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 (awc). Conventional methods to determine awc are based on either hydrate-anhydrate competitive slurries at different aw 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, awc 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, awc 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 awc values in good agreement with those from the conventional methods. By incorporating awc as an additional variable, the hydrate-anhydrate relationship is categorized into four classes based on their dehydration temperature ( T d ) and enthalpy ( Δ H d ) in analogy with the monotropy/enantiotropy classification for crystal polymorphs. In Class 1 ( Δ H d < 0 and T d ≥ 373 K), no awc exists. In Class 2 ( Δ H d > 0 and T d ≥ 373 K ) , awc always exists under conventional crystallization conditions. In Class 3 ( Δ H d < 0 and T d < 373 K ) , awc exists when T > T d . In Class 4 ( Δ H d > 0 and T d < 373 K ) , awc exists only when T < T d . The hydrate-anhydrate pairs of carbamazepine and theophylline belong to Class 4.