Predictive Modeling of Supersaturation-Dependent Crystal Shapes

Several molecular organic crystals are known to exhibit significant changes to their steady-state growth shapes when grown in solutions with different supersaturations. In this article, we describe a first-principles model for the prediction of supersaturation-dependent growth shapes that is capable of capturing this phenomenon. The model begins with the prediction of the growth shape at an arbitrarily low supersaturation, for which all faces present on the steady-state shape grow by spirals. The dominant growth mechanisms (spiral or two-dimensional nucleation) are then determined over a specified range of supersaturations, based on the surface energies of edges present on the faces of the low-supersaturation (spiral growth) shape. These energies are estimated from the set of strong intermolecular interactions contained within each face and solubility parameter data. Steady-state growth shapes are then predicted as a function of supersaturation. A case-study performed on naphthalene grown in ethanol is presented in order to demonstrate the implementation of this model. The predictions from this case study are in remarkable agreement with the results of prior experiments performed for this system.