Efficient determination of critical water activity and classification of hydrate-anhydrate stability relationship

For a pair of hydrated and anhydrous crystals, the hydrate is more stable than the anhydrate when the water activity is above the critical water activity (a_wc). Conventional methods to determine a_wc are based on either hydrate-anhydrate competitive slurries at different a_w or solubilities measured at different temperatures. However, these methods are typically resource-intensive and time-consuming. Here, we present simple and complementary solution- and solid-based methods and illustrate them using carbamazepine and theophylline. In the solution-based method, a_wc can be predicted using intrinsic dissolution rate (IDR) ratio or solubility ratio of the hydrate-anhydrate pair measured at a known water activity. In the solid-based method, a_wc is predicted as a function of temperature from the dehydration temperature and enthalpy obtained by differential scanning calorimetry (DSC) near a water activity of unity. For carbamazepine and theophylline, the methods yielded a_wc values in good agreement with those from the conventional methods. By incorporating a_wc as an additional variable, the hydrate-anhydrate relationship is categorized into four classes based on their dehydration temperature (T_d) and enthalpy (ΔH_d) in analogy with the monotropy/enantiotropy classification for crystal polymorphs. In Class 1 (ΔH_d< 0 and T_d ≥ 373 K), no a_wc exists. In Class 2 (ΔH_d>0andT_d≥373K), a_wc always exists under conventional crystallization conditions. In Class 3 (ΔH_d<0andT_d<373K), a_wc exists when T>T_d. In Class 4 (ΔH_d>0andT_d<373K), a_wc exists only when Td. The hydrate-anhydrate pairs of carbamazepine and theophylline belong to Class 4.