Refreeze experiments of water droplets containing different
types of ice nuclei interpreted by classical nucleation theory
Authors: Kaufmann Lukas , Marcolli Claudia , Luo Beiping , Peter Thomas 
Published: November 2016

Abstract. Homogeneous nucleation of ice in supercooled water droplets is a stochastic process. In its classical description, the growth of the ice phase requires the emergence of a critical embryo from random fluctuations of water molecules between the water bulk and ice-like clusters, which is associated with overcoming an energy barrier. For heterogeneous ice nucleation on ice-nucleating surfaces both, stochastic and deterministic descriptions are in use. Deterministic (singular) descriptions are often favored because the temperature dependence of ice nucleation on a substrate usually dominates the stochastic time dependence, and the ease of representation facilitates the incorporation in climate models. Conversely, classical nucleation theory (CNT) describes heterogeneous ice nucleation as a stochastic process with a reduced energy barrier for the formation of a critical embryo in the presence of an ice-nucleating surface. This reduction is conveniently parameterized in terms of a contact angle α between the ice phase immersed in liquid water and the heterogeneous surface area. This study investigates various ice-nucleating agents in immersion mode by subjecting them to repeated freezing cycles to elucidate and discriminate the time and temperature dependences of heterogeneous ice nucleation. Freezing rates determined from such refreeze experiments are presented for Hoggar Mountain dust, birch pollen washing water and Arizona Test Dust (ATD) and nonadecanol coatings. For the analysis of the experimental data with CNT we assumed the same active site to be always responsible for freezing. Three different CNT-based parame-terizations were used to describe rate coefficients for heterogeneous ice nucleation as a function of temperature, all leading to very similar results: for Hoggar Mountain dust, ATD and larger nonadecanol coated water droplets, the experimentally determined increase of freezing rate with decreasing temperature is too shallow to be described properly by CNT using the contact angle as the only fit parameter. Birch pollen washing water and small nonadecanol coated water droplets show the reverse behavior with temperature dependencies of freezing rates steeper than predicted by CNT formulations. Good agreement of observations and calculations can be obtained when a prefactor β is introduced to the rate coefficient as second fit parameter. Thus, the following microphysical picture emerges: Heterogeneous freezing occurs on ice-nucleating sites that need a minimum (critical) surface area to host embryos of critical size to grow into a crystal. Fits based on CNT suggest that the critical active site area is in the range of 10–50 nm2 depending on sample, temperature, and CNT-based parameterization. Two fitting parameters are needed to characterize individual active sites. The contact angle lowers the energy barrier that has to be overcome to form the critical embryo on the site compared to the homogeneous case where the critical embryo develops in the volume of water. The prefactor β is needed to adjust the calculated slope of freezing rate increase with decreasing temperature to the measured one. When it is large, there are many nucleation attempts and nucleation occurs immediately when the temperature is low enough so that the active site can accommodate a critical embryo. This is the case for active sites of birch pollen washing water and the small droplets coated with nonadecanol. If the prefactor is low, the number of nucleation attempts is low and the increase of freezing rate with decreasing temperature is shallow. This is the case for Hoggar Mountain dust, the large droplets coated with nonadecanol, and ATD. Different hypotheses why the value of the prefactor depends on the nature of the active sites are discussed.