Crystallization of inorganic solids from solution is of interest in several areas such as biomineralization, carbon sequestration, catalysis, photovoltaics, etc. The end-use functionality in some of the industrial applications is determined by the growth morphology of the inorganic crystals. A mechanistic understanding of the growth process will enable the design of functionally desirable inorganic crystalline solids.

The kinetics of crystal growth is governed primarily by the intermolecular interactions between the growth units on crystal surfaces and across the solid-solution interface. Therefore, this modeling effort is focused on the solid-state as well as the solution phase chemistry. The challenges associated with the solid-state chemistry of inorganic crystals, including long-range electrostatic interactions, stoichiometry, electronic structure of surface growth units, etc., were resolved within an easy-to-implement framework. The importance of the solution structure information (from experiments or molecular simulations) has been highlighted appropriately.

This dissertation presents a spiral growth model that predicts the morphology of solution grown crystals (e.g., CaCO₃) at ambient conditions. The model also provides quantitative insights into the kinetics of hydrothermal synthesis of inorganic oxides, such as TiO₂ and ZnO, using the periodic bond chain (PBC) theory.

This mechanistic model could be extended to identify suitable growth modifiers for a wide range of inorganic crystals such as salts and oxides. The ultimate goal is to develop a predictive tool that helps engineer the synthesis of inorganic solids with desired functionality.

Crystal morphology prediction tools have drawn scientific and industrial interest due to the close connection between morphology and crystal properties and performance. Existing multiscale models consider the behavior of growth units at the microscale to inform macroscale predictions, and are continually improving. Such tools aid in narrowing the design space to reduce experimental costs and inform rational process development. This dissertation seeks to improve the understanding of underlying crystal growth mechanisms and enable the development of more robust multiscale models via computational techniques.

Crystal growth is often governed by layered growth mechanisms at the surface. Simulation methodologies are instrumental in modeling surface rare events and provide a route toward calculating relevant parameters such as crystal face growth rates. In particular, we highlight the utility of kinetic Monte Carlo (kMC) simulation methods in this field to accurately model crystal surface dynamics and provide in silico morphology predictions. We consider cases of molecules both with centrosymmetric and noncentrosymmetric growth units and provide various morphology predictions in good agreement with experimental data. We also study impurity-mediated crystal growth systems and develop models to quantify the effect of impurities on crystal growth and on polymorphism. These studies offer computationally driven insights to elucidate mechanistic model expressions appropriate for a more extensive array of crystal systems

Crystal growth shapes must be optimized with respect to product functionality. Rapid in silico calculations of crystal habits, coupled with theoretical understanding of the physical processes that drive them, will enable intelligent navigation across the vast design space of growth conditions. This dissertation focuses on upgrading a multi-scale mechanistic modeling framework to realize such a design aid for systematic shape engineering.

First, underlying kinetic rate expressions for growth unit attachment and detachment are clarified, and the incorporation mechanism is considered. Second, a method for predicting the dominant growth regime operating on each face is introduced, which enables the effect of supersaturation on crystal shape to be accounted for. Third, the effect of solvent on crystal shape is investigated and a practical technique to account for it is detailed. Fourth, a model for the velocity of a step edge with non-centrosymmetric growth units is developed, which can account for complex instability phenomena unique to this general class of crystals. For each model development, predictions are tested against experimental crystal morphologies (or kinetic Monte Carlo simulations for the case of step velocities), to confirm accuracy. Finally, the strategy for overall model execution and automation is detailed.

These developments act to increase predictive accuracy and enable application of mechanistic models to a wider array of systems and growth conditions, while providing insight for rational crystal engineering.

One of the most awe-inspiring class of materials are crystals. These highly ordered groups of atoms/molecules propel our lives through myriad products we humans rely upon. Right from the salt and sugar we consume to elevate the taste of our foods, the silicon chips that form the brains of every computing device we use, to the life saving drugs that have prevented millions if not billions of deaths, all belong to the humble class of materials — the crystal. Therefore, the engineering of this material is crucial to — improve the manufacturing of products that touch our lives daily — ultimately improving the quality of every human life!

The two physical attributes of a crystalline material that have a major impact on its processability and performance are its shape and size. For e.g., in a crystalline catalyst one wants to engineer the shape of the crystal to maximize the area of its reactive surfaces. In pharmaceutical applications, the crystal size distribution may determine the rate of plasma uptake of a drug when the process is dissolution rate limited. Therefore, engineering the shape and size of the crystals is of immense consequence.

In silico tools that can predict the shape and size of a crystal based on inputs such as crystal structure, temperature, supersaturation, etc. are vital to efficiently navigate the process design space. Such tools help achieve the efficiency gains by being a guiding light to experimentalists, thus enabling cheaper and more effective screening. This dissertation lays out the digital design framework to make these predictions starting from a molecule. It focuses on the development of a computational toolkit to predict driving forces for crystallization — a key prediction to enable size predictions — of complex molecules harnessing atomistic simulations.

The understanding of solvent and solute transport mechanisms within swollen homogeneous polymer membranes remains a subject of ongoing debate in membrane science. With these membranes finding increased applications in organic solvent separations, antifouling coatings, and various biological systems and sensors, a deeper comprehension of continuum transport mechanisms is crucial for material characterization and design.

Classically, two models describe solvent transport within these membranes. The pore-flow model, based on fluid mechanics, works for porous membranes, whereas the solution-diffusion model invokes molecular diffusion to treat nonporous membranes. While both models offer valid arguments for swollen polymer membranes, they diverge in their predictions of intramembrane pressure and concentration profiles.

In the first part of this work, we introduce the fluid-solid model, a novel two-phase mechanics model that treats the solvent and membrane matrix as distinct phases, and determines the forces they apply on each other. This novel approach finds both classical models to be valid, to represent complementary approaches to the same phenomenon, and to make identical predictions. This model aligns with recent reverse osmosis measurements, offers a predictive basis for empirical high-pressure limiting flux phenomena, quantitatively agrees with classic measurements, and introduces a framework to analyze nonporous but mechanically heterogeneous membrane materials. Significantly, it identifies the longitudinal osmotic modulus as a critical mechanical parameter dictating swollen nonporous membrane transport.

The second part of this work involves an experimental exploration of the diffusive mechanics of small neutral solutes within hydrophilic neutral swollen membranes. Leveraging microfluidic interferometry, we investigate the diffusion of methanol, ethanol, and isopropanol in polyethylene glycol diacrylate hydrogels. This optical technique enables the measurement of dynamic diffusive concentration gradients within hydrogels, allowing for a discrimination between diffusive mechanisms and commonly used models of gel diffusion. Six diffusion models, categorized by their mechanism (obstruction, hydrodynamic, and free volume) are fitted to the data, with the Lustig and Peppas free-volume model emerging as the most accurate description. This approach simplifies the diffusion of the solute to the probability of a molecule finding an interstitial space within the sea of solute molecules that is large enough to accommodate the solute and close enough for it to make a diffusive jump. However, it exhibits limitations for isopropanol and ethanol at increasing concentrations, attributed to changes in alcohol-water structuring and the formation of alcohol clusters within the fluid phase.

Many materials are capable of organizing into multiple distinct solid phases, each exhibiting a unique set of material properties (e.g., mechanical, optical, electronic, catalytic, etc.). This material property diversity implies that a specific solid form or structure is typically preferred for a specific application. Thus, directing and controlling solid form during crystallization processes is a fundamental solid state engineering challenge. Here, for the first time, a general procedure is presented for designing continuous crystallizers that produce polymorphically pure crystal distributions of a preferred polymorph regardless of that polymorph's relative thermodynamic stability. The design rules were generated by developing and analyzing a multi-polymorph mixed suspension mixed product removal precipitator model, and they have been corroborated both by experimental data generated in our lab and by all of the applicable data in the published literature. These rules were developed to build understanding and aid in the process design of two sustainable energy technologies: carbon capture and utilization as structural materials (CCUSM) and methane pyrolysis (MP). Studying these processes also required the development of new models for calculating interphase mass transport in concentrated, electrolytic, reacting solutions and for describing the reactive transport that occurs in methane pyrolysis membrane reactors. The development and analysis of these models and a thermodynamic minimum energetic cost assessment of a wider set of sustainable energy technologies are also included in the dissertation.