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

Abstract

The freezing of aqueous solutions is of great relevance to multiple fields, yet the kinetics of ice nucleation, its first step, remains poorly understood. The literature focuses on the freezing of microdroplets, and it is unclear if those findings can be generalized and extended to larger volumes such as those used in the freezing of biopharmaceuticals. To this end, we study ice nucleation from aqueous solutions of ten different compositions in vials at the milliliter scale. The statistical analysis of the approximately 6,000 measured nucleation events reveals that the stochastic ice nucleation kinetics is independent of the nature and concentration of the solute. We demonstrate this by estimating the values of the kinetic parameters in the nucleation rate expression for the selected solution compositions, and we find that a single set of parameters can describe quantitatively the nucleation behavior in all solutions. This holds regardless of whether the nucleation rate is expressed as a function of the chemical potential difference, of the water activity difference, or of the supercooling. While the chemical potential difference is the thermodynamically correct driving force for nucleation and hence is more accurate from a theoretical point of view, the other two expressions allow for an easier implementation in mechanistic freezing models in pharmaceutical manufacturing.