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-T g polymers with varying molar masses (M) as obtained from field-cycling 1 H 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 T g 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 Mdependence follows that of T g (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" 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 ∞ 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 ∞ /E coop (T g ) is systematically higher for polymers; i.e., τ(T) displays an Arrhenius behavior extending over a larger temperature range.

Insights into the structural dynamics of poly lactic-co-glycolic acid at terahertz frequencies

“…The C-O bonds are effective electron donors and contribute a large degree of molecular freedom to the copolymer backbone, thereby enhancing torsional motions in the copolymer backbone ( Figure 5, rotation 1). Based on our data, and extensive investigations in the literature 5,[9][10][11][35][36][37] , we hypothesise that the rotational motions of individual polymer segments, described above, and the associated changes in dipole moments are responsible for the observed changes in the terahertz spectra and that the onset of these motions is critical to the β -relaxation process in PLGA. At low temperatures the relative density of the PLGA chain segments is high and the motions of the chain segments are hindered due to their tight packing.…”

Precise synthesis of a series of poly(4-n-alkylstyrene)s and their glass transition temperatures

“…Figure shows the molecular weight dependence of the glass transition temperatures for all poly(4‐n‐alkylstyrene)s. It is obvious that the T g s of a series of polymers increase as the molecular weight and finally they reach asymptotic values at high molecular weight. The similar molecular weight dependence was also reported for polystyrene (PS) and poly(dimethyl siloxane) and others in literatures . It is well‐established that the molecular weight dependence of T g can be described by the following empirical Fox–Flory equation where the T g,∞ is the T g at infinitely high molecular weight and K is polymer‐specific constant.…”

Rubber friction: The contribution from the area of real contact

“…Assuming a similar reduction in T g gives in our case (with T g ≈ 250 K) v 0 ≈ v 0 /1000, so the segmental relaxation time τ = λ/v 0 at the surface glass transition temperature T g would be of order ∼10 s, i.e., similar to what is expected for glassy polymers at T g (note: different glassy polymers exhibit very similar segmental relaxation times at T g ). 29 To summarize, it is assumed that the polymer segments at the rubber surface have higher mobility than in the bulk. Of course, if the polymer segments interact strongly with a substrate, it may have a lower mobility than in the bulk.…”