Crystallization from solutions containing multiple conformers: A new modeling approach for solubility and supersaturation

Abstract

A mechanistic approach to identify the driving force for crystallization and to determine the solubility of solids crystallized from solutions containing multiple conformers is presented. It is assumed that only one conformer, which is referred to as the right conformer (RC), integrates into the crystal surface if the energy barrier of transition between conformers is higher than 10 kcal/mol. Conformers that do not integrate into the crystal surface are lumped into a single conformation which is referred to as the wrong conformer (WC). This approach, which is referred to as the approach of the RC, was applied to two organic substances that presented unusual solubility and crystallization behaviors: constant or retrograde solubility and sharply decreasing crystallization duration with temperature. For both substances, 1H NMR data indicated the presence of multiple conformations in solution and rotomers’ peak coalescence was reached at relatively high temperature indicating high energy barriers of transition between conformers. In addition, ab initio calculations revealed that the RC is the high energy conformer indicating that the WC levels in solution are higher. On the basis of these observations, the approach of the RC was considered to be applicable for the substances studied. This approach considers that the RC is the only species in true equilibrium with the solid at saturation. The intrinsic solubility and the total solubility are introduced for non-ionizable organic molecules and are defined respectively as the concentration of the RC and the concentration of all conformers at saturation. The intrinsic supersaturation (ISS), defined as the concentration of the RC minus the intrinsic solubility, is considered to be the driving force for the crystallization and expressions relating the total solubility and the ISS to crystallization parameters are derived. Computed total solubility was in agreement with either the constant or retrograde solubility observed experimentally for the substances studied. Slow crystallization was attributed to the low levels of the calculated ISS and to crystal growth inhibition caused by high levels of the WC. In addition, this approach provided a simple means for the experimental estimation of the energy difference between the two main conformers. Finally, on the basis of the predicted increase of ISS with temperature, an alternate crystallization procedure based on a single heating ramp was utilized to provide crystals with improved powder properties.