Defect-diffusion models of relaxation

Abstract A model of molecular relaxation in glassy materials is presented to describe configurational fluctuations which decay via the mediation of mobile defects. A mild distribution of free-energy barriers impeding the defect motion can generate a wide distribution of waiting times between defect displacements. When the mean waiting time is longer than the time of an experiment, no characteristic time scale exists. This case directly yields the Kohlrausch- Williams-Watts (KWW) stretched exponential relaxation law. Correlations between defects described by the Ornstein-Zernicke theory of critical fluctuations cause aggregation of defects and produce a Vogel-Fulcher (VF) type law for the disappearance of singlet defects, and therefore a VF law for the dipole relaxation time. The model is also applied to predict the molecular weight dependence of mechanical relaxation times (physical aging) in glassy polymeric systems.