The Ostwald Ratio, Kinetic Phase Diagrams, and Polymorph Maps

From a general formulation of batch crystallization in a polymorphic system, it is shown that the concept of an Ostwald ratio provides a fundamental parameter with which to understand and compute the variation in polymorph composition with time, temperature, and supersaturation. In particular, it defines the conditions under which a system will exhibit sequential development of polymorphs, as per the widely known Ostwald’s Rule of Stages and conversely when either only the stable polymorph will result or when forms appear simultaneously resulting in concomitant polymorphism. The Ostwald ratio is not a constant but varies with temperature, the initial supersaturation, crystal shape, and density. It is shown that its evaluation can lead to a kinetically based phase diagram enabling the construction of polymorph maps in compositional and temperature space. A review of relevant existing kinetic data reveals a lack of information concerning both the relative nucleation and growth rates of polymorphic phases. The specific case of gestodene is used as a means of demonstrating the significance and potential of this approach to the robust design of batch crystallization processes in polymorphic systems.