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⁾

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

where T_g,mix and T_g,i are the glass transition temperature of the mixture and of the components, ω_i 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, ΔC_pi. For mixtures with two or more components this equation is given as

T_g,mix ≈ ∑_i [ω_i · ΔC_pi T_g,i] / ∑_i [ω_i · ΔC_pi ]

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 T_g 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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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)

 

 

Heat Capacity Change at Tg

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