Inferring thermodynamic stability relationship of polymorphs from melting data.

This study investigates the possibility of inferring the thermodynamic stability relationship of polymorphs from their melting data. Thermodynamic formulas are derived for calculating the Gibbs free energy difference (delta G) between two polymorphs and its temperature slope from mainly the temperatures and heats of melting. This information is then used to estimate delta G, thus relative stability, at other temperatures by extrapolation. Both linear and nonlinear extrapolations are considered. Extrapolating delta G to zero gives an estimation of the transition (or virtual transition) temperature, from which the presence of monotropy or enantiotropy is inferred. This procedure is analogous to the use of solubility data measured near the ambient temperature to estimate a transition point at higher temperature. For several systems examined, the two methods are in good agreement. The qualitative rule introduced this way for inferring the presence of monotropy or enantiotropy is approximately the same as The Heat of Fusion Rule introduced previously on a statistical mechanical basis. This method is applied to 96 pairs of polymorphs from the literature. In most cases, the result agrees with the previous determination. The deviation of the calculated transition temperatures from their previous values (n = 18) is 2% on average and 7% at maximum.