formation of clouds in view of the high supersaturations required for homogeneous water droplet nucleation. The methods of quantum chemistry have increasingly been employed to model nucleation due to their high accuracy and efficiency in calculating configurational energies; and nucleation rates can be obtained from the associated free energies of particle formation. However, even in such advanced approaches, it is typically assumed that the nuclei have a classical nature, which is questionable for some systems. The importance of zero-point motion (also known as quantum nuclear dynamics) in modelling small clusters of sulphuric acid and water is tested here using the path integral molecular dynamics method at the density functional level of theory. The general effect of zero-point motion is to distort the mean structure slightly, and to promote the extent of proton transfer with respect to classical behaviour. In a particular configuration of one sulphuric acid molecule with three waters, the range of positions explored by a proton between a sulphuric acid and a water molecule at 300 K (a broad range in contrast to the confinement suggested by geometry optimisation at 0 K) is clearly affected by the inclusion of zero point motion, and similar effects are observed for other configurations.

Excess equimolar radius of liquid drops

The curvature dependence of the surface tension is related to the excess equimolar radius of liquid drops, i.e., the deviation of the equimolar radius from the radius defined by the macroscopic capillarity approximation. Based on the Tolman [J. Chem. Phys. 17, 333 (1949)] approach and its interpretation by Nijmeijer et al. [J. Chem. Phys. 96, 565 (1991)], the surface tension of spherical interfaces is analyzed in terms of the pressure difference due to curvature. In the present study, the excess equimolar radius, which can be obtained directly from the density profile, is used instead of the Tolman length. Liquid drops of the truncated and shifted Lennard-Jones fluid are investigated by molecular dynamics simulation in the canonical ensemble, with equimolar radii ranging from 4 to 33 times the Lennard-Jones size parameter σ. In these simulations, the magnitude of the excess equimolar radius is shown to be smaller than σ/2. This suggests that the surface tension of liquid drops at the nanometer length scale is much closer to that of the planar vapor-liquid interface than reported in studies based on the mechanical route.