Dynamics of asymmetric binary glass formers. II. Results from nuclear magnetic resonance spectroscopy.

Various (2)H and (31)P nuclear magnetic resonance (NMR) spectroscopy techniques are applied to probe the component dynamics of the binary glass former tripropyl phosphate (TPP)/polystyrene-d3 (PS) over the full concentration range. The results are quantitatively compared to those of a dielectric spectroscopy (DS) study on the same system previously published [R. Kahlau, D. Bock, B. Schmidtke, and E. A. Rössler, J. Chem. Phys. 140, 044509 (2014)]. While the PS dynamics does not significantly change in the mixtures compared to that of neat PS, two fractions of TPP molecules are identified, one joining the glass transition of PS in the mixture (α1-process), the second reorienting isotropically (α2-process) even in the rigid matrix of PS, although at low concentration resembling a secondary process regarding its manifestation in the DS spectra. Pronounced dynamical heterogeneities are found for the TPP α2-process, showing up in extremely stretched, quasi-logarithmic stimulated echo decays. While the time window of NMR is insufficient for recording the full correlation functions, DS results, covering a larger dynamical range, provide a satisfactory interpolation of the NMR data. Two-dimensional (31)P NMR spectra prove exchange within the broadly distributed α2-process. As demonstrated by (2)H NMR, the PS matrix reflects the faster α2-process of TPP by performing a spatially highly hindered motion on the same timescale.

Dynamics of asymmetric binary glass formers. I. A dielectric and nuclear magnetic resonance spectroscopy study.

Dielectric spectroscopy as well as (2)H and (31)P nuclear magnetic resonance spectroscopy (NMR) are applied to probe the component dynamics of the binary glass former tripropyl phosphate (TPP)/polystyrene (PS/PS-d3) in the full concentration (cTPP) range. In addition, depolarized light scattering and differential scanning calorimetry experiments are performed. Two glass transition temperatures are found: Tg 1(cTPP) reflects PS dynamics and shows a monotonic plasticizer effect, while the lower Tg 2(cTPP) exhibits a maximum and is attributed to (faster) TPP dynamics, occurring in a slowly moving or immobilized PS matrix. Dielectric spectroscopy probing solely TPP identifies two different time scales, which are attributed to two sub-ensembles. One of them, again, shows fast TPP dynamics (α2-process), the other (α1-process) displays time constants identical with those of the slow PS matrix. Upon heating the α1-fraction of TPP decreases until above some temperature Tc only a single α2-population exists. Inversely, below Tc a fraction of the TPP molecules is trapped by the PS matrix. At low cTPP the α2-relaxation does not follow frequency-temperature superposition (FTS), instead it is governed by a temperature independent distribution of activation energies leading to correlation times which follow Arrhenius laws, i.e., the α2-relaxation resembles a secondary process. Yet, (31)P NMR demonstrates that it involves isotropic reorientations of TPP molecules within a slowly moving or rigid matrix of PS. At high cTPP the super-Arrhenius temperature dependence of τ2(T), as well as FTS are recovered, known as typical of the glass transition in neat systems.

Secondary relaxations in a series of organic phosphate glasses revealed by dielectric spectroscopy.

Dielectric susceptibility spectra of six chemically similar organic phosphate glass formers are analyzed in order to elucidate the spectral evolution of a multitude of secondary (ß) relaxation processes dominating the dielectric loss below the glass transition temperature T(g). By doing the spectral analysis we forgo any data fitting procedure and apply a model independent scaling approach instead. This approach assumes a constant distribution of activation energies g(E) underlying a plurality of thermally activated processes, which determine the ß-relaxation. The scaling reveals temperature independent, asymmetric distributions g(E) for temperatures well below T(g). Simultaneously, the temperature dependence of the relaxation strength of the ß-processes Δε(ß)(T) is yielded, being nearly constant well in the glassy state. Already somewhat below T(g) the spectral scaling fails and reveals an apparent increase of the mean activation energy, leading to a weaker temperature dependence of the mean relaxation times τ(ß)(T). In the same temperature regime Δε(ß)(T) starts to increase drastically, i.e., the softening of the glass near T(g) is reflected directly in the loss of temperature independence of g(E) and Δε(ß)(T). Comparing the different glasses made from phosphate molecules with increasing number of internal degrees of freedom we do not see systematic changes in the spectral evolution. In some cases even identical distributions g(E) are found.

Reorientational dynamics in molecular liquids as revealed by dynamic light scattering: from boiling point to glass transition temperature.

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.

On the cooperative nature of the ß-process in neat and binary glasses: a dielectric and nuclear magnetic resonance spectroscopy study.

By means of dielectric as well as (2)H and (31)P nuclear magnetic resonance spectroscopy (NMR) the component dynamics of the binary glass tripropyl phosphate (TPP)/polystyrene (PS/PS-d3) is selectively investigated for concentrations distributed over the full range. We study the secondary (ß-) relaxation below T(g), which is found in all investigated samples containing TPP, but not in neat polystyrene. The dielectric spectrum of the ß-process is described by an asymmetric distribution of activation energies, essentially not changing in the entire concentration regime; its most probable value is E/k ≅ 24 T(g). Persistence of the ß-process is confirmed by (31)P NMR Hahn-echo and spin-lattice relaxation experiments on TPP, which identify the nature of the ß-process as being highly spatially hindered as found for other (neat) glasses studied previously, or re-investigated within this work. The corresponding (2)H NMR experiments on PS-d3 confirm the absence of a ß-process in neat PS-d3, but reveal a clear signature of a ß-process in the mixture, i.e., polystyrene monomers perform essentially the same type of secondary relaxation as the TPP molecules. Yet, there are indications that some fractions of PS-d3 as well as TPP molecules become immobilized in the mixture in contrast to the case of neat glasses. We conclude that in a binary glass the ß-process introduced by one component induces a highly similar motion in the second component, and this may be taken as an indication of its cooperative nature.

Evolution of the dynamic susceptibility in molecular glass formers: results from light scattering, dielectric spectroscopy, and NMR.

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 ß-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.

From boiling point to glass transition temperature: transport coefficients in molecular liquids follow three-parameter scaling.

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.

Comparative studies of the dynamics in viscous liquids by means of dielectric spectroscopy and field cycling NMR.

(1)H nuclear magnetic resonance (NMR) field cycling relaxometry has been applied to study the dynamics of homologues of glycerol (propylene glycol, 2,3-butandiol, glycerol, threitol, xylitol, sorbitol) and non-alcohol liquids (o-terphenyl, tristyrene, 3-fluoroaniline, m-toluidine). A broad range of temperatures (200-400 K) is covered, including the supercooled state. From the dispersion of the spin-lattice relaxation rate, R(1)(omega) = T(1)(-1)(omega), the susceptibility representation, omegaT(1)(-1)(omega), has been derived and compared with the susceptibility data from dielectric spectroscopy (DS). The DS spectra can be interpolated by a Cole-Davidson (CD) function, yielding correlation times which are attributed to the structural relaxation (alpha-process) in the supercooled state. In contrast to that, most of the (1)H NMR susceptibility spectra show, in addition to the alpha-relaxation peak, a low-frequency excess contribution with amplitudes varying among the systems. Exceptions are o-terphenyl and tristyrene for which DS and NMR susceptibility curves agree well and both can be reproduced by a CD function. Possible explanations of the low-frequency contribution are discussed. In particular the role of translational diffusion probed via the intermolecular coupling of (1)H spins is considered since it may likely generate the low-frequency excess intensity.

Generalization of the Cole-Davidson and Kohlrausch functions to describe the primary response of glass-forming systems.

We introduce a three-parameter step-response function which is based on a generalization of the Cole-Davidson (CD) and Kohlrausch (K) functions, and which provides a highly flexible susceptibility description for viscous liquids. A second parameter α characterizing the overall width, in addition to a parameter ß determining the high-frequency behavior of the susceptibility, allows for a continuous change of the spectral shape from the CD-type to the K-type. We prove that the function fulfills mathematical conditions required for a step-response function. When applying the function to interpolate dielectric spectra of neat (pure) glass formers, it is possible to keep the high-frequency parameter ß temperature-independent while varying the parameter α to account for the change of the overall width. This analysis might suggest that the failure of frequency-temperature superposition in glass formers is reflected by a broadening in the low-frequency region instead of in the high-frequency one.

On the nature of the high-frequency relaxation in a molecular glass former: a joint study of glycerol by field cycling NMR, dielectric spectroscopy, and light scattering.

Fast field cycling (1)H NMR relaxometry is applied to determine the dispersion of spin-lattice relaxation time T(1)(omega) of the glass former glycerol in broad temperature (75-360 K) and frequency (10 kHz-30 MHz) ranges. The relaxation data are analyzed in terms of a susceptibility chi(")(omega) proportional, variantomegaT(1)(omega), related to the second rank (l=2) molecular orientational correlation function. Broadband dielectric spectroscopic results suggest the validity of frequency temperature superposition above the glass transition temperature T(g). This allows to combine NMR data of different temperatures into a single master curve chi(")(omegatau(alpha)) that extends over 15 decades in reduced frequency omegatau(alpha), where tau(alpha) is the structural alpha-relaxation time. This master curve is compared with the corresponding ones from dielectric spectroscopy (l=1) and depolarized light scattering (l=2). At omegatau(alpha)<1, NMR susceptibility is significantly different from both the dielectric and light scattering results. At omegatau(alpha)>1, there rather appears a difference between the susceptibilities of rank l=1 and l=2. Specifically, at omegatau(alpha)>>1, where the susceptibility is dominated by the so-called excess wing, the NMR and light scattering spectra (both l=2) rather coincide with each other and are about three times more intense than the dielectric (l=1) spectrum. This is explained by assuming that the high frequency dynamics correspond to only small-angle excursions. Below T(g), dielectric and NMR susceptibility compare well and exhibit an exponential temperature dependence.