(451c) Polymorph Prediction: A Kinetic Approach

Polymorphs are characteristic identities of crystalline materials that stem from their crystal structures and can offer them significantly different properties such as solubility, morphology, hardness, cleavage, optical properties, heat conductivity, electrical conductivity and piezoelectric effect. The synthesis of crystals of desired polymorphs, based on the applications of interest, requires understanding of the self-assembly of molecules under different crystallization conditions. The self-assembly of molecules to form crystals depends on the atomic configuration of the molecule, flexibility of the molecule, solvent, co-solvent, additives, thermodynamic and hydrodynamic conditions. The molecules are known to self-assemble in 230 space groups or less, where the energy associated with each assembly can be used to infer stability or likeliness of the appearance of the polymorph under equilibrium. One of the methods to compute energies of different polymorphs is the Lattice Energy Minimization¹which does not consider the effect of crystallization conditions on polymorph formation. The non-equilibrium approaches such as Kinetic Monte-Carlo and Molecular Dynamics shows limitations in treating dense systems and longer time scales. The objective of this article is to develop a mechanistic framework to predict polymorphs and associated nucleation kernels as a function of crystallization conditions. The application of this framework to predict polymorphs of Tetrolic acid will be shown.

According to the kinetic theory of nucleation, the critical crystal nuclei are formed by successive transitions of molecules to dimers, trimers, and so on. Clearly, the crystal structure is determined by the self-assembly of molecules to form dimers. The direct relation between the growth synthons² (structure of dimers) in solution with the structural synthons² (molecular building blocks) in the crystal is known as Link Hypothesis. The Link Hypothesis was experimentally verified for various crystalline materials including form I of Tetrolic acid.³According to the Link Hypothesis the structure of growth synthons will determine the crystal structure. We present a stochastic model to predict the formation of growth synthons under different crystallization conditions. The stochastic model is based on the constrained Brownian motion of a pair of molecules in an infinitesimal volume. The successful implementation of this framework will provide a tool for model-based screening of crystallization conditions for synthesis of desired polymorphs.

References:

 (1)       Day, G. M.; Chisholm, J.; Shan, N.; Motherwell, W. D. S.; Jones, W., An assessment of lattice energy minimization for the prediction of molecular organic crystal structures. Crystal growth & design 2004, 4, (6), 1327-1340.

(2)        Desiraju, G. R., Supramolecular synthons in crystal engineering—a new organic synthesis. Angewandte Chemie International Edition in English 2003, 34, (21), 2311-2327.

(3)        Parveen, S.; Davey, R.; Dent, G.; Pritchard, R., Linking solution chemistry to crystal nucleation: the case of tetrolic acid. Chemical communications 2005, (12), 1531-1533.