Estimating the relative stability of polymorphs and hydrates from heats of solution and solubility data

The transition temperature, T(t), of polymorphs is estimated from both their heats of solution and solubilities (or intrinsic dissolution rates) determined at any one temperature (e.g., ambient). At a given temperature, T, the enthalpy difference, DeltaH, between polymorphs, I and II, is equal to the difference between their heats of solution, whereas the free energy difference, DeltaG, can be estimated by the equation, DeltaG = -RTln (c(I)/c(II)) or DeltaG = -RTln (J(I)/J(II)), where c is the solubility and J is the intrinsic dissolution rate. The entropy difference, DeltaS, is evaluated as (DeltaH - DeltaG)/T. Because the heat capacity difference,DeltaC(p) between polymorphs is small enough to be neglected, the transition temperature may be estimated by the equation, T(t) = DeltaH/DeltaS. The thermodynamic stability relationships of the polymorphs (i.e., whether they are enantiotropes or monotropes) are predicted from the value of T(t) and the melting temperature. The T(t) values for auranofin, carbamazepine, chloramphenicol palmitate, cyclopenthiazide, gepirone hydrochloride, lamivudine, MK571, premafloxacin, sulfamerazine, sulfamethoxazole, sulfathiazole, and urapidil, were calculated from reported values of the heats of solution and solubilities (or dissolution rates). The stability relationships deduced from the calculated values of T(t) are in good agreement with those reported using other methods, such as differential scanning calorimetry and interpretation of melting data.