Crystallization and polymorphism — Physico-chemistry of polymorphism

Second in a series of three, this article looks at the physical and thermodynamic principles behind polymorphism.

After showing how the notion of sphere stacking can provide a simple model for understanding the phenomenon of polymorphism and its consequences, a detailed study of the physical forces at play in crystalline stacks is proposed (ionic, Van der Waals and repulsive forces), along with a brief review of polymorphism modeling techniques.

The heart of the article is devoted to an introduction to the thermodynamics of crystalline polymorphism. After recalling the definitions of Gibbs free enthalpy and entropy of a crystalline system, the notions of enantiotropy and monotropy characterizing the relative thermodynamic stabilities as a function of temperature and pressure, for different crystalline forms of the same molecule, are discussed within the framework of pressure/temperature and free enthalpy/temperature diagrams. Examples of monotropic and enantiotropic systems are then described, showing in particular how calorimetric analysis can help classify phenomena. The relationships between the Gibbs free enthalpy difference of two crystalline forms and their saturation solubilities, intrinsic dissolution kinetics and chemical reactivities are then demonstrated. This paragraph is of fundamental importance in understanding the consequences of polymorphism in various fields, particularly in the pharmaceutical field, which are explained in the third fascicule. .

This second article also covers the case of solvates and hydrates and, more succinctly, the case of molecules with chirality (mainly asymmetric carbons).

Finally, a review of the analytical methods used to characterize polymorphism and the methods used to obtain it (polymorphic screening) are discussed, with extensive reference to the literature.