The merging of the dielectric α- and β-relaxations in poly(methyl methacrylate)

Using broad-band dielectric spectroscopy (10(-2)-10(9) Hz) the merging of the alpha- and beta-relaxations has been investigated for a polymer, syndiotactic poly(methyl methacrylate) (PMMA), in which the dielectric losses are dominated by a strong beta-relaxation. The asymmetrically shaped beta-relaxation cannot be described by a Cole-Cole function, not even at low temperatures where the alpha- and beta-relaxations are well separated in frequency. At higher temperatures close to T-g (=404 K), the weak alpha-relaxation enters our dynamic window and rapidly merges with the beta-relaxation. To investigate this merging process we first used a simple addition of two Havriliak-Negami (HN) equations to fit the spectra. The obtained relaxation time for the beta-relaxation then displays a kink in its temperature dependence close to T-g. To gain further understanding of the merging, the data were analyzed by means of a regularization method in order to calculate the corresponding distributions of relaxation times directly from the actual measurements without the need of invoking any parametrical fitting functions. From these distributions we obtained the relaxation functions in time domain which were analyzed by adopting an ansatz proposed by Williams which implies that the alpha-and beta-relaxations are statistically independent processes. The dynamics in the merging region of PMMA can then be described using extrapolations of the beta-processes, i.e., without invoking any change of relaxation mechanism. (C) 1998 American Institute of Physics. [S0021-9606(98)51941-1].