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.

https://pubs.acs.org/doi/pdf/10.1021/acs.cgd.2c01406

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

A synthetic machine learning framework for complex crystallization processes: the case study of the second-order asymmetric transformation of enantiomers

Despite the ubiquity of the crystallization of sodium chloride (NaCl) throughout history, few detailed, well-controlled quantitative studies of the kinetics of NaCl crystallization have been published. Taking advantage of recent advances in technology such as image analysis for crystallite counting and ‘high-throughput’ techniques for characterizing the highly stochastic nucleation process, we report on a detailed examination of the primary and secondary nucleation kinetics of NaCl, crystallized from solution, in water (H2O) and in the isotopologue D2O. We show that crystallization conditions, especially sample agitation, have a very significant effect on crystallization kinetics. We also critically evaluate the workflow employed and the associated nucleation/growth models used to interpret its results, comparing outcomes from NaCl with those from organic crystal systems with which the workflow was originally developed and demonstrated. For primary nucleation, some key assumptions of the workflow and data interpretation are called into question for the NaCl system. Even so, it can still provide direct measurements of secondary nucleation and crystal growth from crystal counting and sizing, providing valuable characterization under consistent controlled conditions to enhance and ‘bring up to date’ the literature on the crystallization of this ubiquitous system.

Nucleation and Growth Kinetics of Sodium Chloride Crystallization from Water and Deuterium Oxide

The effect of fluid shear on the primary nucleation of paracetamol in water, isopropyl alcohol, and acetonitrile was investigated. First, experiments were performed with a Taylor–Couette crystallizer. For all three solvents, a comparable effect of fluid shear on the nucleation kinetics was found: increasing fluid shear results in an increase in the nucleation rate and a decrease in the variability of the induction times. The experimental analysis shows that the mean induction times are dependent on the energy dissipation rate to a power of approximately −1/3. A comparative investigation for paracetamol crystallization in stirred batch crystallizers revealed the same dependence of mean induction times on the energy dissipation rate. Extending this analysis to experimental data sets from the literature confirms this further. To find a physical meaning for this dependency, the results are interpreted in terms of the shear-enhanced mass transfer and shear-enhanced cluster aggregation theories. 

Unraveling the Role of Fluid Shear on Primary Nucleation of Paracetamol through an Energy-Dissipation Rate Analysis

Crystal nucleation is crucial in various fields of science and technology, ranging from materials synthesis to pharmaceutical production. Our research aims to determine the nucleation rates from parallel induction time measurement experiments followed by low-cost external bulk video imaging. Stirred conditions are applied, making our results industry-relevant where the crystallizers are also mixed. The L-Glutamic Acid-water system (L-GA/water) is used as a surrogate. The study is conducted through a series of parallel, small-scale stirred experiments that explore the effects of supersaturation, temperature, and polymer additives on nucleation rates. The methodology involves careful data collection through controlled experimental setup and analysis of induction time distributions that the stochastic nature of nucleation explains the induction time distribution. The discussion section interprets the findings within the context of the research question, highlighting the implications of varying temperature and supersaturation levels as two experimental parameters and polymers on crystal nucleation rates. The specific parameters of supersaturation and temperature dependencies are in the range of those reported in the literature, which validated the developed rapid nucleation rate measurement platform. Stepping outside of these established measurements, analyzing the influence of polymers with high potential in controlling particle size, shape, and polymorphism was touched as well. As an unexpected result, the nucleation rates appeared to depend not only on the chemical structure and amount of the polymer but also on the polymer solution preparation method. The remarkable influence of polymers on nucleation rates was shown that cannot be explained with the solubility altering effect of the polymers alone. 

Rapid, low-cost exploration of nucleation rates in l-glutamic acid crystallization in pure media and the presence of polymers through novel parallel experimentation

Deep Reinforcement Learning-Based Self-Optimization of Flow Chemistry

Scaling up and technology transfer of crystallization processes have been and continue to be a challenge. This is often due to the stochastic nature of primary nucleation, various scale dependencies of nucleation mechanisms, and the multitude of scale-up approaches. To better understand these dependencies, a series of isothermal induction time studies were performed across a range of vessel volumes, impeller types, and impeller speeds. From these measurements, the nucleation rate and growth time were estimated as parameters of an induction time distribution model. Then using machine learning techniques, correlations between the vessel hydrodynamic features, calculated from computational flow dynamic simulations, and nucleation kinetic parameters were analyzed. Of the 18 machine learning models trained, two models for the nucleation rate were found to have the best performance (in terms of % of predictions within experimental variance): a nonlinear random Forest model and a nonlinear gradient boosting model. For growth time, a nonlinear gradient boosting model was found to outperform the other models tested. These models were then ensembled to directly predict the probability of nucleation, at a given time, solely from hydrodynamic features with an overall root mean square error of 0.16. This work shows how machine learning approaches can be used to analyze limited datasets of induction times to provide insights into what hydrodynamic parameters should be considered in the scale-up of an unseeded crystallization process.

https://pubs.acs.org/doi/pdf/10.1021/acs.cgd.2c00192

Machine Learning-Derived Correlations for Scale-Up and Technology Transfer of Primary Nucleation Kinetics

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Deep Reinforcement Learning-Based Self-Optimization of Flow Chemistry

Machine Learning-Derived Correlations for Scale-Up and Technology Transfer of Primary Nucleation Kinetics