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The amorphous state: first-principles derivation of the Gordon–Taylor equation for direct prediction of the glass transition temperature of mixtures; estimation of the crossover temperature of fragile glass formers; physical basis of the “Rule of 2/3”

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Abstract

Predicting the glass transition temperature (Tg) of mixtures has applications that span across industries and scientific disciplines. By plotting experimentally determined Tg values as a function of the glass composition, one can usually apply the Gordon–Taylor (G–T) equation to determine the slope, k, which subsequently can be used in Tg predictions. Traditionally viewed as a phenomenological/empirical model, this work proposes a physical basis for the G–T equation. The proposed equations allow for the calculation of k directly and, hence, they determine/predict the Tg values of mixtures algebraically. Two derivations for k are provided, one for strong glass-formers and the other for fragile mixtures, with the modeled trehalose–water and naproxen–indomethacin systems serving as examples of each. Separately, a new equation is described for the first time that allows for the direct determination of the crossover temperature, Tx, for fragile glass-formers. Lastly, the so-called “Rule of 2/3”, which is commonly used to estimate the Tg of a pure amorphous phase based solely on the fusion/melting temperature, Tf, of the corresponding crystalline phase, is shown to be underpinned by the heat capacity ratio of the two phases referenced to a common temperature, as evidenced by the calculations put forth for indomethacin and felodipine.

Graphical abstract: The amorphous state: first-principles derivation of the Gordon–Taylor equation for direct prediction of the glass transition temperature of mixtures; estimation of the crossover temperature of fragile glass formers; physical basis of the “Rule of 2/3”

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Publication details

The article was received on 19 Jun 2017, accepted on 13 Jul 2017 and first published on 13 Jul 2017


Article type: Paper
DOI: 10.1039/C7CP04124A
Citation: Phys. Chem. Chem. Phys., 2017, Advance Article
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    The amorphous state: first-principles derivation of the Gordon–Taylor equation for direct prediction of the glass transition temperature of mixtures; estimation of the crossover temperature of fragile glass formers; physical basis of the “Rule of 2/3”

    P. J. Skrdla, P. D. Floyd and P. C. Dell’Orco, Phys. Chem. Chem. Phys., 2017, Advance Article , DOI: 10.1039/C7CP04124A

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