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

Abstract

Using broad-band dielectric spectroscopy (10−2–109 Hz) the merging of the α- and β-relaxations has been investigated for a polymer, syndiotactic poly(methyl methacrylate) (PMMA), in which the dielectric losses are dominated by a strong β-relaxation. The asymmetrically shaped β-relaxation cannot be described by a Cole–Cole function, not even at low temperatures where the α- and β-relaxations are well separated in frequency. At higher temperatures close to Tg (=404 K), the weak α-relaxation enters our dynamic window and rapidly merges with the β-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 β-relaxation then displays a kink in its temperature dependence close to Tg. 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 α- and β-relaxations are statistically independent processes. The dynamics in the merging region of PMMA can then be described using extrapolations of the β-relaxation from low temperatures and the kink in the temperature dependence of the relaxation time of the β-relaxation obtained in the simple addition approach, is explained in terms of overlapping effects between the α- and β-processes, i.e., without invoking any change of relaxation mechanism.