Gordon-Taylor copolymer equation

The Gordon-Taylor copolymer equation (Equation 4) has been applied to the Tg data in this study to determine if the blends are single-... 

The quantity Tg displays positive deviations from additivity, ATg 130 K, which points toward strong interactions between OH groups of EVOH. In terms of the Gordon-Taylor [1952] equation with mass fraction Wi of component i in the copolymer. 

In the Gordon-Taylor equation (4) Tg is the glass temperature of the copolymer or of the miscible polymer blend, respectively, w and Tg. are the weight fractions resp. glass temperatures of the components. K is a model specific parameter, i.e., ifoT = P ... 

M. Gordon (University of Essex) You said your copolymer effect on T agreed with the Gordon-Taylor equation. That equation was derived in 195 without using the notion of free volume it follows from considering ideal mixing of (overall) molar volumes. As the notional way of splitting overall volumes into free and occupied volumes is controversial I wonder if for your theory it is necessary at all. 

Tg values of several important homopolymers are hsted in reference [2], The values were determined on samples of non-crosslinked emulsion polymers. In crosslinked polymers, Tg is shifted to higher temperatures as a result of the restricted chain mobility. A number of approximations for calculating the Tg of copolymers have been proposed in the literature [26], The Gordon-Taylor equation usually produces reliable results ... 

Styrene forms a homopolymer with a of 100.0°C. The rubbery copolymer with butadiene commonly called styrene-butadiene rubber (SBR) has a Tg of -60°C, whereas the copolymer used for coatings has a of 28.0°C. If a copolymer is made with equal weights of butadiene and vinyl acetate (Tg of polyvinylacetate = 28°C), what is expected for this new copolymer Assume the vahdity of the Gordon-Taylor equation with the same k for any pair of monomers as long as monomer 1 is butadiene. SBR is 25.0 wt% styrene copolymer (coatings) is 25.0 wt% butadiene. 

Figure 5-10. Composition dependence of Tg for a series of random styrene-butadiene copolymers compared to the predicted curve calculated on the basis of equation (5-27) with k = 0.34. [After M. Gordon and J. S. Taylor, J. Appl. Chem. 2, 493 (1952).]...

The description of the historic Gordon-T ay lor and Wood equations for the glass transition of solutions and copolymers can be found in Gordon M, Taylor IS (1952) Ideal Copolymers and the Second-order Transitions of Synthetic Rubbers. I. Noncrystalline Copolymers. J Appl Chem 2 493-500 Wood LA (1958) Glass Transition Temperatures of Copolymers. 1 Polymer Sci 28 319-330 for the relationship to the volume changes, see Kovacs AJ (1964) Glass Transition in Amorphous Polymers. Phenomenological Study. Fortschr Hochpolym Forsch 3 394-508. 

The dependence of the glass transition temperature on copolymer composition has been treated by Gordon and Taylor using a volume approach. In their development for ideal copolymers, Gordon and Taylorassume additivity of volumes of the two components in both rubbery and glassy states. Then two equations result... 

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