Gordon-Taylor and Fox Equations for Glass Transition Temperature

The glass transition of binary mixtures of compatible or plasticized polymers usually occurs in a temperature region that is intermediate between the transition temperature regions of the two components. The Fox and Gordon–Taylor equations are two simple algebraic models used to identify this intermediate temperature region. This Demonstration offers a graphical and numerical comparison of the two models for a wide range of hypothetical mixtures. It computes and plots the representative glass transition temperature versus the weight fraction of one component (e.g., the plasticizer's). You can vary the representative glass transition temperatures and of the two ingredients and the value of the constant in the Gordon–Taylor model.


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Snapshot 1: large discrepancy between the two models
Snapshot 2: small discrepancy between the two models
Snapshot 3: the two models can overlap
The concept of a unique glass transition temperature's existence in polymers, including biopolymers and solid foods, has been seriously criticized in recent years [1, 2, 3, 4]. Nevertheless, the glass transition temperature is still widely used in polymer and food technology as a marker of the temperature range where the transition occurs.
Binary mixtures of compatible polymers either with different glass transition temperatures or plasticized with a low molecular weight compound usually undergo the transition at an intermediate temperature range, which has been described mathematically by a variety of models [5]. Two of the simplest mathematically are the Fox and Gordon–Taylor models. They can be written, respectively, in the forms and , where or is the mixture's glass transition temperature (in K), and the temperatures of the components (in K), the weight fraction of the component with the lower transition temperature, which can be a plasticizer, and an adjustable constant in the Gordon–Taylor model's equation.
This Demonstration offers visual comparison of the two models. It computes and plots and simultaneously and displays the numerical values of these terms at any chosen value of , which appear as moving dots on the two curves. You can vary , , , and , as well as the plot ordinate's upper limit.
The main objective of the Demonstration is to offer a general comparison, not to account for any particular system. Consequently, not all the hypothetical entries have real-life counterparts.
[1] R. J. Seyler (ed.), Assignment of the Glass Transition, Philadelphia: ASTM, 1994.
[2] T. McLeish, P. Olmsted, and I. Hamley, "Emerging Themes in Polymer Theory," Emerging Themes in Polymer Science (A. J. Ryan, ed.), Cambridge, UK: Royal Society of Chemistry, 2001.
[3] E.-J. Donth, The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials, New York: Springer, 2001.
[4] M. Peleg, "On Modeling Changes in Food and Biosolids at and around Their Glass Transition Temperature Range," CRC Critical Reviews in Food Science and Nutrition, 36(1–2), 1996 pp. 49–67. doi:10408399609527718.
[5] W. Brostow, R. Chiu, I. M. Kalogeras, and A. Vassilikou–Dova, "Prediction of Glass Transition Temperatures: Binary Blends and Copolymers," Materials Letters, 62(17–18), 2008 pp. 3152–3155. doi:10.1016/j.matlet.2008.02.008.
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