Polymorphism is a fundamental property of crystals whereby a single compound may adopt numerous crystal structures with distinct properties. This structure multiplicity leads to materials with distinct physical properties (e.g., solubility, catalytic activity) that impact their performance in numerous applications. About 75% of the compounds deposited in the Cambridge Structural Database (CSD) crystallize in more than one structure. Crystal structure polymorphism manifests a free energy landscape, which, in contrast to that for protein folding, has not been optimized by evolution and contains not one minimum, but multiple local minima with similar free energies. Crystal structure multiplicity is magnified by the propensity of crystals to incorporate solvent molecules, creating solvates. Crystal polymorphs appear and transform via pathways that are not fully dictated by their stabilities. Observed trends often contradict the Ostwald rule of stages, according to which less stable polymorphs appear first, emphasizing how current state-of-the-art theories of crystallization cannot predict stable crystal structures and the transitions between them.
We rely on the premise that the polymorph to appear first is the one with the fastest rate of nucleation. In turn, the main parameter, which determines the nucleation barrier and the nucleation rate, is the surface free energy of the interface between the nucleus and the crystallization medium. We present an analytical model for the scaling of the nucleation barrier with the crystallization enthalpy . Preliminary results with mefenamic acid support these scaling relations. We experimentally measure the nucleation rates of the individual crystal forms and evaluate . As a measure of their relative stabilities we use their solubilities to evaluate the crystallization free energies . The crystallization enthalpies of the individual crystal forms are measured from the temperature correlation of their solubilities.
This model represents an innovative strategy to predict and control intercrystalline transformations. Filling this gap in current state-of-the-art models will significantly impact the pharmaceutical and chemical industries.
