THE MERGING OF THE DIELECTRIC ALPHA-RELAXATIONS AND BETA-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 polyme r, syndiotactic poly(methyl methacrylate) (PMMA), in which the dielect ric losses are dominated by a strong beta-relaxation. The asymmetrical ly shaped beta-relaxation cannot be described by a Cole-Cole function, not even at low temperatures where the alpha- and beta-relaxations ar e well separated in frequency. At higher temperatures close to T-g (=4 04 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-relaxat ion then displays a kink in its temperature dependence close to T-g. T o gain further understanding of the merging, the data were analyzed by means of a regularization method in order to calculate the correspond ing distributions of relaxation times directly from the actual measure ments 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 i ndependent processes. The dynamics in the merging region of PMMA can t hen be described using extrapolations of the beta-processes, i.e., wit hout invoking any change of relaxation mechanism. (C) 1998 American In stitute of Physics. [S0021-9606(98)51941-1].