Volume and enthalpy relaxation in glassy polymers

Constitutive relations are derived for the evolution of specific volume and specific enthalpy in amorphous glassy polymers after thermal treatment. The Robertson approach is extended to infinite ensembles of cells, and a nonlinear partial differential equation is developed for the probability density of free volume. This equation is resolved explicitly under plausible assumptions, whose validity is verified by comparison with observations for polystyrene. As a result, two ordinary differential equations are obtained for the excess specific volume and the excess specific enthalpy, which provide a molecular basis for the Kovacs phenomenological relations. It is demonstrated that in one-step thermal tests, the rate of change in the specific enthalpy exceeds by twice that for the specific volume. This conclusion is confirmed by experimental data for polycarbonate and polystyrene.