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The nucleation of ice from aqueous solutions is a process essential to myriad environmental and industrial processes, but the physical factors affecting the capacity of different solutes to depress the homogeneous nucleation temperature of ice are yet poorly understood. In this work, we demonstrate that for many binary aqueous solutions of non-ionic solutes, this depression is dominated by the entropy of the liquid phase. Employing the classic Turnbull interpretation of the interfacial free energy γ∼TSliquid−Ssolid and estimating solution entropies with a Flory-style modification of the ideal entropy of mixing that accounts for solute size effects, we demonstrate that mixing entropy alone predicts experimental homogeneous nucleation temperatures across a wide variety of non-ionic solutions. We anticipate that this physical insight will not only enhance a fundamental understanding of homogeneous nucleation processes across fields but also open new avenues to the rational design of aqueous solutions for desired nucleation behaviors. 

The propensity of water to remain in a metastable liquid state at temperatures below its equilibrium melting point holds significant potential for cryopreserving biological material such as tissues and organs. The benefits conferred are a direct result of progressively reducing metabolic expenditure due to colder temperatures while simultaneously avoiding the irreversible damage caused by the crystallization of ice. Unfortunately, the freezing of water in bulk systems of clinical relevance is dominated by random heterogeneous nucleation initiated by uncharacterized trace impurities, and the marked unpredictability of this behavior has prevented the implementation of supercooling outside of controlled laboratory settings and in volumes larger than a few milliliters. Here, we develop a statistical model that jointly captures both the inherent stochastic nature of nucleation using conventional Poisson statistics as well as the random variability of heterogeneous nucleation catalysis through bivariate extreme value statistics. Individually, these two classes of models cannot account for both the time-dependent nature of nucleation and the sample-to-sample variability associated with heterogeneous catalysis, and traditional extreme value models have only considered variations of the characteristic nucleation temperature. We conduct a series of constant cooling rate and isothermal nucleation experiments with physiological saline solutions and leverage the statistical model to evaluate the natural variability of kinetic and thermodynamic nucleation parameters. By quantifying freezing probability as a function of temperature, supercooled duration, and system volume while accounting for nucleation site variability, this study also provides a basis for the rational design of stable supercooled biopreservation protocols.