Dielectric spectra of a series of polydimethylsiloxanes and polystyrenes were measured covering a wide range of molecular weights M including the monomeric limit. From spectral analysis the time constants τ R (T) of the segmental dynamics are extracted, allowing determination of the glass-transition temperatures T g (M) and τ R (M) as well as the parameters D(M) and T 0 (M), respectively, ∆(M) ) T g -T 0 , of the Vogel-Fulcher-Tammann equation. In addition, we analyzed fragility m(M) including here also data on polybutadiene. It turns out that all the quantities show particularities as a function of M which are not explained by common wisdom. T g (M) as well as T 0 (M) data reveal a noncontinuous M dependence with three distinct regimes which may become plausible when comparing our results with rheological and NMR data. We attribute the three regimes to simple liquid, Rouse, and entanglement dynamics, i.e., T g (M) and T 0 (M) traces show kinks at the Rouse unit M R and entanglement molecular weight M e . Fragility m(M) shows only one kink at M e . This fact can be explained by the behavior of ∆(M), which increases with M in the simple liquid regime but saturates already at M R ; a similar behavior is observed for the exponential prefactor τ 0 (M). We conclude that polymer dynamics specifically modify glassy dynamics.
The phenomenon of the glass transition is an unresolved problem in condensed matter physics. Its prominent feature, the super-Arrhenius temperature dependence of the transport coefficients, remains a challenge to be described over the full temperature range. For a series of molecular glass formers, we combined τ(T) collected from dielectric spectroscopy and dynamic light scattering covering a range 10(-12) s < τ(T) < 10(2) s. Describing the dynamics in terms of an activation energy E(T), we distinguish a high-temperature regime characterized by an Arrhenius law with a constant activation energy E(∞) and a low-temperature regime for which E(coop)(T) ≡ E(T)-E(∞) increases exponentially while cooling. A scaling is introduced, specifically E(coop)(T)/E(∞) [proportionality] exp[-λ(T/T(A)-1)], where λ is a fragility parameter and T(A) a reference temperature proportional to E(∞). In order to describe τ(T) still the attempt time τ(∞) has to be specified. Thus, a single interaction parameter E(∞) describing the high-temperature regime together with λ controls the temperature dependence of low-temperature cooperative dynamics.
We determine the reorientational correlation time τ of a series of molecular liquids by performing depolarized light scattering experiments (double monochromator, Fabry-Perot interferometry, and photon correlation spectroscopy). Correlation times in the range 10(-12) s-100 s are compiled, i.e., the full temperature interval between the boiling point and the glass transition temperature T(g) is covered. We focus on low-T(g) liquids for which the high-temperature limit τ ≅ 10(-12) s is easily accessed by standard spectroscopic equipment (up to 440 K). Regarding the temperature dependence three interpolation formulae of τ(T) with three parameters each are tested: (i) Vogel-Fulcher-Tammann equation, (ii) the approach recently discussed by Mauro et al. [Proc. Natl. Acad. Sci. U.S.A. 106, 19780 (2009)], and (iii) our approach decomposing the activation energy E(T) in a constant high temperature value E∞ and a "cooperative part" E(coop)(T) depending exponentially on temperature [Schmidtke et al., Phys. Rev. E 86, 041507 (2012)]. On the basis of the present data, approaches (i) and (ii) are insufficient as they do not provide the correct crossover to the high-temperature Arrhenius law clearly identified in the experimental data while approach (iii) reproduces the salient features of τ(T). It allows to discuss the temperature dependence of the liquid's dynamics in terms of a E(coop)(T)/E∞ vs. T/E∞ plot and suggests that E∞ controls the energy scale of the glass transition phenomenon.
Polyisoprenes (PI) covering a wide range of molecular weights (M in g/mol) from 652 ≤ M ≤ 4.36 × 105 are investigated by dielectric spectroscopy. Normal mode (τn) and segmental (or α-) relaxation (τα) are considered. The normal mode spectra are singled out by subtracting the spectra of the segmental relaxation. This yields the full spectrum including its high-frequency cutoff. Regarding the Rouse regime (1040 < M < 9910 ≅ M c ≅ 2M e), we are able to construct a master curve which is quantitatively reproduced by the Rouse theory provided that a weak stretching (βK = 0.8) of the correlation function is introduced for each mode. In the low M limit (M < 1040) the normal mode can not any longer be clearly identified. In the entanglement regime (M > M c) the normal mode spectrum exhibits a power-law behavior ε′′ ∝ ν−γ at high frequencies with an exponent continuously changing until it saturates around M r ≅ 105, yielding γ = 0.26 ± 0.01. Moreover, the M dependence of the ratio τn/τα changes from M 4.0 at M c < M < M r to M 3.0 at M > M r. The latter exponent is that of pure tube reptation; yet, the exponent γ = 0.26 is not compatible with the reptation model. Nevertheless, both findings we take as evidence for another characteristic molecular weight, namely, M r ≅ 20M e, beyond which entanglement dynamics are fully established. Analyzing the strength of the normal mode relaxation as a function of M yields Gaussian statistics of the chains at M > 2000, i.e., well below M c. Including data from field cycling NMR, we provide master curves for both the segmental as well as the terminal relaxation time as a function of T − T g, where T g denotes the glass transition temperature.
Although broadly studied, molecular glass formers are not well investigated above their melting point. Correlation times down to 10(-12) s are easily accessible when studying low-T(g) systems by depolarized light scattering, employing a tandem-Fabry-Perot interferometer and a double monochromator. When combining these techniques with state-of-the-art photon correlation spectroscopy (PCS), broad band susceptibility spectra become accessible which can compete with those of dielectric spectroscopy (DS). Comparing the results with those from DS, optical Kerr effect, and NMR, we describe the evolution of the susceptibilities starting from the boiling point T(b) down to T(g), i.e., from simple liquid to glassy dynamics. Special attention is given to the emergence of the excess wing contribution which is also probed by PCS and which signals a crossover of the spectral evolution. The process is attributed to a small-angle precursor process of the α-relaxation, and the apparent probe dependent stretching of the α-process is explained by a probe dependent contribution of the excess wing. Upon cooling, its emergence is linked to a strong decrease of the strength of the fast dynamics which is taken as reorientational analog of the anomaly of the Debye-Waller factor. Many glass formers show in addition a slow β-process which manifests itself rather universally in NMR, in DS, however, with different amplitudes, but not at all in PCS experiments. Finally, a three-parameter function is discussed interpolating τ(α)(T) from T(b) to T(g) by connecting high- and low-temperature dynamics.
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