Glass transition temperatures of copolymers

The Gordon‐Taylor equation relating the glass transition temperature θ of a copolymer to the glass transition temperatures θ₁ and θ₂ of the homopolymers is equivalent to where c₁ and c₂ are the weight fractions of the constituents and A₁ and A₂ are constants. It can be recast into the following forms suitable for linear plots and where k = A₂/A₁. Data from the literature on 10 copolymer systems, including butaciene‐styrene copolymers, give linear plots, verifying the equation within experimental error. However, the observed value of k is in most cases significantly smaller than the ratio of the differences of the volume‐temperature coefficients for each homopolymer in the rubbery and glassy states, as required by the derivation of Gordon and Taylor. The glass transition temperature (in °C.) for a butadiene‐styrene copolymer prepared by emulsion polymerization at 50°C. may be calculated from the weight fraction c₂ of bound styrene as and for a similar 5° copolymer as