Corresponding States Concept for Simple Supercooled Liquids Identifying a Change of Diffusion Mechanism above the Glass Transition Temperature

NMR Relaxometry Accessing the Relaxation Spectrum in Molecular Glass Formers

It is a longstanding question whether universality or specificity characterize the molecular dynamics underlying the glass transition of liquids. In particular, there is an ongoing debate to what degree the shape of dynamical susceptibilities is common to various molecular glass formers. Traditionally, results from dielectric spectroscopy and light scattering have dominated the discussion. Here, we show that nuclear magnetic resonance (NMR), primarily field-cycling relaxometry, has evolved into a valuable method, which provides access to both translational and rotational motions, depending on the probe nucleus. A comparison of ¹H NMR results indicates that translation is more retarded with respect to rotation for liquids with fully established hydrogen-bond networks; however, the effect is not related to the slow Debye process of, for example, monohydroxy alcohols. As for the reorientation dynamics, the NMR susceptibilities of the structural (α) relaxation usually resemble those of light scattering, while the dielectric spectra of especially polar liquids have a different broadening, likely due to contributions from cross correlations between different molecules. Moreover, NMR relaxometry confirms that the excess wing on the high-frequency flank of the α-process is a generic relaxation feature of liquids approaching the glass transition. However, the relevance of this feature generally differs between various methods, possibly because of their different sensitivities to small-amplitude motions. As a major advantage, NMR is isotope specific; hence, it enables selective studies on a particular molecular entity or a particular component of a liquid mixture. Exploiting these possibilities, we show that the characteristic Cole-Davidson shape of the α-relaxation is retained in various ionic liquids and salt solutions, but the width parameter may differ for the components. In contrast, the low-frequency flank of the α-relaxation can be notably broadened for liquids in nanoscopic confinements. This effect also occurs in liquid mixtures with a prominent dynamical disparity in their components.

Nuclear Spin Relaxation in Viscous Liquids: Relaxation Stretching of Single-Particle Probes

Spin-lattice relaxation rates R₁(ω,T), probed via high-field and field-cycling nuclear magnetic resonance (NMR), are used to test the validity of frequency-temperature superposition (FTS) for the reorientation dynamics in viscous liquids. For several liquids, FTS is found to apply so that master curves can be generated. The susceptibility spectra are highly similar to those obtained from depolarized light scattering (DLS) and reveal an excess wing. Where FTS works, two approaches are suggested to access the susceptibility: (i) a plot of deuteron R₁(T) vs the spin-spin relaxation rate R₂(T) and (ii) a plot of R₁(T) vs an independently measured reference time τ_ref(T). Using single-frequency scans, (i) allows one to extract the relaxation stretching as well as the NMR coupling constant. Surveying 26 data sets, we find Kohlrausch functions with exponents 0.39 < β_K ≤ 0.67. Plots of the spin-spin relaxation rate R₂─rescaled by the NMR coupling constant─as a function of temperature allow one to test how well site-specific NMR relaxations couple to a given reference process. Upon cooling of flexible molecule liquids, the site-specific dynamics is found to merge, suggesting that near T_g the molecules reorient essentially as a rigid entity. This presents a possible resolution for the much lower stretching parameters reported here at high temperatures that contrast with the ones that were reported to be universal in a recent DLS study close to T_g. Our analysis underlines that deuteron relaxation is a uniquely powerful tool to probe single-particle reorientation.

Molecular dynamics simulations vs field-cycling NMR relaxometry: Structural relaxation mechanisms in the glass-former glycerol revisited

We combine field-cycling (FC) relaxometry and molecular dynamics (MD) simulations to study the rotational and translational dynamics associated with the glassy slowdown of glycerol. The ¹H NMR spin-lattice relaxation rates R₁(ω) probed in the FC measurements for different isotope-labelled compounds are computed from the MD trajectories for broad frequency and temperature ranges. We find high correspondence between experiment and simulation. Concerning the rotational motion, we observe that the aliphatic and hydroxyl groups show similar correlation times but different stretching parameters, while the overall reorientation associated with the structural relaxation remains largely isotropic. Additional analysis of the simulation results reveals that transitions between different molecular configurations are slow on the time scale of the structural relaxation at least at sufficiently high temperatures, indicating that glycerol rotates at a rigid entity, but the reorientation is slower for elongated than for compact conformers. The translational contribution to R₁(ω) is well described by the force-free hard sphere model. At sufficiently low frequencies, universal square-root laws provide access to the molecular diffusion coefficients. In both experiment and simulation, the time scales of the rotational and translational motions show an unusually large separation, which is at variance with the Stokes-Einstein-Debye relation. To further explore this effect, we investigate the structure and dynamics on various length scales in the simulations. We observe that a prepeak in the static structure factor S(q), which is related to a local segregation of aliphatic and hydroxyl groups, is accompanied by a peak in the correlation times τ(q) from coherent scattering functions.

The role of the dynamic crossover temperature and the arrest in glass-forming fluids

We discuss the role of the dynamic glass-forming fragile-to-strong crossover (FSC) in supercooled liquids. In the FSC, significant dynamic changes such as the decoupling (the violation of the Stokes-Einstein relation) of homologous transport parameters, e.g., the density relaxation time τ and the viscosity η, occur at a characteristic temperature T(c). We study the FSC using a scaling law approach. In particular, we use both forms of the mode-coupling theory (MCT): the original (ideal) and the extended form, which explicitly describes energy hopping processes. We demonstrate that T(c) plays the most important physical role in understanding dynamic arrest processes.

Strong and Fragile Behavior in Liquid Polymers

In the light of the strong and fragile classification of simple liquids we review some of the relaxation data for some well-known polymers to see the extent to which a similar pattern may be manifested. Relaxation time data rather than viscosity data are used in the polymer case to avoid complications from long chain effects on the Vogel-Fulcher equation pre exponent. A combination of light scattering and 13C NMR data seem to provide the most reliable guide to the microviscosity of interest to the classification. A pattern similar to that for viscous liquids is recovered with polyisobutylene, the “strongest” chain polymer and bisphenol polycarbonate, the most fragile. The extent to which correlations of other properties with fragility, found in the non-polymeric liquids cases, will carry over to the polymer case is still being evaluated, though the work of Hodge on the analysis of the more complicated problem of non-linear thermal relaxation, suggests the carry over may be extensive.

Coupling and decoupling between translational and rotational dynamics in a supercooled molecular liquid

We use molecular dynamics simulations to investigate the coupling and decoupling between translational and rotational dynamics in a glass-forming liquid of dumbbells. We find that the coupling between the translational (tau_{q;{*}};{C}) and rotational (tau_{2}) relaxation times increases with decreasing temperature T, whereas the coupling decreases between the translational (D_{t}) and rotational (D_{r}) diffusivities. In addition, the T dependence of D_{t} decouples from that of 1/tau_{2}. We show that the decreasing coupling between D_{t} and D_{r} is only apparent due to the inadequacy of the concept of the rotational diffusion constant for describing the reorientational dynamics in the supercooled state. We also argue that the coupling between tau_{q;{*}};{C} and tau_{2} and the decoupling between D_{t} and 1/tau_{2} can be consistently understood in terms of the growing dynamic length scale.

Connections of activated hopping processes with the breakdown of the Stokes-Einstein relation and with aspects of dynamical heterogeneities

We develop an extended version of the mode-coupling theory (MCT) for glass transition, which incorporates activated hopping processes via the dynamical theory originally formulated to describe diffusion-jump processes in crystals. The dynamical-theory approach adapted here to glass-forming liquids treats hopping as arising from vibrational fluctuations in the quasiarrested state where particles are trapped inside their cages, and the hopping rate is formulated in terms of the Debye-Waller factors characterizing the structure of the quasiarrested state. The resulting expression for the hopping rate takes an activated form, and the barrier height for the hopping is "self-generated" in the sense that it is present only in those states where the dynamics exhibits a well defined plateau. It is discussed how such a hopping rate can be incorporated into MCT so that the sharp nonergodic transition predicted by the idealized version of the theory is replaced by a rapid but smooth crossover. We then show that the developed theory accounts for the breakdown of the Stokes-Einstein relation observed in a variety of fragile glass formers. It is also demonstrated that characteristic features of dynamical heterogeneities revealed by recent computer simulations are reproduced by the theory. More specifically, a substantial increase of the non-Gaussian parameter, double-peak structure in the probability distribution of particle displacements, and the presence of a growing dynamic length scale are predicted by the extended MCT developed here, which the idealized version of the theory failed to reproduce. These results of the theory are demonstrated for a model of the Lennard-Jones system, and are compared with related computer-simulation results and experimental data.

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.

Spin-Lattice Relaxation and Rotational Motion of Aromatic Triplet-State Molecules in Supercooled Alkane Solvents (Part 1)

The phosphorescence of phenazine (PZ) and quinoxaline (QX) was investigated after pulsed laser excitation in the glass-transition range of several alkane solvents. Three relaxation processes of PZ and QX in the metastable triplet state, T1, were studied as a function of temperature: (1) the decay of the selective population of the strongly phosphorescent triplet substate T1x due to spin-lattice relaxation (SLR), (2) the time-dependent red shift of the phosphorescence spectrum due to the solvation of triplet-state molecules, and (3) the decay of the phosphorescence polarization due to orientational relaxation (OR). Various aspects and connections of the mechanisms governing the three relaxation phenomena are discussed. The relaxation dynamics were characterized at temperatures above the glass-transition temperature of the respective solvent, where the fundamental processes involved are strongly dependent upon the solvent viscosities. For the systems treated here, OR and solvation were satisfactorily described by a Vogel-Fulcher-Tammann temperature behavior. SLR also depends on properties of the alkane solvent above the glass transition. Upon cooling, SLR becomes independent of the specific solvent properties and is based on mechanisms that are typical for amorphous glasses or solids. (This particular aspect will be the subject of a subsequent publication, part 2).

Light-scattering study of a supercooled epoxy resin

The dynamics of the fragile glass-forming liquid diglycidyl ether of bisphenol-A was studied by depolarized Rayleigh-Brillouin light-scattering and photon correlation spectroscopy above the glass transition, in the temperature range from 261 to 473 K and in the frequency range from 1 Hz to 300 GHz. The structural (alpha-) relaxation process was revealed and no signature of the secondary relaxation previously evidenced by dielectric spectroscopy at about 0.1 GHz was observed. The characteristic time of the alpha process differs from that determined by dielectric spectroscopy of an amount, which increases with increasing temperature. The relaxation times were compared with viscosity data to test the predictions of the classic Stokes-Einstein-Debye model. The tau proportional, variant eta behavior was verified for dielectric data, while a fractional power law of viscosity tau proportional, variant eta(0.89) was obtained for light-scattering relaxation times, extending over more than seven decades in viscosity and time. This deviation of light scattering from viscosity data could be interpreted in terms of cooperative motion in the supercooled liquid with a characteristic length xi(a) proportional, variant(T-T0)(-v) where T(0)=229 K is the Vogel temperature and v is close to 2 / 3 which is consistent with the prediction of the fluctuation theory of glass transition.

Rotational Motion of a Solute Molecule in a Highly Viscous Liquid Studied by 13C NMR: 1,3-Dibromoadamantane in Polymeric Chlorotrifluoroethene

The viscosity-dependent retarding effect of a polymeric solvent on the rotation of small solute molecules is investigated by 13C NMR relaxation measurements. It is found that the relaxation data of 1,3-dibromoadamantane in highly viscous polymeric chlorotrifluoroethene can be explained neither by isotropic nor by realistic anisotropic tumbling in a single environment. The experimental data are rationalized in terms of fast exchange between at least two environments with correlation times differing by up to two orders of magnitude. The study shows that a uniform retardation of molecular tumbling by a polymeric solvent, desirable for shifting the NMR observation window in studies of intramolecular mobility, is not always feasible. Copyright 1998 Academic Press.