Physical aging in amorphous polymers far below the glass transition temperature

Constitutive equations are derived for the viscoelastic response and enthalpy recovery in amorphous polymers quenched far below the glass transition temperature. The model is based on the concept of cooperative relaxation, which treats a polymer as an ensemble of independent relaxing regions. Any flow unit is trapped in a cage, where it randomly hops in the potential well being thermally activated. Rearrangement occurs, when a relaxing region reaches in a hop some liquid-like state. Structural relaxation in a disordered medium after quenching is thought of as an increase in roughness of the energy landscape. Using plausible hypotheses about the rearrangement process, stress-strain relations are derived which account for the effect of physical aging on the viscoelastic behavior, and a formula is developed for the increment of the specific enthalpy. These relationships are validated using experimental data in mechanical and calorimetric tests on polycarbonate and polystyrene. Fair agreement is demonstrated between observations and results of numerical simulation.