Characterizing liquid-solid phase transitions for mechanistic model-based process design

Abstract

Freezing, freeze-drying and crystallization are central to the manufacture of pharmaceuticals and fine chemicals. They all involve a phase transition from the liquid to the solid, and it is the inherent complexity of this transition that renders process design challenging. This thesis aims to deepen the mechanistic understanding of the liquid-solid phase transition and to utilize the knowledge gained for rational process design. It has been motivated by unexpected challenges encountered in the commercial freezing process of the Janssen COVID-19 vaccine, where no ice formed in vials filled with the drug product despite being stored at -20°C for multiple days. This observation served as the starting point for extensive studies on freezing, aimed both at elucidating the role of fundamental phenomena such as crystal nucleation and growth as reported in Part I, and at understanding the process at industrially-relevant scales as reported in Part II. The ensuing insights inspired investigations into complex systems in crystallization from solution, which are reported in Part III of this thesis. Part I focuses on the phenomenon of ice nucleation, which denotes the onset of the phase transition. Its slow kinetics were the main reason for the aforementioned issue related to the Janssen COVID-19 vaccine. To study ice nucleation, I first developed a methodology for measuring its rate in aqueous solutions filled in vials. I then used this method to assess the effects of solution composition and of particulate impurities on the nucleation rate. A key finding was that ice nucleation is slower in samples prepared under particulate-free conditions compared to less clean conditions, because it is driven by the availability of so-called heterogeneous nucleation sites. To further assess the effect of volume on ice nucleation, I studied the freezing process of aqueous solutions in micro-droplets in collaboration with the research groups of Prof. Dr. Andrew deMello and of Prof. Dr. Ulrike Lohmann. Part II discusses the development of mechanistic models for freezing processes and their validation with experimental data. In particular, I developed a suite of three freezing models that all consider the stochastic nature of nucleation, and I made them openly available in the form of a Python package termed SNOW: Stochastic Nucleation Of Water. The first model simulates the freezing stage in a freeze-drying process, where a large number of vials is densely packed in two dimensions on a shelf. The predictions of this model have been validated experimentally with a newly developed experimental setup for the batch-scale online monitoring of freeze-drying using infrared thermography. The second model simulates the commercial freezing process of the Janssen COVID-19 vaccines, where tens of thousands of vials have been stacked in three dimensions on a pallet; the model correctly predicted all relevant experimental trends that were observed in engineering runs. The third model simulates freezing in a single container with spatial resolution. It was validated using the data generated in Part I and revealed that thermal gradients within a vessel may affect the time at which ice nucleation happens. Inspired by the experimental studies on ice nucleation in Part I and the modeling efforts in Part II, I investigated three complex systems in crystallization from solution, as reported in Part III. Crystallization is characterized by the occurrence of two types of nucleation, called primary and secondary nucleation, whereby the latter refers to the nucleation of new crystals promoted by existing crystals. I theoretically assessed two challenges related to secondary nucleation: first I studied the interplay of primary and secondary nucleation and how it affects the accuracy of methods for the measurement of nucleation rates. Second, I analyzed the stability of the steady state in a continuous crystallizer in which crystal growth and secondary nucleation take place. The resulting mathematical framework is particularly useful for describing the crystallization of systems with multiple solid forms - such as polymorphic or chiral compounds. A specific crystallization process of chiral compounds - solid-state deracemization - has been assessed in more detail, whereby I could elucidate its governing mechanism through a rigorous theoretical analysis supported by experiments. In conclusion, the results obtained in this thesis have aided the understanding and design of industrially relevant processes that involve liquid-solid phase transitions. The quantitative description of the ice nucleation rate, the suite of openly available mechanistic freezing models, and the theoretical results achieved in describing complex crystallization systems promise to be of broad interest both to fundamental scientists and to practitioners in industry.