Merging of the dielectric alpha and beta relaxations in glass-forming polymers

The merging of the main and the secondary dielectric relaxations in a serie s of six polymers has been investigated by using broadband dielectric spect roscopy (10(-2)-10(9) Hz). The data have been analyzed in two different way s. In one case, the whole relaxation process has been modeled by the simple addition of the relaxation functions corresponding to the main and seconda ry relaxations. In the other case, we have used the approach first proposed by Williams and Watts (Williams, G.; Watts, C.D. In NMR, Basic Principles and Progress; Diehl, P., Fluck, E., Kosfeld R, Eds.; Springer-Verlag, Berli n, 1971; Vol. 4, pp 271-285). This approach can be formally reduced to the addition of two terms, one corresponding to the main relaxation and the oth er to a combination of the functions corresponding to the main and secondar y relaxations extrapolated from low temperatures. Both methods of analysis happen to describe the experimental data successfully in the merging region . In the framework of the Williams and Watts approach, the experimental beh avior in the merging range is explained simply as a natural consequence of the extrapolation of the low-temperature relaxation behavior. However, usin g the simple addition method, this is not possible, which in this framework would be interpreted as due to a change of the secondary relaxation mechan ism in the merging region. Therefore, the Williams and Watts approach provi des the simplest physical picture for describing the merging of the a and P relaxations. Finally, the results obtained in this framework are interpret ed using a free-energy landscape model.