Classical nucleation theory of homogeneous freezing of water: thermodynamic and kinetic parameters

Abstract

The probability of homogeneous ice nucleation under a set of ambient conditions can be described by nucleation rates using the theoretical framework of Classical Nucleation Theory (CNT). This framework consists of kinetic and thermodynamic parameters, of which three are not well-defined (namely the interfacial tension between ice and water, the activation energy and the prefactor), so that any CNT-based parameterization of homogeneous ice formation is less well-constrained than desired for modeling applications. Different approaches to estimate the thermodynamic and kinetic parameters of CNT are reviewed in this paper and the sensitivity of the calculated nucleation rate to the choice of parameters is investigated. We show that nucleation rates are very sensitive to this choice. The sensitivity is governed by one parameter - the interfacial tension between ice and water, which determines the energetic barrier of the nucleation process. The calculated nucleation rate can differ by more than 25 orders of magnitude depending on the choice of parameterization for this parameter. The second most important parameter is the activation energy of the nucleation process. It can lead to a variation of 16 orders of magnitude. By estimating the nucleation rate from a collection of droplet freezing experiments from the literature, the dependence of these two parameters on temperature is narrowed down. It can be seen that the temperature behavior of these two parameters assumed in the literature does not match with the predicted nucleation rates from the fit in most cases. Moreover a comparison of all possible combinations of theoretical parameterizations of the dominant two free parameters shows that one combination fits the fitted nucleation rates best, which is a description of the interfacial tension coming from a molecular model [Reinhardt and Doye, J. Chem. Phys., 2013, 139, 096102] in combination with the activation energy derived from self-diffusion measurements [Zobrist et al., J. Phys. Chem. C, 2007, 111, 2149]. However, some fundamental understanding of the processes is still missing. Further research in future might help to tackle this problem. The most important questions, which need to be answered to constrain CNT, are raised in this study.

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

“…48 The Turnbull correlation relates the interfacial energy of a solid in its melt in the homogeneous nucleation regime to the change in enthalpy of the phase change ∆H m at the equilibrium melting temperature, 48 σ s,l (T hom ) ∝ ∆H m (T m ), and has sometimes been applied for deriving σ i,l in ice nucleation studies, e.g., Refs. 28, 49, and 50, see detailed discussion in Ickes et al 1 This relationship was originally derived for describing homogeneous nucleation of various metals from their melts, but it was shown to also work for alkali halides. 51 More recently, in a computational study of water and ice confined in nanopores, the Turnbull correlation was found to be consistent also in the supercooled range of water, revealing the same temperature dependence of σ i,l (T) and ∆H m (T), i.e., σ i,l (T)/∆H m (T) ≈ const.…”

“…1,56 In this study, we have selected a subset [56][57][58][59][60][61][62][63][64][65][66][67][68] of the available data sets for the purposes of constraining the new parameterization. The criteria for selection were (i) minimal and well defined uncertainties, (ii) good reproducibility within the data set, and (iii) an internal droplet pressure of about 1 bar.…”

“…In the past, it was common to represent homogeneous ice nucleation in atmospheric cloud models with a threshold function at which all droplets froze at either 233 K or 235 K (−40 • C or −38 • C, respectively), but in a recent study, it was shown that it is very important to represent the temperature dependence of homogeneous nucleation correctly and that homogeneous nucleation starts to strongly influence a cloud at temperatures as high as about 240 K, 8 a result that is supported by a recent theoretical analysis using a freezing-relaxation concept. 9 At present, there is a considerable divergence of parameterizations for homogeneous nucleation which produce significant differences in cloud models, 1,8 hence there is a clear need for an improved description of this critical and atmospherically highly relevant process.…”

“…1 Knowledge of ice nucleation kinetics is perhaps most important for the accurate description of ice particle formation in clouds arising in Earth's atmosphere. Clouds are sometimes observed to supercool to temperatures approaching and even below 238 K, 2-6 a temperature range where homogeneous ice nucleation becomes increasingly probable.…”

Ice crystal number concentration estimates from lidar-radar satellite remote sensing. Part 1: Method and evaluation

“…These relationships rely on strong assumptions that have shortcomings 25 (Grosvenor et al, 2018) but nonetheless provide N d values that compare well against in situ observations (Painemal and Zuidema, 2011) and can be used to establish climatologies (Bennartz and Rausch, 2017). Such relationships are less trivial for ice clouds due to the high complexity and variability of ice nucleation processes Lohmann, 2002, 2003;Ickes et al, 2015). Recent attempts have been made, e.g.…”