Prediction of the Synergistic Glass Transition Temperature of Coamorphous Molecular Glasses Using Activity Coefficient Models

The glass transition temperature (Tg) of a binary miscible mixture of molecular glasses, termed a coamorphous glass, is often synergistically increased over that expected for an athermal mixture due to the strong interactions between the two components. This synergistic interaction is particularly important for the formulation of coamorphous pharmaceuticals since the molecular interactions and resulting Tg strongly impact stability against crystallization, dissolution kinetics, and bioavailability. Current models that describe the composition dependence of Tg for binary systems, including the Gordon-Taylor, Fox, Kwei, and Braun-Kovacs equations, fail to describe the behavior of coamorphous pharmaceuticals using parameters consistent with experimental ΔCP and Δα. Here, we develop a robust thermodynamic approach extending the Couchman and Karasz method through the use of activity coefficient models, including the two-parameter Margules, non-random-two-liquid (NRTL), and three-suffix Redlich-Kister models. We find that the models, using experimental values of ΔCP and fitting parameters related to the binary interactions, successfully describe observed synergistic elevations and inflections in the Tg versus composition response of coamorphous pharmaceuticals. Moreover, the predictions from the NRTL model are improved when the association-NRTL version of that model is used. Results are reported and discussed for four different coamorphous systems: indomethacin-glibenclamide, indomethacin-arginine, acetaminophen-indomethacin, and fenretinide-cholic acid.