On the use of process analytical technologies and population balance equations for the estimation of crystallization kinetics. A case study

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.

Secondary Nucleation by Interparticle Energies. III. Nucleation Rate Model

A nucleation rate model for describing the kinetics of secondary nucleation caused by interparticle energies (SNIPEs) is derived theoretically, verified numerically, and validated experimentally. The theoretical derivation reveals that the SNIPE mechanism can be viewed as enhanced primary nucleation, i.e., primary nucleation with a lower thermodynamic energy barrier (for nucleation) and a smaller critical nucleus size, both caused by the interparticle interactions and the associated energy between the surface of a seed crystal and a molecular cluster in solution, as shown in part I of this series. In the case of a sufficiently agitated suspension, the model depends on four parameters: two reflecting primary nucleation kinetics and the other two accounting for the intensity and effective spatial range of the interparticle interactions. As a numerical verification of the model, we show that the nucleation kinetics described by the SNIPE rate model is in quantitative agreement with those given by the kinetic rate equation model developed in part II of this series. A sensitivity analysis of the SNIPE rate model is conducted to present the effect of key model parameters on the nucleation kinetics. Moreover, the SNIPE rate model is validated by fitting the model to the time-resolved data of secondary nucleation experiments as well as to two other, well-known secondary nucleation rate models. Importantly, all of the estimated parameter values for the SNIPE model were consistent with the theoretical estimates, while some of the estimated parameter values for one of the well-known secondary nucleation models deviated from the corresponding theoretical values significantly.

Real-Time Monitoring of Solid-Liquid Slurries: Optimized Synthesis of Tetrabenazine

Solid-liquid slurries are vital and increasingly prevalent in the pharmaceutical and chemical industries. Despite the importance of these heterogeneous systems, process control and optimization are fundamentally hindered by a lack of compatible real-time analytical techniques. We present herein an online HPLC monitoring platform enabling access to real-time compositional information on slurries. We demonstrate the system by investigating the heterogeneous synthesis reaction of tetrabenazine. Furthermore, we integrated our online HPLC platform with the orthogonal monitoring techniques of a pH probe and a microscopic imaging probe to provide additional mechanistic insight. These combined insights enable the optimization of tetrabenazine synthesis in terms of reaction time, byproduct formation, and diastereomeric purity of the final product.

Acoustic emission detection of crystallization in two forms: monohydrate and anhydrous citric acid

Reliable monitoring of solution crystallization processes is important to provide further insight into process dynamics and to improve process control in the regimen of Process Analytical Technology (PAT), e.g. as the case studied here: detection of crystallization of the anhydrous and monohydrate forms of Citric Acid (CA). To set up the relationship between acoustic emission (AE) and crystallization form, two experiments (monohydrate and anhydrous citric acid) were carried out to specify the features and origins of the different acoustic signals emitted during batch cooling solution crystallization processes. Two kinds of AE experimental variables convey information about the development of crystallization processes: frequency and acoustic energy variables. The experimental results show notably that though it has less acoustic bursts, the acoustic activity generated by the crystallization of the monohydrate form of CA actually releases more acoustic energy than the crystallization of anhydrous form. It is also shown that the form of the crystallization is associated with the percentage of absolute energy. The proportion of the absolute energy [150-700 KHz] released by CA_m (43% of total absolute energy) in the total energy [0-700 KHz] is much more than that of CA_a (3% of total absolute energy).