A Structural−Kinetic Approach to Model Face-Specific Solution/Crystal Surface Energy Associated with the Crystallization of Acetyl Salicylic Acid from Supersaturated Aqueous/Ethanol Solution

Abstract

Classical homogeneous nucleation theory has been integrated with molecular modeling techniques to model the effects of cluster shape-anisotropy associated with nucleation from solution. In this approach, the geometric shape of a crystal nucleus is modeled assuming it equates to the predicted growth morphology of the resultant macroscopic crystal with the later simulated via an attachment energy model using empirical intermolecular force calculations adopting the atom−atom approximation. A new coupled model integrating nucleation theory, morphological simulation and solvent binding calculations, has been developed and combined with experimental nucleation data for the case example of acetyl salicylic acid (aspirin) crystallizing from an aqueous/ethanol solution. Nucleation parameters, such as critical nucleus size and specific surface energy, have been calculated and compared for the cases of both isotropic (spherical) and anisotropic (polyhedral) nucleus models. A comparison between nucleation data modeled on the basis of both shaped polyhedral and spherical clusters reveals a larger critical nucleus size for the anisotropic (Dequivalent = 16.54 Å at 40 °C) compared to the isotropic (D = 13.07 Å at 40 °C) shape model. Theoretical molecular modeling calculations of the specific surface energy anisotropy in solution show the specific surface energy for the habit planes of aspirin to vary from 3.65 mJ/m2 for the dominant {100} facet to 113 mJ/m2 for the minor {1̄11} facet. A comparison between the dominant crystal habit planes, notably, the hydrophilic {100} and hydrophobic {002}, reveals them to be more differentiated in terms of their specific surface energy in solution (3.65 and 10.90 mJ/m2) than in a vacuum (829 and 904 mJ/m2), respectively, in good agreement with their known surface chemistry. The total, specific surface energy (41.9 mJ/m2) in solution calculated via molecular modeling for the polyhedral-shaped clusters was found to be somewhat larger, but still in pleasing general agreement with that calculated from experimental nucleation data as determined using induction time measurements assuming a spherical nucleus (3.99 mJ/m2). The potential for the further development of this overall modeling approach is reviewed.