A computational investigation of nucleation processes in organic crystals

Abstract

Nucleation processes are ubiquitous in nature and technology. For instance, cloud formation in the atmosphere, the casting of metals, protein crystallization, biomineralization, the production of porous materials, and separation of pharmaceutical compounds from solution are a few examples of relevant nucleation processes. One pathway for nucleation to occur is homogeneous nucleation, in which an embryo of a more stable phase forms within an original metastable medium. Homogeneous nucleation is an activated process, meaning that a free energy barrier must be overcome for the transition to take place, and the height of the free energy barrier determines the rate at which the process will occur. Despite considerable advances in both theoretical and experimental techniques to date, determining nucleation mechanisms for real systems remains a considerable technical challenge. The aim of this thesis is therefore to apply molecular simulation techniques to elucidate nucleation mechanisms in organic crystals. Specifically, the newly developed methods of aimless shooting and likelihood maximization are applied for the first time to study nucleation processes in complex and technically relevant systems. The first portion of the thesis examines polymorphism, or the ability of a material to pack in different crystal lattices whilst retaining the same chemical composition. Transformation to a more stable polymorph can readily occur in the solid state, which has broad implications in pharmaceutical processing. To date, over 160 mechanisms have been proposed for polymorph transitions in the solid state, but none have been definitively verified. A model compound, terephthalic acid, is chosen for computational studies because it is similar in size to a small molecule therapeutic and exhibits a common bonding motif for organic crystals. Using aimless shooting and likelihood maximization, the mechanism of the solid state polymorph transformation in terephthalic acid is shown to be comer nucleation. The mechanism shows that for a given nucleus size, the interfacial area between the crystalline domains is minimized, thus reducing the unfavorable surface free energy penalty required for nucleation to occur.

(cont.) Furthermore, based on the results presented, it is anticipated that corner nucleation may be a common mechanism for many polymorph transformations in hydrogen bonded crystalline materials. The second portion of the thesis investigates the mechanism of freezing a subcooled liquid to form a crystal. This phenomenon has widespread application across many technical domains. Similar studies to date on freezing have been limited to model systems, such as Lennard-Jones particles or hard spheres. Benzene is chosen as a model compound. A periodic system is constructed and aimless shooting and likelihood maximization are applied to determine the nature of the critical nucleus. Local order analysis is implemented to distinguish among solid and liquid-like molecules. Preliminary results indicate that the critical nucleus is on the order of 200-300 molecules at 50 K subcooling. This thesis demonstrates that the complementary molecular simulation techniques of aimless shooting and likelihood maximization offer fundamental insight into nucleation mechanisms in molecular crystals. Knowledge of the mechanism from likelihood maximization is essential for accurate free energies and pathway optimization methods, and it should therefore be applied in computational studies of rare events prior to free energy or rate constant calculations. Moreover, these methods provide quantitative understanding of the important physical variables that determine experimentally observable rates and can further aid in experimental design.