Temperature Dependence of the Segmental Relaxation Time of Polymers Revisited

We analyze the temperature dependenee of the segmental.,relaxation tithe tau of several low-T-g polymers with varying molar masses (M) as obtained from field-cycling NMR relaxometry And dielectric speotroscopy. They are compared with those of molecular liquids (ML). Time constants in the range 3 X 10(-12) s-1000 s, i.e., between T-g and 413 K, are covered., Describing tau(T) by the Vogel-Fulcher-Tammann (VET) eq a systematic difference with respect to ML is found. While VET fails for the latter it works well for polymers. The apparent activation energy at high temperatures Shows a trend toward a temperature independent value E-infinity For polymers, its M-dependence follows that of T-g(M), thus E-infinity(M) can be described by a Fox-Flory equation. Attempting to understand the difference among the two Classes of liquids, we take recourse to our approach first applied to ML [J. Chem. Phys. 2013, 139, 084504]; i.e., we decompose the temperature-dependent activation energy E(T) controlling tau(T) in a constant high-temperature value E-infinity(M) and a cooperative part E-coop(T). The latter turns out to depend exponentially on temperature, as in ML. Introducing a plot in terms of E-coop(T)/E-infinity vs T/E-infinity, a master curve for each polymer series is revealed. Taking averaged parameters for all polymers a Three-parameter fit well interpolates tau(T) up to highest temperatures, Describing molecular and polymer liquids within the same approach, the difference lies in the fact that the ratio E-infinity/E-coop(T-g) is systematically higher for polymers; tau(T) displays an Arrhenius behavior extending over a larger temperature range.