Merging of the dielectric α and β relaxations in glass-forming polymers

The merging of the main and the secondary dielectric relaxations in a series of six polymers has been investigated by using broadband dielectric spectroscopy (10(-2)-10(9) Hz). The data have been analyzed in two different ways. In one case, the whole relaxation process has been modeled by the simple addition of the relaxation functions corresponding to the main and secondary 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, Berlin, 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 other to a combination of the functions corresponding to the main and secondary 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 behavior in the merging range is explained simply as a natural consequence of the extrapolation of the low-temperature relaxation behavior. However, using the simple addition method, this is not possible, which in this framework would be interpreted as due to a change of the secondary relaxation mechanism in the merging region. Therefore, the Williams and Watts approach provides the simplest physical picture for describing the merging of the a and P relaxations. Finally, the results obtained in this framework are interpreted using a free-energy landscape model.