A physically constrained classical description of the homogeneous nucleation of ice in water

Abstract

Liquid water can persist in a supercooled state to below 238 K in the Earth's atmosphere, a temperature range where homogeneous nucleation becomes increasingly probable. However, the rate of homogeneous ice nucleation in supercooled water is poorly constrained, in part, because supercooled water eludes experimental scrutiny in the region of the homogeneous nucleation regime where it can exist only fleetingly. Here we present a new parameterization of the rate of homogeneous ice nucleation based on classical nucleation theory. In our approach, we constrain the key terms in classical theory, i.e., the diffusion activation energy and the ice-liquid interfacial energy, with physically consistent parameterizations of the pertinent quantities. The diffusion activation energy is related to the translational self-diffusion coefficient of water for which we assess a range of descriptions and conclude that the most physically consistent fit is provided by a power law. The other key term is the interfacial energy between the ice embryo and supercooled water whose temperature dependence we constrain using the Turnbull correlation, which relates the interfacial energy to the difference in enthalpy between the solid and liquid phases. The only adjustable parameter in our model is the absolute value of the interfacial energy at one reference temperature. That value is determined by fitting this classical model to a selection of laboratory homogeneous ice nucleation data sets between 233.6 K and 238.5 K. On extrapolation to temperatures below 233 K, into a range not accessible to standard techniques, we predict that the homogeneous nucleation rate peaks between about 227 and 231 K at a maximum nucleation rate many orders of magnitude lower than previous parameterizations suggest. This extrapolation to temperatures below 233 K is consistent with the most recent measurement of the ice nucleation rate in micrometer-sized droplets at temperatures of 227-232 K on very short time scales using an X-ray laser technique. In summary, we present a new physically constrained parameterization for homogeneous ice nucleation which is consistent with the latest literature nucleation data and our physical understanding of the properties of supercooled water. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

Temperature-dependent formation of NaCl dihydrate in levitated NaCl and sea salt aerosol particles

“…The diffusion activation energy is given by Figure 8(a)) not only reproduces the experimental data of Garbacz and Price but also follows the power law (PL) parameterization of Koop and Murray, 60 which was shown to provide the most physically consistent description of nucleation of ice in supercooled water. The applicability of this parameterization is limited to the temperature range above 225 K as shown by the deviation of our VFT curve and the PL curve below this temperature (compare red and blue solid lines in Figure 8(a)).…”

“…To do so, we had to develop a parameterization of water diffusivity based on the data published by Garbacz and Price. 58 To reduce the level of uncertainty associated with this parameterization, we constrained the parametrization by requiring it to follow the self-diffusivity of pure water recently made available for temperature range down to 220 K. 60 Nevertheless, the extrapolation of this parameterization beyond available experimental data should be treated with caution.…”

Size-dependent ice nucleation by airborne particles during dust events in the eastern Mediterranean

“…Cloud droplets can supercool to 238 K before homogeneous freezing occurs (Koop and Murray, 2016;Rosenfeld and Woodley, 2000). At warmer temperatures, heterogeneous ice nucleation (HIN), whereby the presence of aerosol particles lowers the required energy barrier to form a stable ice nucleus, is the common pathway of ice formation Pruppacher and Klett, 1997;Khvorostyanov and Curry, 2004;Hoose and Möhler, 2012).…”

Evaporating laminar microjets for studies of rapidly evolving structural transformations in supercooled liquids

“…for the development of more reliable climate models [13]. Despite their large uncertainties, the reported nucleation rates were significantly smaller than those expected on the basis of extrapolations of results from previous experiments [82]. These deviations were interpreted in terms of a crossover in the behaviour of the temperature dependence of water's diffusivity from non-Arrhenius to Arrhenius [79].…”