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This work presents a generalized framework to assess the accuracy of methods to estimate primary and secondary nucleation rates from experimental data. The crystallization process of a well-studied model compound was simulated by means of a novel stochastic modeling methodology. Nucleation rates were estimated from the simulated data through multiple methods and were compared with the true values. For primary nucleation, no method considered in this work was able to estimate the rates accurately under general conditions. Two deterministic methods that are widely used in the literature were shown to overpredict rates in the presence of secondary nucleation. This behavior is shared by all methods that extract rates from deterministic process attributes, as they are insensitive to primary nucleation if secondary nucleation is sufficiently fast. Two stochastic methods were found to be accurate independent of whether secondary nucleation is present, but they underestimated rates in the case where a large number of primary nuclei are formed. We hence proposed a criterion to probe the accuracy of stochastic methods for arbitrary data sets, thus providing the theoretical foundations required for their rational use. Finally, we showed how both primary and secondary nucleation rates can be inferred from the same set of detection time data by combining deterministic and stochastic considerations.

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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.