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

Abstract

The glass transition temperature (T g) 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 T g strongly impact stability against crystallization, dissolution kinetics, and bioavailability. Current models that describe the composition dependence of T g 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 ΔC P 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 ΔC P and fitting parameters related to the binary interactions, successfully describe observed synergistic elevations and inflections in the T g 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.

Estimation of Component Activities and Molar Excess Gibbs Energy of 19 Binary Liquid Alloys from Partial Pair Distribution Functions in Literature

“…Equation ( 23) is the original form derived by Wilson in his work [15]. If this equation were used for calculation, Equations ( 7), (13), and ( 23) would be in conflict, as Wilson expressed the local mole fraction as a function of the molecular pair potential, which differs from the expression used in this work. Equation ( 13) is more appropriate, so A ij and A ji were rewritten in this work.…”

“…Engineers usually obtain the model parameters by using experimentally-determined excess Gibbs energy and activity to fit a regression equation [5][6][7][8][9][10]. Therefore, it is challenging to use the thermodynamic models to estimate gas-liquid equilibrium without relying on experimental thermodynamic values [11][12][13]. In 1999, Sam et al used ab initio molecular dynamics (AIMD) simulations to obtain the molecular pair potential from clusters of eight atoms composed of water and alcohol (acid) as the UNIQUAC model parameters.…”

Glass Transition Temperatures of Organic Mixtures from Isoprene Epoxydiol-Derived Secondary Organic Aerosol

“…Kwei attributed the quadratic term q normalK normalw normale normali x normala ( 1 − x a ) to the effect of hydrogen bonding forming cross linkages in the polymer mixtures. Studies have used the Kwei equation to fit and explain the T g -composition relation of hydrogen bonding polymer mixtures. − In addition, the Kwei equation can also provide a good fit to the measured T g of binary mixtures of molecular liquids. − For example, the quadratic term of the Kwei equation used to fit the T g of binary blends of trehalose and choline dihydrogen phosphate was attributed to hydrogen bonding . The Kwei equation has the potential to predict the T g of SOA mixtures when the Gordon–Taylor equation fails, particularly in the cases of substantial intermolecular interactions.…”

Composition‐dependentglass transition temperature in mixtures: Evaluation of configurational entropy models*

“…It is noted that this form is the same as the correction used in the Kwei model ( qx 1 x 2 ). Other more complicated expressions have also been used, especially for systems with stronger intermolecular interactions in which excess enthalpic effects are considered, [ 19,20 ] systems where phase separation occurs, [ 21 ] and systems where the T g s of the two components are very different [ 22 ] ; however, these models are not of interest here because our aim is to examine nearly ideal miscible systems in which intermolecular interactions do not vary appreciably with composition.…”

“…intermolecular interactions in which excess enthalpic effects are considered, [19,20] systems where phase separation occurs, [21] and systems where the T g s of the two components are very different [22] ; however, these models are not of interest here because our aim is to examine nearly ideal miscible systems in which intermolecular interactions do not vary appreciably with composition.…”