Homogeneous Ice Nucleation Rate in Water Droplets

Abstract

To predict the radiative forcing of clouds it is necessary to know the rate with which ice homogeneously nucleates in supercooled water. Such rate is often measured in drops to avoid the presence of impurities. At large supercooling small (nanoscopic) drops must be used to prevent simultaneous nucleation events. The pressure inside such drops is larger than the atmospheric one by virtue of the Laplace equation. In this work, we take into account such pressure raise in order to predict the nucleation rate in droplets using the TIP4P/Ice water model. We start from a recent estimate of the maximum drop size that can be used at each supercooling avoiding simultaneous nucleation events [Espinosa et al. J. Chem. Phys., 2016]. We then evaluate the pressure inside the drops with the Laplace equation. Finally, we obtain the rate as a function of the supercooling by interpolating our previous results for 1 and 2000 bar [Espinosa et al. Phys. Rev. Lett. 2016] using the Classical Nucleation Theory expression for the rate. This requires, in turn, interpolating the ice-water interfacial free energy and chemical potential difference. The TIP4P/Ice rate curve thus obtained is in good agreement with most droplet-based experiments. In particular, we find a good agreement with measurements performed using nanoscopic drops, that are currently under debate. The successful comparison between model and experiments suggests that TIP4P/Ice is a reliable model to study the water-to-ice transition and that Classical Nucleation Theory is a good framework to understand it.