This thesis describes the development of an empirical model of focus beam reflectance measurements (FBRM) and the application of the model to monitoring batch cooling crystallization and extracting information on crystallization kinetics. Batch crystallization is widely used in the fine chemical and pharmaceutical industries to purify and separate solid products. The crystal size distribution (CSD) of the final product greatly influences the product characteristics, such as purity, stability, and bioavailability. It also has a great effect on downstream processing. To achieve a desired CSD of the final product, batch crystallization processes need to be monitored, understood, and controlled. FBRM is a promising technique for in situ determination of the CSD. It is based on scattering of laser light and provides a chord-length distribution (CLD), which is a complex function of crystal geometry. In this thesis, an empirical correlation between CSDs and CLDs is established and applied in place of existing first-principles FBRM models. Built from experimental data, the empirical mapping of CSD and CLD is advantageous in representing some effects that are difficult to quantify by mathematical and physical expressions. The developed model enables computation of the CSD from measured CLDs, which can be followed during the evolution of the crystal population during batch cooling crystallization processes. Paracetamol, a common drug product also known as acetaminophen, is selected as the model compound in this thesis study. The empirical model was first established and verified in a paracetamol-nonsolvent (toluene) slurry, and later applied to the paracetamol-ethanol crystallization system. Complementary to the FBRM measurements, solute concentrations in the liquid phase were determined by in situ infrared spectra, and they were jointly implemented to monitor the crystallization process. The framework of measuring the CSD and the solute concentration allows the estimation of crystallization kinetics, including those for primary nucleation, secondary nucleation, and crystal growth. These parameters were determined simultaneously by fitting the full population balance model to process measurements obtained from multiple unseeded paracetamol-ethanol crystallization runs. The major contributions of this thesis study are (1) providing a novel methodology for using FBRM measurements to estimate CSD; (2) development of an experimental protocol that provided data sets rich in information on crystal growth and primary and secondary nucleation; (3) interpretation of kinetics so that appropriate model parameters could be extracted from fitting population balances to experimental data; (4) identification of the potential importance of secondary nucleation relative to primary nucleation. The protocol and methods developed in this study can be applied to other systems for evaluating and improving batch crystallization processes.

Controlling the size and size distribution of colloidal nanoparticles have gained extraordinary attention as their physical and chemical properties are strongly affected by size. Ligands are widely used to control the size and size distribution of nanoparticles; however, their exact roles in controlling the nanoparticle size distribution and the way they affect the nucleation and growth kinetics are poorly understood. Therefore, understanding the nucleation and growth mechanisms and developing theoretical/modeling framework will pave the way towards controlled synthesis of colloidal nanoparticles with desired sizes and polydispersity. This dissertation focuses on identifying the possible roles of ligands and size on the kinetics of nanoparticle formation and growth using in-situ characterization tools such as small-angle X-ray scattering (SAXS) and kinetic modeling. The presented work further focuses on developing kinetic models to capture the main nucleation and growth reactions and examines how ligand-metal interactions could potentially alter the rate of nucleation and growth rates, and consequently the nanoparticle size distribution. Additionally, this work highlights the importance of using multi-observables including the concentration of nanoparticles, size and/or precursor consumption, and polydispersity to differentiate between different nucleation and growth models and extract accurate information on the rates of nanoparticle nucleation and growth. Specifically, during the formation and growth of colloidal nanoparticles, complex reactions are occurring and as such nucleation and growth can take place through various reaction pathways. Therefore, sensitivity analysis was applied to effectively compare different nucleation and growth models and identify the most important reactions and obtain a reduced model (e.g. a minimalistic model) required for efficient data analysis. In the following chapters, a more sophisticated modeling approach is presented (population balance model) capable of capturing the average-properties of nanoparticle size distribution. PBM allows us to predict the growth rate of nanoparticles of different sizes, the ligand surface coverage for each individual size, and the parameters involved in altering the size distribution. Additionally, thermodynamic calculations of nanoparticle growth and ligand-metal binding as a function of size and ligand surface coverage were conducted to further shed light on the kinetics of nanoparticle formation and growth. The combination of kinetic modeling, in-situ SAXS and thermodynamic calculations can significantly advance the understanding of nucleation and growth mechanisms and guide toward controlling size and polydispersity. / Doctor of Philosophy / The synthesis of colloidal metal nanoparticles with superior control over size and size distribution, and has attracted much attention given the wide applications of these nanomaterials in the fields of catalysis, photonics, and electronics. Obtaining nanoparticles with desired sizes and polydispersity is vital for enhancing the consistency and performance for specific applications (e.g., catalytic converters for automotive emission). Ligands are often employed to prevent agglomeration and also control the nanoparticle size and size distribution. Ligands can affect the precursor reactivity and therefore the reduction/nucleation by binding with the metal precursor. Nucleation refers to the assimilation of few atoms to form initial nuclei acting as templates for nanoparticle growth. Additionally, ligands can bind with the nanoparticle surface sites and change the rate of surface growth and therefore the final nanoparticle size. Despite strong effects of ligands in the colloidal nanoparticle synthesis, their exact role in the nucleation and growth kinetics is yet to be identified. Additionally, nucleation and growth models capable of unraveling the underlying mechanisms of nucleation and growth in the presence of ligands are still lacking in the literature. Therefore, obtaining nanoparticles with desired sizes and polydispersity mostly relies on trial-and-error approach making the synthesis costly and inefficient. As such, developing models capable of predicting suitable synthesis conditions is contingent upon understanding the chemistry and mechanism involved during nanoparticles formation. Therefore, in this study, novel kinetic models were developed to capture the nucleation and growth kinetics of colloidal metal nanoparticles under different synthetic conditions (different types of solvents, different concentrations of ligand and metal). In-situ SAXS was further employed to measure the average diameter, concentration of nanoparticles, and polydispersity during the synthesis and extract the nucleation and growth rates (evolution of concentration of nanoparticles and size). First, an average-property model was developed to account for ligand-metal bindings and capture the size and concentration of nanoparticles during the synthesis. Then, a more complex modeling approach; PBM, accompanied by the thermodynamic calculations of surface growth and ligand-nanoparticle binding enthalpies was implemented to capture the size distribution. As it will be shown later, the determination of the underlying mechanisms resulted in a highly predictive kinetic model capable of predicting the synthetic conditions to obtain nanoparticles with desired sizes. The proposed methodology can serve as a powerful tool to synthesize nanoparticles with specific sizes and polydispersity.

<p>  </p> <p>Crystallization is a purity and particle control unit operation commonly used in industries such as pharmaceuticals, agrochemicals, and energetics. Often, the active ingredient’s crystal mean size, polymorphic form, morphology, and distribution can impact the critical quality attributes of the final product. The active ingredient typically goes through a series of process development iterations to optimize and scale-up production to reach production scale. Guided by the FDA, the paradigm shift towards continuous processing and crystallization has shown benefits in introducing cheaper and greener technologies and relieving drawbacks of batch processing. To achieve successful batch scale-up or robust continuous crystallization design, process intensification of unit operations, crystallization techniques, and utilizing data driven approaches are effective in designing optimal process parameters and achieving target quality attributes. </p> <p>In this thesis, a collection or toolbox of various process intensification techniques was developed to aid in control, optimization, and digitalization of crystallization processes. The first technique involves developing a novel control algorithm to control agrochemical crystals of high aspect ratio to improve the efficiency of downstream processes (filtration, washing, and drying). The second technique involves the further improvement of the first technique through digitalization of the crystallization process to perform simulated optimization and obtain a more nominal operating profile while reducing material consumption and experimentation time. The third method involves developing a calibration procedure and framework for in-line video microscopy. After a quick calibration, the in-line video microscopy can provide accurate real-time measurements to allow for future control capabilities and improve data scarcity in crystallization processes. The last technique addresses the need for polymorphic control and process longevity for continuous tubular crystallizers. Through a sequential stirred tank and tubular crystallizer experimental setup, the control of polymorphism, particle mean size, and size distribution were characterized. Each part of this thesis highlights the importance and benefits of process intensification by creating a wholistic process intensification framework coupled with novel equipment, array of PAT tools, feedback control, and model-based digital design.</p>

<p dir="ltr">The purification of most active pharmaceutical ingredients (APIs) is primarily achieved through crystallization, conducted in batch, semi-batch, or continuous modes. Recently, continuous crystallization has gained interest in the pharmaceutical industry for its potential to reduce manufacturing costs and maintenance. Crystal characteristics such as size, purity, and polymorphism significantly affect downstream processes like filtration and tableting, as well as physicochemical properties like bioavailability, flowability, and compressibility. Developing an optimal operation that meets the critical quality attributes (CQAs) of these crystal properties is essential.</p><p dir="ltr">This dissertation begins by focusing on designing an innovative integrated crystallization system to enhance control over crystalline material properties. The system expands the attainable region of crystal size distribution (CSD) by incorporating multiple Mixed-Suspension Mixed-Product Removal (MSMPR) units and integrating wet milling, classification, and a recycle loop, enhancing robustness and performance. Extensive simulations and experimental data validate the framework, demonstrating significant improvements in efficiency and quality. The framework is further generalized to optimize crystallizer networks for controlling critical quality attributes such as mean size, yield, and CSD by evaluating various network configurations to identify optimal operating parameters.</p><p dir="ltr">The final part of this work concentrates on using the framework to improve continuous production of a commercial API, Atorvastatin calcium (ASC), aiming for higher yield and lower costs. This approach establishes an attainable region to increase crystal sizes and productivity. Due to ASC’s nucleation-dominated nature, the multi-stage system could not grow the crystals sufficiently to bypass granulation, the bottleneck process in ASC manufacturing. Therefore, spherical agglomeration was proposed as an intensification process within an integrated two-stage crystallization spherical agglomeration system to control the size and morphology of ASC crystals and improve downstream processing and tableting. This method proved highly successful, leading to the development of an end-to-end continuous manufacturing process integrating reaction, crystallization, spherical agglomeration, filtration, and drying. This modular system effectively addressed challenges in integrating various unit operations into a coherent continuous process with high production rates.</p>