(612a) Calculation of Free Energy Barriers for Attachment of Molecules during Crystal Growth and Nucleation

Physical properties of crystalline materials depend upon their molecular structure and shape. Following the adoption of Quality by Design approaches by the Food and Drug Administration, the theoretical and computational approaches are increasingly implemented to predict structure (polymorphs), shape and properties of the crystalline materials. The most common method to predict crystal structure is the lattice energy minimization technique, which calculates the configuration of molecules in the lattice and its energy using the state-of-the-art optimization algorithms. Whereas the theoretical methods to predict crystal shape relies on the calculation of growth rates using either the interfacial energy or the kink energy. Such methods for the crystal structure and shape prediction depend on the estimation of crystal energies and hence to fail to capture the underlying dynamics of nucleation and growth, where solute molecules continuously attach to and detach from the crystal surfaces in a supersaturated solution. In order to effectively model the dynamics of crystallization processes, it is essential to know the free energy barriers for the attachment and detachment of solute molecules. Here we propose a method to calculate free energy barriers for the attachment and detachment of molecules using the double-well potential method. This approach consists of finding the configuration of molecules in the solvation shell, followed by the construction of the double-well potential diagrams to calculate free energy barriers. Application of the proposed method to calculate growth rates and nucleation rates of Glutamic acid will be shown.