Cooperative relaxation processes in polymers

Abstract

The basic mode of relaxation in polymer molecules involves the rotation of a conformer, with a time scale of the order of picoseconds. This fast relaxation process, however, cannot take place easily in the condensed state crowded by densely packed conformers, necessitating the intermolecular cooperativity among them. The domain of cooperativity grows at lower temperatures, towards the infinite size at the Kauzman zero entropy temperature, though the system deviates from the equilibrium as the glass transition intervenes at about 50°C above that temperature. From the temperature dependence of the domain size, the well-known Vogel equation is derived, which we consider is the basic origin of the empirical WLF and free volume equations. The molar volume is a crucial factor in determining molar free volume. The molecular weight of a conformer with a density correction, therefore, can be used as a parameter in determining the T g of liquids and amorphous polymers. A larger size conformer means a higher glass transition temperature. A conformer at the chain end, on the other hand, has a higher enthalpy, i.e., a smaller effective size for that conformer. If a conformer is reacted trifunctionally, the resulting conformer is a combination of the two conformers and T g increases, but a further addition of another conformer to that branch point reduces the average size of the conformers, so T g decreases. The model for cooperative relaxation can be directly applied to predicting T g S from the chemical structure of polymers, the kinetics and T g S of thermosets during the crosslinking reaction, the distribution of relaxation times from the domain size distribution at a given temperature, the dynamics of the physical aging process, and other complex behaviors of polymers and liquids near the glass transition temperature.