Description of physical aging kinetics of glassy polymers by interpretation of parameters of the Kohlrausch-Williams-Watts relaxation function via simulation

The empirical Kohlrausch-Williams-Watts (KWW) relaxation function has been widely used to describe the nonexponential relaxation behavior of glassy polymers during their physical aging. The characteristic relaxation time (τ_{KWW}) and the stretching parameter (β_{KWW}) of the KWW equation are obtained from experimental relaxation data by a curve-fitting procedure. However, knowing the values of KWW parameters is not sufficient to completely characterize the physical aging kinetics of glassy materials in order to compare, for example, the aging rate of different systems. To be able to overcome such problems, at least, an exact interpretation of these parameters is absolutely vital and then it would be quite desirable to convert them into a single relaxation-time constant. This approach, indeed, provides the possibility to directly evaluate and compare the kinetics and aging rate of different systems as well as different methods used for monitoring the physical aging of the same materials. To do these, a method based on the notion of the relaxation spectrum is employed which is modeled via the well-known statistical distribution of log-normal. By detailed numerical simulations, some explicit expressions between KWW parameters with descriptor parameters of the distribution are established. From this point of view, it is tried to interpret τ_{KWW} and β_{KWW} and convert them into a single relaxation-time constant. Finally, the results of suggested simulations are compared with those obtained in the literature.