Aspects of simple, non-cooperative relaxations

The lower limit for the activation energies of internal motions in polymers is defined by a relationship corresponding to an activation entropy of zero. We associate this characteristic with non-cooperative motions of molecular segments. While these motions are localized in space, they are very diffuse in frequency or time. Examples are side-group relaxations and certain motions within the crystalline regions. Local-mode γ relaxations of the main chain appear to involve a spectrum of motions in which the limiting low-temperature, high-frequency component has an activation entropy close to zero. Glass transitions characteristically have very large apparent activation energies and entropies. This is attributed to a spectrum of motions that is sampled differently at different temperatures. At temperatures well above T g, the apparent activation energy again approaches a value corresponding to a zero activation entropy. For a wide variety of relaxations, the distribution of relaxation times corresponds to a distribution of activation enthalpies having a width at half-maximum of 5–6 kcal mol −1.