Impulsive stimulated light scattered from glass‐forming liquids. II. Salol relaxation dynamics, nonergodicity parameter, and testing of mode coupling theory

Angell plot from the potential energy landscape perspective

Within the scenario of the potential energy landscape (PEL), a thermodynamic model has been developed to uncover the physics behind the Angell plot. In our model, by separating the barrier distribution in PELs into a Gaussian-like and a power-law form, we obtain a general relationship between the relaxation time and the temperature. The wide range of the experimental data in the Angell plot, as well as the molecular-dynamics data, can be excellently fitted by two characteristic parameters, the effective barrier (ω) and the effective width (σ) of a Gaussian-like distribution. More importantly, the fitted ω and σ^{2} for all glasses are found to have a simple linear relationship within a very narrow band, and fragile and strong glasses are well separated in the ω-σ^{2} plot, which indicates that glassy states appear only in a specific region of the PEL.

Revisiting impulsive stimulated thermal scattering in supercooled liquids: Relaxation of specific heat and thermal expansion

Impulsive stimulated thermal scattering (ISTS) allows one to access the structural relaxation dynamics in supercooled molecular liquids on a time scale ranging from nanoseconds to milliseconds. Till now, a heuristic semi-empirical model has been commonly adopted to account for the ISTS signals. This model implicitly assumes that the relaxation of specific heat, C, and thermal expansion coefficient, γ, occur on the same time scale and accounts for them via a single stretched exponential. This work proposes two models that assume disentangled relaxations, respectively, based on the Debye and Havriliak-Negami assumptions for the relaxation spectrum and explicitly accounting for the relaxation of C and γ separately in the ISTS response. A theoretical analysis was conducted to test and compare the disentangled relaxation models against the stretched exponential. The former models were applied to rationalize the experimental ISTS signals acquired on supercooled glycerol. This allows us to simultaneously retrieve the frequency-dependent specific heat and thermal expansion up to the sub-100 MHz frequency range and further to compare the fragility and time scale probed by thermal, mechanical, and dielectric susceptibilities.

Ultraviolet and visible Brillouin scattering study of viscous relaxation in 3-methylpentane down to the glass transition

Brillouin light scattering spectra from transverse and longitudinal acoustic waves in liquid and supercooled 3-methylpentane have been collected from room temperature down to 80 K, just above the glass transition. Spectra at different wave vectors have been obtained using 532 nm and 266 nm excitation. We found evidence of a shear relaxation with a characteristic time of 100 s at the glass transition which only partly accounts for the relaxation observed in the propagation and attenuation of the longitudinal modes. The inclusion of a relaxing bulk viscosity contribution with a relaxation time of the order of 10(2) ns at the glass transition is found to adequately reproduce the experimental data including transient grating data at a much lower frequency. A consistent picture of relaxed shear and bulk moduli as a function of temperature is derived. These two quantities are found to be related by a linear relation suggesting that a Cauchy-like relation holds also above the glass transition.

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.

Relaxational Dynamics and Strength in Supercooled Liquids from Impulsive Stimulated Thermal Scattering

Impulsive stimulated thermal scattering (ISTS), a time-domain light scattering technique, provides a more than 6-decade time range from sub-ns to many ms. It permits characterization of the structural relaxation dynamics and determination of the relaxation strength or Debye-Waller factor in supercooled liquids, and thus allows testing of the mode coupling theory of the liquidglass transition. ISTS experiments were performed on glass formers salol, butylbenzene, and the molten salt [Ca(N03)]0.4[KNO3]0.6. The relaxational dynamics and the Debye-Waller factorfq=0 were obtained. A square-root anomaly was observed in fq=0 (T) at a crossover temperature Tc for all three materials, consistent with the prediction of mode coupling theory.

Transport properties of glass-forming liquids suggest that dynamic crossover temperature is as important as the glass transition temperature

It is becoming common practice to partition glass-forming liquids into two classes based on the dependence of the shear viscosity η on temperature T. In an Arrhenius plot, ln η vs 1/T, a strong liquid shows linear behavior whereas a fragile liquid exhibits an upward curvature [super-Arrhenius (SA) behavior], a situation customarily described by using the Vogel-Fulcher-Tammann law. Here we analyze existing data of the transport coefficients of 84 glass-forming liquids. We show the data are consistent, on decreasing temperature, with the onset of a well-defined dynamical crossover η(×), where η(×) has the same value, η(×) ≈ 10(3) Poise, for all 84 liquids. The crossover temperature, T(×), located well above the calorimetric glass transition temperature T(g), marks significant variations in the system thermodynamics, evidenced by the change of the SA-like T dependence above T(×) to Arrhenius behavior below T(×). We also show that below T(×) the familiar Stokes-Einstein relation D/T ∼ η(-1) breaks down and is replaced by a fractional form D/T ∼ η(-ζ), with ζ ≈ 0.85.

High frequency dynamics in liquids and supercritical fluids: A comparative inelastic x-ray scattering study

The microscopic dynamics of four prototype systems (water, ammonia, nitrogen, and neon) across the critical temperature has been investigated by means of high-resolution inelastic x-ray scattering. The experimental line shape has been described using a model based on the memory function formalism. Two main relaxations, the thermal and the structural one, were observed in all the investigated systems. We found that the microscopic mechanism driving the structural relaxation clearly changes, being mainly governed by intermolecular bond rearrangements below the critical temperature and by binary collisions above it. Moreover, we observed that the relative weight of the thermal relaxation systematically increases on approaching the critical temperature, thus allowing for the observation of a transition from an adiabatic to an isothermal regime of sound propagation. Finally, we found the presence of an additional instantaneous relaxation, likely related to the coupling between collective vibrational modes and intramolecular degrees of freedom.

Optical generation of gigahertz-frequency shear acoustic waves in liquid glycerol

Picosecond laser ultrasonic techniques for acoustic wave generation and detection have been employed to probe shear acoustic waves in liquid glycerol at gigahertz frequencies. The experimental approach uses a unique laser pulse shaping technique and a crystallographically canted metal layer to generate frequency-tunable transverse acoustic waves, and uses time-domain coherent Brillouin scattering to detect the waves after they propagate through a liquid layer and into a solid substrate. A linear frequency dependence is found for both the shear speed and attenuation rate in glycerol.

Analysis of a heterodyne-detected transient-grating experiment on a molecular supercooled liquid. I. Basic formulation of the problem

We present the basic equations necessary to interpret heterodyne-detected transient-grating experiments performed on a supercooled liquid composed of anisotropic molecules. The final expressions are given under a form suitable for their direct application to a test case.

Supercooled water relaxation dynamics probed with heterodyne transient grating experiments

We report results from a heterodyne-detected transient grating experiment on liquid and supercooled water in a wide temperature range, from -17.5 to 90 degrees C. The measured signal covers an extremely large time window with an excellent signal-to-noise ratio that enables the investigation in a single experiment of the sound speed and attenuation, thermal diffusivity, and temperature dependence of the dielectric constant. The experimental data clearly show the effect of the density and the temperature fluctuations on the water dielectric function. In order to describe the experimental results, we introduce a comprehensive hydrodynamic model taking into account the coupled density and temperature variables and their relevance in the definition of the spontaneous and forced dielectric variations. We use this model to describe the measured signal in transient grating experiments, including the heating and the electrostrictive sources produced by the laser excitation. The fitting procedure enables the safe extraction of several dynamic properties of liquid and supercooled water: the sound velocity and its damping, the thermal diffusivity, and the ratio between the dielectric thermodynamic derivatives. The measured parameters are compared to the literature data and discussed in the complex scenario of water physics.

Slow dynamics of salol: a pressure- and temperature-dependent light scattering study

We study the slow dynamics of salol by varying both temperature and pressure using photon correlation spectroscopy and pressure-volume-temperature measurements, and compare the behavior of the structural relaxation time with equations derived within the Adam-Gibbs entropy theory and the Cohen-Grest free volume theory. We find that pressure-dependent data are crucial to assess the validity of these model equations. Our analysis supports the entropy-based equation, and estimates the configurational entropy of salol at ambient pressure approximately 70% of the excess entropy. Finally, we investigate the evolution of the shape of the structural relaxation process, and find that a time-temperature-pressure superposition principle holds over the range investigated.

Brillouin scattering study of salol: exploring the effects of rotation-translation coupling

Brillouin scattering in liquids composed of optically and mechanically anisotropic molecules is affected by coupling between rotational and translational dynamics. While this effect has been extensively studied in depolarized (VH) scattering where it produces the "Rytov dip," recent theoretical analyses by Pick, Franosch show that it should also produce observable effects in polarized (VV) scattering [Eur. Phys. J. B 31, 217 (2003)]; 31, 229 (2003)]]. To test this theory, we carried out Brillouin scattering studies of the molecular glassformer salol in the temperature range 210-380 K, including VH-backscattering, VH-90 degrees, and VV-90 degrees spectra. The data were analyzed consistently to determine the effects of rotation-translation coupling on both the polarized and depolarized spectra. A previously unanticipated feature predicted by these authors was observed: a narrow negative region in the q -dependent part of the 90 degrees VV spectra, which we designate as the "VV dip." It is an analog of the Rytov dip observed at high temperatures in the 90 degrees VH spectra, which is also accurately described by this theory. Analysis of the 90 degrees VV spectra was carried out both with and without inclusion of translation-rotation coupling in order to determine quantitatively the role this coupling plays.

Nonequilibrium thermodynamic description of the coupling between structural and entropic modes in supercooled liquids

The density response of supercooled glycerol to an impulsive stimulated thermal grating (q=0.63 microm(-1)) has been studied in the temperature range (T=200-340 K) where the structure rearrangement (alpha relaxation) and the thermal diffusion occur on the same time scale. A strong interaction between the two modes occurs giving rise to a dip in the T dependence of the apparent thermal conductivity and a flattening of the apparent alpha-relaxation time upon cooling. A nonequilibrium thermodynamic model for the long time response has been developed. The model is capable to reproduce the experimental data and to explain the observed phenomenology.

Acoustic and relaxation processes in supercooled orthoterphenyl by optical-heterodyne transient grating experiment

The dynamics of the fragile glass-forming orthoterphenyl have been investigated by transient grating experiments with an heterodyne detection technique. We measured the relaxation processes of this glass former over more than six decades in time with an excellent signal-to-noise ratio. Acoustic, structural, and thermal relaxations have been clearly identified in a time-frequency window not covered by previous spectroscopic studies and their characteristic dynamic parameters have been measured as a function of temperature and wave vector. A detailed comparison with the density response function, calculated on the basis of generalized hydrodynamic model, has been worked out.

Molecular mode-coupling theory applied to a liquid of diatomic molecules

We study the molecular mode-coupling theory for a liquid of diatomic molecules. The equations for the critical tensorial nonergodicity parameters F(m)(ll('))(q) and the critical amplitudes of the beta relaxation H(m)(ll('))(q) are solved up to a cutoff l(co)=2 without any further approximations. Here l,m are indices of spherical harmonics. Contrary to previous studies, where additional approximations were applied, we find in agreement with simulations that all molecular degrees of freedom vitrify at a single temperature T(c). The theoretical results for the nonergodicity parameters and the critical amplitudes are compared with those from simulations. The qualitative agreement is good for all molecular degrees of freedom. To study the influence of the cutoff on the nonergodicity parameter, we also calculate the nonergodicity parameters for an upper cutoff l(co)=4. In addition, we also propose a method for the calculation of the critical nonergodicity parameter from the liquid side of transition.

Wide-band acoustic spectroscopy of biological material based on a laser-induced grating technique

A laser-induced transient grating technique enables fast noncontact acoustic measurements on transparent biological materials in a frequency range from tens of megahertz to 1 GHz. We have applied this method to the characterization of bovine vitreous and found high-frequency acoustic attenuation values to be close to those of water, with a quadratic dependence on frequency, in contrast to low-frequency data. The potential of the technique for studying other biological materials, such as human stratum corneum, is demonstrated.