An extreme value statistics model of heterogeneous ice nucleation for quantifying the stability of supercooled aqueous systems

Abstract

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.