Stability prediction of amorphous benzodiazepines by calculation of the mean relaxation time constant using the Williams-Watts decay function.

The enthalpic relaxation of three amorphous benzodiazepines, diazepam, temazepam and triazolam was studied using differential scanning calorimetry for ageing temperatures which were below the glass transition temperature, and ageing times up to 16 h. Experimental determination of the relaxation enthalpy and the heat capacity change, both accompanying the glass transition, enabled us to calculate the extent of relaxation of the amorphous drugs at specific ageing conditions. Fitting of the relaxation function to the Williams-Watts two parameter decay function led to calculation of the mean relaxation time constant tau and the molecular relaxation time distribution parameter beta. The mean relaxation time constants for the three drugs increased from approximately ten h at the glass transition temperature with more than eight orders of magnitude at 66 K below the glass transition temperature. It was found that the benzodiazepines exhibited significant molecular mobility until approximately 50 K below the glass transition temperature; below this temperature molecular mobility becomes unimportant with respect to the shelf life stability. Hence the presented procedure provides the formulation scientist with a tool to set storage conditions for amorphous drugs and glassy pharmaceutical products.