Depolarized-light-scattering study of orthoterphenyl and comparison with the mode-coupling model

Glass spectrum, excess wing phenomenon, and master curves in molecular glass formers: A multi-method approach

The relaxation spectra of glass formers solely displaying an α-peak and excess wing contribution collected by various methods are reanalyzed to pin down their different spectral evolution. We show that master curve construction encompassing both α-peak and emerging excess wing works for depolarized light scattering (DLS) and nuclear magnetic resonance (NMR) relaxometry. It reveals the self-part of the slow dynamics' spectrum. Master curves are to be understood as a result of a more extensive scaling covering all temperatures instead of strict frequency-temperature superposition. DLS and NMR display identical relaxation spectra; yet, comparing different systems, we do not find a generic structural relaxation at variance with recent claims. Dielectric spectroscopy (DS) spectra show particularities, which render master curve construction obsolete. The DS α-peak is enhanced or suppressed with respect to that of DLS or NMR, yet, not correlated to the polarity of the liquid. Attempting to single out the excess wing from the overall spectrum discloses a stronger exponential temperature dependence of its amplitude compared to that below Tg and a link between its exponent and that of the fast dynamics' spectrum. Yet, such a decomposition of α-peak and excess wing appears to be unphysical. Among many different glasses, the amplitude of the excess wing power-law spectrum is found to be identical at Tg, interpreted as a relaxation analog to the Lindemann criterion.

On the intensity of light scattered by molecular liquids-Comparison of experiment and quantum chemical calculations

The intensity of light scattered by liquids has been studied for over a century since the valuable microscopic information about the molecules can be obtained, such as the anisotropy of the molecular polarizability tensor or preferred orientations of neighboring molecules. However, in modern dynamic light scattering experiments, the scattering intensity is usually disregarded, unlike in dielectric spectroscopy, which can be considered as a complementary experimental method, where the dielectric strength is routinely evaluated. The reason lies partly on the fact that the exact form of the equations relating the macroscopically measured light scattering intensity to the microscopic properties of the molecules is debated in the literature. Therefore, as a first step, we compare anisotropy parameters from the literature, calculated from light scattering intensities using different equations, with quantum chemical calculations for over 150 medium-sized molecules. This allows us to identify a consistent form of equations. In a second part, we turn to the depolarized light scattering spectra of 13 van der Waals liquids and some mixtures thereof, recorded with a combination of Tandem-Fabry-Perót and Raman spectroscopies, giving direct access to the reorientational dynamics of the molecules. We discuss how the strength of the structural α-relaxation is connected to the anisotropy parameter, what implication this has for the shape of the α-relaxation, how the components of a mixture-also for the case of ionic liquids-can be identified in this way, and how orientational correlation parameters can be extracted. Additionally, we point out for the example of n-alkanes that for highly flexible molecules, the reorientational motion might not be the decisive source of the depolarized scattered light. We also show that light scattering might serve as a sensitive tool to check the accuracy of a conformer ensemble obtained by quantum chemical calculations.

Jump-precursor state emerges below the crossover temperature in supercooled o-terphenyl

In a supercooled liquid, the crossover temperature T_{c} separates a high-temperature region of diffusive dynamics from a low-temperature region of activated dynamics. A molecular-dynamics simulation of all-atom, flexible o-terphenyl [Eastwood et al., J. Phys. Chem. B 117, 12898 (2013)10.1021/jp402102w] is analyzed with advanced statistical methods to reveal the molecular features associated with this crossover. The simulations extend to an α-relaxation time of 14 μs (272.5 K), two orders of magnitude slower than at T_{c} (290 K). At T_{c} and below, a distinct state emerges that immediately precedes an orientational jump. Compared to the initial, tightly caged state, this jump-precursor state has a looser cage, with solid-angular excursions of 0.054-0.0125 × 4π sr. At T_{c} (290 K), rate heterogeneity is already the dominant cause of stretched relaxation. Exchange within the distribution of rates is faster than α relaxation at T_{c}, but becomes equal to it at the lowest temperature simulated (272.5 K). The results trend toward a recent experimental observation near the glass transition (243 K) [Kaur et al., Phys. Rev. E 98, 040603(R) (2018)10.1103/PhysRevE.98.040603], which saw exchange substantially slower than α relaxation. Overall, the dynamic crossover comprises multiple phenomena: the development of heterogeneity, an increasing jump size, an emerging jump-precursor state, and a lengthening exchange time. The crossover is neither sharp, nor a simple superposition of the high- and low-temperature regimes; it is a broad region that contains unique and complex phenomena.

On the glass transition and correlation functions

Correlation functions are the basis for the understanding of many thermodynamic systems that can be directly observed by scattering experiments. In this manuscript, the correlation functions include the steric repulsion of atoms that also leads to distinct shells of neighbors. A free energy is derived on the basis of these assumptions, and in the following the temperature dependence of the density (or specific volume), the typical time scale of the α-relaxation, and the heat capacity. From this, I argue that the glass transition is dominated by the vicinity of a first-order phase transition. While the correlation length stays rather constant in the vicinity of the glass transition, the intensity of the fluctuations is considerably increasing. The scattering amplitude is connected to the cluster size, also introduced in the cooperativity argument. Additionally, correlations of loops are discussed. The additional correlations describe rather small structures. Applying this to scattering intensities, a correlation peak was described that may be connected to the “Boson Peak” or a “cooperativity length.” The new concept of correlation functions on sterically repulsive atoms may find more attention in the wider field of physics.

Fast logarithmic Fourier-Laplace transform of nonintegrable functions

We present an efficient and very flexible numerical fast Fourier-Laplace transform that extends the logarithmic Fourier transform introduced by Haines and Jones [Geophys. J. Int. 92, 171 (1988)GJINEA0956-540X10.1111/j.1365-246X.1988.tb01131.x] for functions varying over many scales to nonintegrable functions. In particular, these include cases of the asymptotic form f(ν→0)∼ν^{a} and f(|ν|→∞)∼ν^{b} with arbitrary real a>b. Furthermore, we prove that the numerical transform converges exponentially fast in the number of data points, provided that the function is analytic in a cone |Imν|<θ|Reν| with a finite opening angle θ around the real axis and satisfies |f(ν)f(1/ν)|<ν^{c} as ν→0 with a positive constant c, which is the case for the class of functions with power-law tails. Based on these properties we derive ideal transformation parameters and discuss how the logarithmic Fourier transform can be applied to convolutions. The ability of the logarithmic Fourier transform to perform these operations on multiscale (nonintegrable) functions with power-law tails with exponentially small errors makes it the method of choice for many physical applications, which we demonstrate on typical examples. These include benchmarks against known analytical results inaccessible to other numerical methods, as well as physical models near criticality.

Discontinuity in Fast Dynamics at the Glass Transition of ortho-Terphenyl

The dynamics of the molecular glass former ortho-terphenyl through the glass transition were observed with two-dimensional infrared vibrational spectroscopy measurements of spectral diffusion using the small probe molecule phenylselenocyanate. Although the slow diffusive motions were not visible on the experimental time scale, a picosecond-scale exponential relaxation was observed at temperatures from above to well below the glass transition temperature. The characteristic time scale has a smooth temperature dependence from the liquid into the glass phase, but the range of vibrational frequencies the probe samples displayed a discontinuity at the glass transition temperature. Complementary pump-probe experiments associate the observed motion with density fluctuations. The key features of the dynamics are reproduced with a simple corrugated well potential energy surface model. In addition, the temperature dependence of the homogeneous vibrational dephasing was found to have a T² functional form, where T is the absolute temperature.

Coupling of Caged Molecule Dynamics to JG β-Relaxation III: van der Waals Glasses

In the first two papers separately on the polyalcohols and amorphous polymers of this series, we demonstrated that the fast dynamics observed in the glassy state at high frequencies above circa 1 GHz is the caged dynamics. We showed generally the intensity of the fast caged dynamics changes temperature dependence at a temperature THF nearly coincident with the secondary glass transition temperature Tgβ lower than the nominal glass transition temperature Tgα. The phenomenon is remarkable, since THF is determined from measurements of fast caged dynamics at short time scales typically in the ns to ps range, while Tgβ characterizes the secondary glass transition at which the Johari-Goldstein (JG) β-relaxation time τJG reaches a long time of ∼10(3) s, determined directly either by positronium annihilation lifetime spectroscopy, calorimetry, or low frequency dielectric and mechanical relaxation spectroscopy. The existence of the secondary glass transition originates from the dependence of τJG on density, previously proven by experiments performed at elevated pressure. The fact that THF ≈ Tgβ reflects the density dependence of the caged dynamics and coupling to the JG β-relaxation. The generality of the phenomenon and its theoretical rationalization implies the same should be observable in other classes of glass-formers. In this paper, III, we consider two archetypal small molecular van der Waals glass-formers, ortho-terphenyl and toluene. The experimental data show the same phenomenon. The present paper extends the generality of the phenomenon and explanation from the polyalcohols, a pharmaceutical, and many polymers to the small molecular van der Waals glass-formers.

The Modified VFT law of glass former materials under pressure: Part II: Relation with the equation of state

The dynamical properties of glass formers (GFs) as a function of P, V, and T are reanalyzed in relation with the equations of state (EOS) proposed recently (Eur. Phys. J. E 37, 113 (2014)). The relaxation times τ of the cooperative non-Arrhenius α process and the individual Arrhenius β process are coupled via the Kohlrausch exponent n S(T, P). In the model n S is the sigmoidal logistic function depending on T (and P, and the α relaxation time τ α of GFs above T g verifies the pressure-modified VFT law: log τ α ∼ E β /nsRT, which can be put into a form with separated variables: log τ α ∼ f(T)g(P). From the variation of n S and τ α with T and P the Vogel temperature T 0 (τ α → ∝, n S = 0) and the crossover temperature (also called the merging or splitting temperature) T B (τ α ∼ τ β, n S ∼ 1) are determined. The proposed sm-VFT equation fits with excellent accuracy the experimental data of fragile and strong GFs under pressure. The properties generally observed in organic mineral and metallic GFs are explained: a) The Vogel temperature is independent of P (as suggested by the EOS properties), the crossover is pressure-dependent. b) In crystallizable GFs the T B (P) and Clapeyron curves T m(P) coincide. c) The α and β processes have the same ratio of the activation energies and volume, E*/V* (T- and P-independent), the compensation law is observed, this ratio depends on the anharmonicity Slater-Grüneisen parameter and on the critical pressure P* deduced from the EOS. d) The properties of the Fan Structure of the Tangents (FST) to the isotherms and isobars curves log τ versus P and T and to the isochrones curves P(T). e) The scaling law log τ = f(V (Λ) ) and the relation between Γ and γ. We conclude that these properties should be studied in detail in GFs submitted to negative pressures.

Extracting energy and structure properties of glass-forming liquids from structural relaxation time

A comprehensive examination of the kinetic liquid model (Wang et al 2010 J. Phys.: Condens. Matter 22 455104) is carried out by fitting the structural relaxation time of 26 different glass-forming liquids in a wide temperature range, including most of the well-studied materials. Careful analysis of the compiled reported data reveals that experimental inaccuracies should not be overlooked in any 'benchmark test' of relating theories or models (e.g. in Lunkenheimer et al 2010 Phys. Rev. E 81 051504). The procedure, accuracy, ability, and efficiency of the kinetic liquid model are discussed in detail and in comparison with other available fitting methods. In general, the kinetic liquid model could be verified by 17 of the 26 compiled data sets and can serve as a meaningful approximative method for analyzing these liquids. Nonetheless, further experimental examinations in a wide temperature range are needed and are called for. Through fitting, the microscopic details of these liquids are extracted, namely, the enthalpy, entropy, and cooperativity in structural relaxation, which may facilitate further quantitative analysis to both the liquidus and glassy states of these materials.

Correlating the stretched-exponential and super-Arrhenius behaviors in the structural relaxation of glass-forming liquids

Following the report of a single-exponential activation behavior behind the super-Arrhenius structural relaxation of glass-forming liquids in our preceding paper, we find that the non-exponentiality in the structural relaxation of glass-forming liquids is straightforwardly determined by the relaxation time, and could be calculated from the measured relaxation data. Comparisons between the calculated and measured non-exponentialities for typical glass-forming liquids, from fragile to intermediate, convincingly support the present analysis. Hence the origin of the non-exponentiality and its correlation with liquid fragility become clearer.

Single-exponential activation behavior behind the super-Arrhenius relaxations in glass-forming liquids

The reported relaxation time for several typical glass-forming liquids was analyzed by using a kinetic model for liquids which invoked a new kind of atomic cooperativity--thermodynamic cooperativity. The broadly studied 'cooperative length' was recognized as the kinetic cooperativity. Both cooperativities were conveniently quantified from the measured relaxation data. A single-exponential activation behavior was uncovered behind the super-Arrhenius relaxations for the liquids investigated. Hence the mesostructure of these liquids and the atomic mechanism of the glass transition became clearer.

A new interpretation of dielectric data in molecular glass formers

Literature dielectric data of glycerol, propylene carbonate, and ortho-terphenyl show that the measured dielectric relaxation is a decade faster than the Debye expectation but still a decade slower than the breakdown of the shear modulus. From a comparison of time scales, the dielectric relaxation seems to be due to a process which relaxes not only the molecular orientation but also the entropy, the short range order, and the density. On the basis of this finding, we propose an alternative to the Gemant-DiMarzio-Bishop extension of the Debye picture.

Self-Diffusion of Supercooled o-Terphenyl near the Glass Transition Temperature

Self-diffusion coefficients for the low molecular weight glass former o-terphenyl have been measured near Tg by isothermally desorbing thin film bilayers of deuterio and protio o-terphenyl in a vacuum chamber. We observe translational diffusion that is about 100 times faster at Tg + 3 K than the Stokes-Einstein prediction. Predictions from random first order transition theory and a dynamic facilitation approach are in reasonable agreement with our results; in these approaches, enhanced translational diffusion is associated with spatially heterogeneous dynamics. Self-diffusion controls crystallization in o-terphenyl for most of the supercooled liquid regime, but at temperatures below Tg + 10 K, the reported crystallization rate increases suddenly while the self-diffusion coefficient does not. This work and previous work on trisnaphthylbenzene both find a self-diffusion-controlled crystal growth regime and an enhancement in self-diffusion near Tg, suggesting that these phenomena are general characteristics of fragile low molecular weight glass formers. We discuss the width of the relaxation time distributions of o-terphenyl and trisnaphthylbenzene as they relate to the observation of enhanced translational diffusion.

On the dielectric susceptibility spectra of supercooled o-terphenyl

Supercooled o-terphenyl has been the subject of many investigations including dielectric relaxation spectroscopy. Due to the low dielectric strength and the tendency to crystallize at elevated temperatures, a detailed shape analysis of the loss profile from the glass transition temperature Tg to approximately 1.2 Tg is not available for the neat glass former. Assessing the origin of the different temperature dependencies of translational and rotational motions in supercooled liquids and its possible connection to heterogeneity requires this knowledge regarding the possible changes in the relaxation-time distribution across the 100 s-100 ns relaxation-time range. This note provides this information for o-terphenyl on the basis of a master curve representation: time-temperature superposition applies with a constant stretching exponent of beta=0.5 in the range of interest.

Role of the density in the crossover region of o-terphenyl and poly(vinyl acetate)

The coupling between the reorientation of molecular probes and the density in one low-molar mass glass former [ o -terphenyl (OTP)] and one polymer [poly(vinyl acetate) (PVAc)] is studied in the Goldstein's crossover region where the structural (alpha) and the secondary (beta) relaxations bifurcate. The coupling is found to be strong in OTP and virtually absent in PVAc. The probes sense both the alpha and beta relaxations, and locate their splitting accurately. It is concluded that the density affects the relaxation occurring in the crossover region of OTP but not of PVAc at subnanometer length scales. The findings are compared with recent assessments of the role of the molecular packing close and above the glass transition temperature T(g).

Temperature and pressure study of Brillouin transverse modes in the organic glass-forming liquid orthoterphenyl

Transverse Brillouin spectra of orthoterphenyl are measured in the (250-305 K; 0.1-100 MPa) temperature-pressure range, which corresponds to the supercooled phase of this organic glass former. We show that the analysis of these spectra combined with an extrapolation of the reorientation times under pressure leads to an estimate of the static shear viscosity in a pressure range whose validity extends beyond the range of the Brillouin measurements. The relative contributions of temperature and of density to the change of this reorientation time measured along an isobar are extracted from our results in a large temperature range extending from the liquid to the low temperature supercooled state. They appear to be always of the same order of magnitude. It is also shown that in the range of the experiment, the orientational time is depending on a unique parameter built on temperature and density.

Universality of the dynamic crossover in glass-forming liquids: a "magic" relaxation time

Analysis of experimental data on the structural relaxation time tau(alpha) in various glass formers revealed its universality at the critical temperature T(c) of the mode-coupling theory. In most glass formers studied ln tau(alpha)(T(c))=-(6.5-7.5). Possible reasons for such a universality are discussed.

Dynamics of supercooled liquids confined to the pores of sol-gel glass: a dynamic light scattering study

Dynamics of low molecular weight and polymeric glass forming liquids in confined geometries has been studied by means of depolarized dynamic light scattering: photon correlation spectroscopy and Fabry-Perot interferometry. The pore size of the glassy matrix amounted to 2.5, 5.0, and 7.5 nm. The glass transition temperature T(g) of these liquids in confined geometries has been measured using differential scanning calorimetry. A systematic decrease of T(g) (up to 25 K) with decreasing pore size has been observed. The relaxation times of the alpha process at constant temperature were decreasing with decreasing pore size (up to 6 orders of magnitude at T(g)), while the width of their distribution was increasing. The change of the relaxation times can be assigned to the change of T(g) in confined geometries. After correcting the activation plots for the shift of T(g) a master curve was obtained for all pore sizes and the bulk material. The effect of chemical modification of the surface of the porous matrix on the dynamics of ortho-terphenyl has also been studied. These dramatic changes of the T(g) and the relaxation time of confined liquids can be explained by simple thermodynamic arguments. There is no indication that they are related to the change of the correlation length of cooperative dynamics.

Relaxation processes in an epoxy resin studied by time-resolved optical Kerr effect

The dynamics of the epoxy resin phenyl glycidyl ether, a fragile glass-forming liquid, is investigated in the liquid and supercooled phases by time-resolved optical Kerr effect experiment with an heterodyne detection technique. We tested the mode-coupling theory and found that the predicted dynamic scenario allows to reproduce properly the measured signal, for t>1 ps, in the whole temperature interval investigated. Furthermore, the values of T(c) and lambda, obtained from the analysis of three different and independent dynamic regimes (alpha regime, von Schweidler, beta regime), are in remarkable agreement. Moreover, relaxation times obtained from optical Kerr effect and dielectric spectroscopy measurements are compared. The two time scales differ only for a constant factor in the whole temperature interval investigated.

Brillouin-scattering study of propylene carbonate: an evaluation of phenomenological and mode coupling analyses

Brillouin-scattering spectra of the molecular glass-forming material propylene carbonate (PC) in the temperature range 140 K to 350 K were analyzed using both the phenomenological Cole-Davidson memory function and a hybrid memory function consisting of the Cole-Davidson function plus a power-law term representing the critical decay part of the fast beta relaxation. The spectra were also analyzed using the extended two-correlator schematic mode-coupling theory (MCT) model recently employed by Götze and Voigtmann to analyze depolarized light backscattering, dielectric, and neutron-scattering spectra of PC [Phys. Rev. E 61, 4133 (2000)]. We assess the ability of the phenomenological and MCT fits, each with three free fitting parameters, to simultaneously describe the spectra and give reasonable values for the alpha-relaxation time tau(alpha).

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.