Process Analytical Technology Obtained Metastable Zone Width, Nucleation Rate and Solubility of Paracetamol in...

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 10²¹ and 10²² molecules/m³·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/m². 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.