Enthalpy recovery in glassy materials: heterogeneous versus homogenous models

Models of enthalpy relaxations of glasses are the basis for understanding physical aging, scanning calorimetry, and other phenomena that involve non-equilibrium and non-linear dynamics. We compare models in terms of the nature of the relaxation dynamics, heterogeneous versus homogeneous, with focus on the Kovacs-Aklonis-Hutchinson-Ramos (KAHR) and the Tool-Narayanaswamy-Moynihan (TNM) approaches. Of particular interest is identifying the situations for which experimental data are capable of discriminating the heterogeneous from the homogeneous scenario. The ad hoc assumption of a single fictive temperature, T(f), is common to many models, including KAHR and TNM. It is shown that only for such single-T(f) models, enthalpy relaxation of a glass is a two-point correlation function in reduced time, implying that experimental results are not decisive regarding the underlying nature of the dynamics of enthalpy relaxation. We also find that the restriction of the common TNM model to a Kohlrausch-Williams-Watts type relaxation pattern limits the applicability of this approach, as the particular choice regarding the distribution of relaxation times is a more critical factor compared with isothermal relaxation experiments. As a result, significant improvements in fitting calorimetry data can be achieved with subtle adjustments in the underlying relaxation time distribution.