Gordon-Taylor Equation

Several approaches have been proposed for estimating the glass transition temperature of mixtures and random copolymers from knowledge of the properties of the pure components. Although different in detail, the proposed relationships are all based on the additivity of basic thermophysical properties. One of the most popular equations for predicting glass transition temperatures of amorphous mixtures and random copolymers is the Gordon-Taylor equation:(1)

Tg,mix[ω1 · Tg,1 + K · ω2 · Tg,2] / [ω1 + K · ω2 ]

where Tg,mix and Tg,i are the glass transition temperature of the mixture and of the components, ωi is the mass fraction of component i and K is an adjustable fitting parameter. If no experimental data are available, the constant K can be set equal to the change of the heat capacity when crossing from the glass to the rubber state, ΔCpi. For mixtures with two or more components this equation is given as

Tg,mixi [ωi · ΔCpi Tg,i] / i [ωi · ΔCpi ]

The Gordon-Taylor equation has been shown to be successful for fitting the glass transition temperature of many random copolymers. It can also be used to describe the composition dependence of miscible polymer blends exhibiting negative and positive deviation if K is treated as an adjustable parameter. However, the Gordon-Taylor equation should only be applied to blends and mixtures with relative weak specific intermolecular interactions. Otherwise, large deviations from the true Tg of the mixture can be expected. A suitable example would be a blend of polystyrene (PS) and poly(2,6-dimethyl-p-phenylene oxide) (PPO). Both polymers have similar structural groups and no specific interactions are present. The predicted values for such a blend (see below) are in good agreement with the experimental values (2)

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Glass Transition Temperature of PS-PPO blends

Weight Fraction PS Exper. Tg (K) Predicted Tga (K) Predicted Tgb (K)
0 489 489 489
0.2 461 460 459
0.4 434 435 434
0.5 425 424 423
0.6 413 414 413
0.8 396 395 395
1.0 379 379 379
The glass transition temperatures have been calculated with the software 3Ps-Tg from Triton Road.
acalculated with experimental discontinuous increment in specific heat
bcalculated with predicted discontinuous increment in specific heat

Glass Transition Temperature of PS-PPO blends

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References
  1. M. Gordon, J. S. Taylor, J. Appl. Chem. 2, 495 (1952)
  2. L. An, D. He, J. Jing et al., Eur. Polym. J., Vol. 33, No 9, 1523 - 1528 (1997)
  • Summary

    Gordon-Taylor Equation

    describes the composition dependence of the transition temperature of amorphous mixtures and random copolymers.

  • The Gordon-Taylor equation should only be applied to miscible blends and random copolymers with relative weak specific intermolecular interactions.

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Heat Capacity Change at Tg

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