Modeling the crystal shape of polar organic materials: Prediction of urea crystals grown from polar and nonpolar solvents

The shape of a crystal is an important characteristic which can influence fundamental properties of the material, including the rate of dissolution, solubility, stability in storage, and compressibility. Understanding the mechanism by which a material with distinct internal structure crystallizes and forms different shapes will enable the engineer to manipulate the crystallization process, so that the desired shape is obtained. There are numerous models for predicting the shape of vapor-grown compounds. Three of the most prominent models: the Bravais-Friedel-Dormay-Harker (BFDH) model, the equilibrium model, and the attachment energy model, have been explored in this article. In addition, we have developed a model based on a detailed analysis of the BCF growth mechanism supplemented by additional terms to account for the adhesion surface energy at the solid-liquid interface. Polar solute-nonpolar solvent interactions were incorporated into the model by a geometric mean approximation for the adhesion surface energy. Polar solute-polar solvent interactions were incorporated using a method developed by Fowkes. A description of the size and the nature of the intermolecular interactions along the different growth directions is a prerequisite for application of the model, which does not require complex calculations. Application of the model to a polar molecular crystal-urea, grown from polar solvents (water and methanol) resulted in a prismatic elongated shape which resembles that observed in the laboratory. This shape is different from the distinctive, well-faceted cubic shape of urea grown from the vapor. We chose benzene as a representative nonpolar solvent and used our model to predict the shape of urea grown from benzene.