Direct Measurements of Primary Nucleation Rates of p-Aminobenzoic Acid and Glutamic Acid and Comparison with Predictions from Induction Time Distributions

Rapid Assessment of Crystal Nucleation and Growth Kinetics: Comparison of Seeded and Unseeded Experiments

In this work, we outlined an experimental workflow enabling the rapid assessment of primary and secondary nucleation and crystal growth kinetics. We used small-scale experiments in agitated vials with in situ imaging for crystal counting and sizing to quantify nucleation and growth kinetics of α-glycine in aqueous solutions as a function of supersaturation at isothermal conditions. Seeded experiments were required to assess crystallization kinetics when primary nucleation is too slow, especially at lower supersaturations often encountered in continuous crystallization processes. At higher supersaturations, we compared results from seeded and unseeded experiments and carefully analyzed interdependencies of primary and secondary nucleation and growth kinetics. This approach allows for the rapid estimation of absolute values of primary and secondary nucleation and growth rates without relying on any specific assumptions about functional forms of corresponding rate expressions used for estimation approaches based on fitting population balance models. Quantitative relationships between nucleation and growth rates at given conditions provide useful insights into crystallization behavior and can be explored to rationally manipulate crystallization conditions for achieving desirable outcomes in batch or continuous crystallization processes.

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

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.

Online Monitoring of the Concentrations of Amorphous and Crystalline Mesoscopic Species Present in Solution

Despite the growing evidence for the existence of amorphous mesoscopic species in a solution and their crucial roles in crystallization, there has been the lack of a suitable method to measure the time-resolved concentrations of amorphous and crystalline mesospecies in a lab-scale stirred reactor. This has limited experimental investigations to understand the kinetics of amorphous and crystalline mesospecies formation in stirred solutions and made it challenging to measure the crystal nucleation rate directly. Here, we used depolarized light sheet microscopy to achieve time-resolved measurements of amorphous and crystalline mesospecies concentrations in solutions at varying temperatures. After demonstrating that the concentration measurement method is reasonably accurate, precise, and sensitive, we utilized this method to examine mesospecies formation both in a mixture of two miscible liquids and in an undersaturated solution of dl-valine, thus revealing the importance of a temperature change in the formation of metastable and amorphous mesospecies as well as the reproducibility of the measurements. Moreover, we used the presented method to monitor both mesospecies formation and crystal nucleation in dl-valine solutions at four different levels of supersaturation, while achieving the direct measurement of the crystal nucleation rates in stirred solutions. Our results show that, as expected, the inherent variability in nucleation originating from its stochastic nature reduces with increasing supersaturation, and the dependence of the measured nucleation rate on supersaturation is in reasonable agreement with that predicted by the classical nucleation theory.

Accounting for the Presence of Molecular Clusters in Modeling and Interpreting Nucleation and Growth

The effect of molecular cluster formation on the estimation of kinetic parameters for primary nucleation and growth in different systems has been studied using computationally generated data and three sets of experimental data in the literature. It is shown that the formation of molecular clusters decreases the concentration of monomers and hence the thermodynamic driving force for crystallization, which consequently affects the crystallization kinetics. For a system exhibiting a strong tendency to form molecular clusters, accounting for cluster formation in a kinetic model is critical to interpret kinetic data accurately, for instance, to estimate the specific surface energy γ from a set of primary nucleation rates. On the contrary, for a system with negligible cluster formation, a consideration of cluster formation does not affect parameter estimation outcomes. Moreover, it is demonstrated that using a growth kinetic model that accounts for cluster formation allows the estimation of γ from typical growth kinetic data (i.e., de-supersaturation profiles of seeded batch crystallization), which is a novel method of estimating γ developed in this work. The applicability of the novel method to different systems is proven by showing that the estimated values of γ are closely comparable to the actual values used for generating the kinetic data or the corresponding estimates reported in the literature.

Isothermal Crystallization and Time-Temperature Transformation of Amorphous Nifedipine: A Case of Polymorphism Formation and Conversion

Crystallization of active pharmaceutical ingredients (APIs) from the supercooled liquid state is an important issue in determining the stability of amorphous pharmaceutical dispersions. In the present study, the isothermal crystallization from the supercooled liquid state of the pharmaceutical compound nifedipine was investigated by both rheological and differential scanning calorimetry (DSC) measurements, and the crystallization kinetics was fitted to the Johnson-Mehl-Avrami (JMA) equation. Both the crystallization induction time and completion time from the two methods were used to construct the time-temperature-transformation (TTT) diagram for nifedipine. A model based on a modification of classical homogeneous nucleation and crystal growth theory was employed to fit the induction and completion time curves. Both DSC and rheological methods give similar results for the crystallization kinetics of the nifedipine. From the crystallization kinetics modeling, the solid-liquid interfacial surface tension σ_SL of nifedipine was estimated and the value was found to be consistent with prior results obtained from melting point depression measurements as a function of crystal size. Evidence is shown that for temperatures below 110 °C, at the early stage of nucleation, NIF first nucleates into the metastable β'-form and later converts into the stable α-form during the isothermal crystallization. We are also able to report the heat of fusion of the γ'-NIF based on the calorimetric experiments.