Temperature Dependence of the Segmental Relaxation Time of Polymers Revisited

Abstract

We analyze the temperature dependence of the segmental relaxation time τ of several low-Tg polymers with varying molar masses (M) as obtained from field-cycling 1H NMR relaxometry and dielectric spectroscopy. They are compared with those of molecular liquids (ML). Time constants in the range 3 × 10–12 s–1000 s, i.e., between Tg and 413 K, are covered. Describing τ(T) by the Vogel–Fulcher–Tammann (VFT) eq a systematic difference with respect to ML is found. While VFT 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∞. For polymers, its M-dependence follows that of Tg(M), thus E∞(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 τ(T) in a constant high-temperature value E∞(M) and a “cooperative part” Ecoop(T). The latter turns out to depend exponentially on temperature, as in ML. Introducing a plot in terms of Ecoop(T)/E∞ vs T/E∞, a master curve for each polymer series is revealed. Taking averaged parameters for all polymers a three-parameter fit well interpolates τ(T) up to highest temperatures. Describing molecular and polymer liquids within the same approach, the difference lies in the fact that the ratio E∞/Ecoop(Tg) is systematically higher for polymers; i.e., τ(T) displays an Arrhenius behavior extending over a larger temperature range.