Glass Transition Temperature of Homogeneous Blends and Copolymers

The volume change of mixing is the difference of the volume of a blend and that of ideal blend, calculated with additive equation. The glassy state is non-equilibrium state and thus has the excess volume against equilibrium state. If the glass transition temperature, Tg, of a blend, TgB, is not equal to Tg calculated with Gordon-Taylor equation, TgAv, the volume change of mixing changes discontinuously at TgB because excess volumes vitrified at TgB and TgAv is different. The situation is similar for enthalpy and entropy. Assuming that volume change, enthalpy or entropy of mixing at TgB is proportional to the product of mole fractions of component polymers, equations to express the composition dependence of TgB are derived. The obtained equations reproduced observed Tg of blends well. Using TgB thus obtained, Tg of alternating copolymer, and, probability of the presence of hetero sequence in copolymer, the equations to express Tg of copolymers are derived.