Structural Origin of Anisotropic Thermal Expansion of Molecular Crystals and Implication for the Density Rule Probed with Four ROY Polymorphs

Abstract

The objective of this work was to investigate the molecular origin of the differences in the thermal expansivity of four ROY polymorphs (Y, R, OP, and ON) using variable temperature single crystal X-ray diffractometry (VT-SCXRD). Thermal expansivity was found to be directly influenced by the crystal packing and the number and type of directional interactions, such as hydrogen bonds, involved in packing. Polymorphs with layered molecular packing, i.e., ON, OP, and R, show higher volume expansivity, where the axial component of the expansion is the largest in the directions perpendicular to the hydrogen-bonded layers and the smallest along the layers. Polymorph Y shows the least volume expansivity, which corresponds to the presence of a denser hydrogen-bonded network structure in the crystal, and absence of apparent molecular layers. The largest overall expansivity is observed for polymorph ON that lacks intermolecular hydrogen bonds and exhibits a layered packing pattern along two axes. The differences in the thermal expansivity of the ROY polymorphs lead to violations of the density rule in polymorph stability prediction due to crossover in crystal density with change in temperature, which means the rank order of crystal density of polymorphs is temperature-dependent. Thus, at absolute zero, the most thermodynamically stable polymorph Y is predicted to not have the highest density, which violates the density rule. Likewise, for all enantiotropic polymorphs undergoing the density crossover phenomenon, the density rule is valid only within the temperature range bracketed by the temperatures of density crossover (Td) and thermodynamic transition (Tt). For all monotropic polymorphs, the density rule is valid only above Td.