Characterizing and measuring the ice nucleation kinetics of aqueous solutions in vials

Thermodynamics Explains How Solution Composition Affects the Kinetics of Stochastic Ice Nucleation

“…First, freezing experiments have to be carried out under well-controlled conditions to ensure that the experimentally observed variability in nucleation temperatures is indeed dominated by the stochastic nature of nucleation and not by experimental error. Doing so is challenging at all scales; , the instrument we use here allows for highly automated, long-term freeze–thaw experiments. We achieve a temperature accuracy of about ±0.15 K that we consider sufficient compared to the width of the measured nucleation temperature distributions, which is on the order of 5–7 K. Second, the experimental data set must comprise nucleation temperatures both from a large number of vials and from a large number of freeze–thaw cycles: a single experiment hence comprises 12 freeze–thaw cycles in 15 vials, amounting to 180 nucleation events.…”

“…The temperature-independent prefactors k μ , k a , and k T are vial-specific constants with values that are log-norm distributed across vials; their negative decadic logarithm assumes a mean value of a μ , a a , or a T and a standard deviation of c μ , c a , or c T , respectively. Such a distributed parameter is required to account for the experimentally observed variability in nucleation sites among vials. ,,,, To keep the notation simple, subscripts for J and the associated kinetic parameters are used only when referring to a specific rate expression. While more complex rate expressions could be used to describe the nucleation kinetics, such as those based on the classical nucleation theory (CNT), ,, we refrained from doing so: as we discuss below, all three power law expressions well describe the experimental data, so that more complex models would provide little benefit.…”

“…16−18 Still, mechanistic descriptions of ice nucleation in models for the freezing of these products have become available only recently. 13,17,19 This is largely because research on ice nucleation has traditionally been driven by the atmospheric sciences. 20−23 To mimic the properties of cloud droplets, freezing experiments have been predominantly carried out in microdroplets.…”

Conceptual Validation of Stochastic and Deterministic Methods To Estimate Crystal Nucleation Rates

“…We highlight that such averaging is inaccurate under two conditions. First, in the case of heterogeneous nucleation, nucleation events are enabled by nucleation sites on external surfaces. , These sites, however, may be distributed arbitrarily within the system. , Since external surfaces such as crystallizer walls may also act as nucleation sites, the primary nucleation frequency may not scale linearly with volume in real processes. , Second, process conditions may vary within the volume; thermal gradients and hydrodynamic variabilities may be present and may alter the local nucleation rate. , …”

“…Primary nucleation is an activated process, and therefore, it is stochastic. ,,− Repetitions of a crystallization experiment under identical conditions hence exhibit a certain degree of variability. Conceptually, one may infer the primary nucleation kinetics by linking the experimental variability to the inherent stochasticity of nucleation. ,,, During a crystallization process, all crystals nucleate in a stochastic manner, whereby earlier nucleation events affect later ones in two ways: first, nuclei deplete supersaturation via crystal growth, and second, they provide active sites for secondary nucleation.…”