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Cooling crystallization experiments of curcumin in isopropanol confirmed that curcumin can crystallize via classical or nonclassical pathways, depending on the levels of supersaturation and supercooling. Light microscopy analysis revealed that classical crystallization produces needle-shaped single crystals with an equilibrium habit, while nonclassical crystallization results in spherulitic mesocrystals. Through a series of experiments under various conditions, we developed a crystal habit phase diagram for curcumin in pure isopropanol. Presented here for the first time, this diagram illustrates the relationship between supersaturation, supercooling, and crystal habit, offering a valuable guide for controlling curcumin crystallization pathways.

Crystallization via nucleation can isolate active pharmaceutical ingredients from their crudes. While chemical engineering textbooks provide theoretical knowledge on crystallization and nucleation theories, they often fall short in providing provide practical insights on the nucleation mechanism. To bridge this gap, we introduced a virtual experiment on nucleation in second-year chemical engineering classrooms. The main goal is to educate students on crystallization procedures in research and process industries, teaching them how to analyse and manage collected data while integrating theoretical knowledge. This includes conveying the kind of information that can be obtained from a crystallisation process and instructing students on how to analyse and manage the data collected in the light of the theories learned. We devised an original chemical engineering problem on nucleation, derived directly from the raw data collected in the classroom from virtual experiments. This method differs from the conventional approach of solving standard textbook problems. The textbook problems, regrettably often lack crucial information on how nucleation rate or surface free energy are directly obtained from raw data. By the conclusion of the virtual experiment, students have acquired a comprehensive understanding encompassing both practical and theoretical aspects of crystallization, with a particular focus on nucleation. The methodologies elucidated in this study can be applied across a spectrum of chemical engineering modules, including process engineering, unit operations in chemical engineering, mass transfer, and can even be integrated into specialized courses dedicated to crystallization.

Developing theory-informed standard operating procedures (SOPs) for the continuous crystallisation of pharmaceuticals still remains a bottleneck. For the continuous manufacturing of pharmaceuticals, the current methods rely on the laborious trial-and-error approach to identify process conditions such as the dilution rate (flow per unit volume of reactor) and initial supersaturation, where the productivity will be at maximum at steady-state conditions. This approach, while proven and considered to be useful, lacks or ignores the information obtained from batch kinetics. Herein for the first time, we propose a theoretical method to develop batch kinetics-informed theoretical procedures for the continuous manufacturing of a model compound curcumin in isopropanol. The theoretical approach uses batch kinetic constants to theoretically identify the optimum dilution rate and the corresponding mass of the model compound curcumin when crystallised, as well as its productivity at steady-state conditions as a function of initial supersaturation. The theory-informed procedures will serve as a valuable guideline to develop operating procedures for the continuous production of the target compound and thus eliminate the trial-and-error approach used to develop the protocols for the continuous manufacturing of pharmaceuticals. We also showed that our methods allow for the estimation of the dilution rate that corresponds to washout conditions (i.e., where all the crystals in the crystalliser will be washed out due to the high flow rate of the input stream) during the continuous manufacturing of crystals.

The Langmuir isotherm is used to determine the properties of a theoretical “holy grail” adsorbent that can meet the US Department of Energy’s methane storage target of 0.5 g/g and 266 v/v. For a storage tank operating between 5 and 65 bar, the adsorbent requires a maximum adsorption capacity of 0.8388 g/g, a binding affinity of 0.05547 bar–1, and a material density of 377 g/L. For a tank operating between 5 and 80 bar, the binding affinity should be 0.05 bar–1, with the same capacity and density. The Langmuir isotherm is also applied to calculate the necessary adsorbent properties, including the number of adsorption sites and binding energies, to achieve the volumetric storage target of 266 v/v based on the material’s density.

Background: Metastable zone width (MSZW) and solubility are crucial for developing crystallization procedures in the purification of active pharmaceutical ingredients (APIs). Traditionally, determining these properties involves labor-intensive methods that can take weeks or even months. With advancements in process analytical technologies (PAT) and the increasing focus on quality by design (QbD) in pharmaceutical manufacturing, more efficient and reliable protocols are needed. In this study, we employ in situ Fourier Transform Infrared (FTIR) spectroscopy and Focused Beam Reflectance Measurement (FBRM) to establish protocols for measuring solubility at different temperatures and MSZW at varying cooling rates. Methods: We experimentally determined MSZW and solubility using FTIR spectroscopy and FBRM. IR spectra were analyzed to obtain solubility concentrations, while FBRM counts were used to extract MSZW and supersolubility concentrations. The collected data were assessed using four theoretical models, including a newly developed model based on classical nucleation theory. By fitting experimental MSZW data to these models, we determined nucleation kinetics and thermodynamic parameters. Results: Our novel model exhibited excellent agreement with experimental MSZW data across different cooling rates, demonstrating its robustness. The nucleation rate constant and nucleation rate ranged between 10(2)(1) and 10(2)(2) molecules/m(3)s. The Gibbs free energy of nucleation was calculated as 3.6 kJ/mol, with surface energy values between 2.6 and 8.8 mJ/m(2). The estimated critical nucleus radius was in the order of 10(-)(3) m. Conclusions: The protocols we developed for predicting MSZW and solubility of paracetamol using PAT can serve as a guideline for other APIs. Our theoretical model enhances the predictive accuracy of nucleation kinetics and thermodynamics, contributing to optimized crystallization processes.

We propose a new mathematical model based on the classical nucleation theory to predict the nucleation rate, kinetic constant, and Gibbs free energy of nucleation using metastable zone width (MSZW) data as a function of solubility temperature. Unlike widely used models by N & yacute;vlt, Kubota, and Sangwal, which are limited in capturing the impact of varying cooling rates, the proposed model allows direct estimation of nucleation rates from MSZW data obtained under different cooling conditions. This is particularly advantageous for continuous or semi-batch crystallisation design, where cooling rate is a critical variable. The model has been successfully validated using experimental data from 22 solute-solvent systems, including 10 APIs, one API intermediate, lysozyme, and glycine, as well as 8 inorganic compounds. Predicted nucleation rates span from 1020 to 1024 molecules per m3 s for APIs, and up to 1034 molecules per m3 s for lysozyme, the largest molecule studied. Gibbs free energy of nucleation varies from 4 to 49 kJ mol-1 for most compounds, reaching 87 kJ mol-1 for lysozyme. The model also enables accurate prediction of induction time and key thermodynamic parameters such as surface free energy, critical nucleus size, and number of unit cells-based solely on MSZW data obtained at different cooling rates.

In this work, we report the new protocols that are developed to determine the shape factors of Form I paracetamol crystals using a combination of techniques that rely on the state-of-the-art X-ray computed tomography and Morphologi G3. The determined shape factors successfully predicted the crystal growth rate of paracetamol in 2-propanol and the length of the crystals growing in the supersaturated solution. X-ray computed tomography and optical microscopy can be effectively combined to predict crystal shape factors with reasonable accuracy.

Impurities play a critical role in crystal growth by adsorbing onto growth steps and reducing step advancement rates. In this study we introduce the Statistical Distribution Model (SDM), which incorporates the random distribution of immobile impurities using Poisson statistics. We define two key parameters: the velocity reduction factor (A), which quantifies how strongly an impurity reduces step velocity once pinned, and the pinning probability scaling constant (B), which reflects how likely it is for impurity pairs to fall within a critical pinning distance. Using these two parameters, we classify impurities into at least five types, ranging from those that weakly reduce velocity and rarely pin to those that strongly inhibit growth through frequent pinning events. Depending on impurity strength and coverage, we show that SDM accurately describes three commonly observed behaviors during the growth of crystals in impure solutions: complete growth arrest, partial inhibition, and linear reduction in velocity. The model shows excellent agreement with experimental data from ADP, KBr, and sucrose systems, offering improved insight into impurity-induced growth kinetics.