A MODEL FOR INTERMOLECULAR COOPERATIVITY IN CONFORMATIONAL RELAXATIONS NEAR THE GLASS-TRANSITION

Some of the basic molecular and thermodynamic factors that affect the relaxation behavior above and below the glass transition temperature are discussed. A model is proposed for segmental relaxation that requires intermolecular cooperativity. A domain of cooperativity is defined as a group of segments that must undergo relaxation simultaneously. As the density is increased by changes in temperature or pressure, the domain size, as specified by the number z of the interlocked segments, grows and the conformational entropy decreases more than it would in isolated chains. In the process, it becomes progressively more difficult to maintain thermodynamic equilibrium, and the glass transition ensues. It can be shown that for a given drop in temperature, the increase in the domain size z is greater for a polymer with a larger conformer, which as a result undergoes the glass transition at a higher temperature. Thus, this model employs the basic concepts of the theory of Adam and Gibbs, although the specifics vary. A relaxation function is formulated based on the domain size distribution. The resulting equation gives a better fit to the dielectric and viscoelastic data than the Kohlrausch-Williams-Watts equation, particularly at extremely high frequency or short times. The theory is extended into the nonequilibrium glassy state by fixing the entropy at the fictive temperature. In the glassy state, the breadth of the relaxation spectrum increases because of the domain size-dependent spread in the activation energy for the segmental relaxation.