A detailed test of mode-coupling theory on all time scales: Time domain studies of structural relaxation in a supercooled liquid

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.

The Interplay between the Theories of Mode Coupling and of Percolation Transition in Attractive Colloidal Systems

In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of the nature of such processes represents one of the most challenging unsolved problems in the field of material science. In this context, two important theories have contributed significantly to the interpretation of these phenomena: the Mode-Coupling theory (MCT) and the Percolation theory (PT). These theories are rooted on the two pillars of statistical physics, universality and scale laws, and their original formulations have been subsequently modified to account for the fundamental concepts of Energy Landscape (EL) and of the universality of the fragile to strong dynamical crossover (FSC). In this review, we discuss experimental and theoretical results, including Molecular Dynamics (MD) simulations, reported in the literature for colloidal and polymer systems displaying both glass and sol-gel transitions. Special focus is dedicated to the analysis of the interferences between these transitions and on the possible interplay between MCT and PT. By reviewing recent theoretical developments, we show that such interplay between sol-gel and glass transitions may be interpreted in terms of the extended F13 MCT model that describes these processes based on the presence of a glass-glass transition line terminating in an A3 cusp-like singularity (near which the logarithmic decay of the density correlator is observed). This transition line originates from the presence of two different amorphous structures, one generated by the inter-particle attraction and the other by the pure repulsion characteristic of hard spheres. We show here, combining literature results with some new results, that such a situation can be generated, and therefore experimentally studied, by considering colloidal-like particles interacting via a hard core plus an attractive square well potential. In the final part of this review, scaling laws associated both to MCT and PT are applied to describe, by means of these two theories, the specific viscoelastic properties of some systems.

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.

The polarizability response of a glass-forming liquid reveals intrabasin motion and interbasin transitions on a potential energy landscape

Potential energy landscape (PEL) concepts have been useful in conceptualizing the effects of intermolecular interactions on dynamic and thermodynamic properties of liquids and glasses. "Basins", or regions of reduced potential energy associated with locally preferred molecular packing are important PEL features. The molecular configurations at the bottom of these basins are referred to as inherent structures (ISs). Experimental methods for directly characterizing PEL features such as these are rare, largely relegating PEL concepts to theory and simulation studies, and impeding their exploration in real systems. Recently, we showed that quasielastic neutron scattering (QENS) data from propylene carbonate (PC) exhibit signatures of picosecond timescale motion that are consistent with intrabasin motion and interbasin transitions [Cicerone et al., J. Chem. Phys., 2017, 146, 054502]. Here we present optically-heterodyne-detected optical Kerr effect (OHD-OKE) spectroscopy studies on PC. The data exhibit signatures of motion within and transitions between basins that agree quantitatively with and extend the QENS results. We show that the librational component of the OKE response corresponds to intrabasin dynamics, and the enigmatic intermediate OKE response corresponds to interbasin transition events. The OKE data extend the measurement range of these parameters and reveal their utility in characterizing PEL features of real systems.

Dynamic Heterogeneities in Colloidal Supercooled Liquids: Experimental Tests of Inhomogeneous Mode Coupling Theory

The dynamics in supercooled liquids slow enormously upon approaching the glass transition, albeit without significant change of liquid structure. This empirical observation has stimulated development of many theoretical models which attempt to elucidate microscopic mechanisms in glasses and glass precursors. Here, quasi-two-dimensional colloidal supercooled liquids and glasses are employed to experimentally test predictions of widely used models: mode coupling theory (MCT) and its important extension, inhomogeneous MCT (IMCT). We measure two-point dynamic correlation functions in the glass forming liquids to determine structural relaxation times, τ_α, and mode coupling exponents, a, b, and γ; these parameters are then used to extract the mode coupling dynamic crossover packing area-fraction, ϕ _c. This information, along with our measurements of supercooled liquid spatiotemporal dynamics, permits characterization of dynamic heterogeneities in the samples and facilitates direct experimental tests of the scaling predictions of IMCT. The time scales at which dynamic heterogeneities are largest, and their spatial sizes, exhibit power law growth on approaching ϕ _c. Within experimental error, the exponents of the measured power laws are close to the predictions of IMCT.

Viscosity and real-space molecular motion of water: Observation with inelastic x-ray scattering

Even though viscosity is one of the fundamental properties of liquids, its microscopic origin is not fully understood. We determined the spatial and temporal correlation of molecular motions of water near room temperature and its temperature variation on a picosecond timescale and a subnanometer spatial scale, through high-resolution inelastic x-ray scattering measurement. The results, expressed in terms of the time-dependent pair correlation function called the Van Hove function, show that the timescale of the decay of the molecular correlation is directly related to the Maxwell relaxation time near room temperature, which is proportional to viscosity. This conclusion validates our earlier finding that the topological changes in atomic or molecular connectivity are the origin of viscosity in liquids.

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.

Depolarized light scattering spectra of molecular liquids: Described in terms of mode coupling theory

Depolarized light scattering spectra of eight molecular liquids as obtained from applying tandem-Fabry-Pérot interferometry and double monochromator are analyzed in the frame work of the mode coupling theory (MCT). The susceptibility spectra are fitted to the numerical solution of the schematic F12 model of MCT and the validity of the asymptotic laws is discussed. The model is able to quantitatively describe the spectra up to the boiling point, where the main (structural) relaxation and the contribution of the microscopic (vibrational) dynamics essentially merge, and down to the moderately super-cooled liquid where glassy dynamics establishes. The changes of the spectra with temperature are mapped to only two control parameters, which show a smooth variation with temperature. Strong correlation between experimental stretching parameters and extrapolated values from the model is found. The numerical solutions are extrapolated down to Tc, where the asymptotic scaling laws can be applied. Although the spectra apparently follow scaling relations, the application of the asymptotic laws usually overestimates Tc by up to 12 K. In all the cases, the experimental spectra are outside the applicability regime of the asymptotic laws. This is explained by more or less strong vibrational contributions. Within a phenomenological approach which extends the spectral analysis down to Tg and which allows for separating fast and slow dynamics, the strength of the fast dynamics 1 - frel is revealed. It shows the cusp-like anomaly predicted by MCT; yet, the corresponding critical temperature is significantly higher than that derived from the F12 model. In addition, we demonstrate that close to Tg, the susceptibility minimum is controlled by the interplay of the excess wing and the fast dynamics contribution.

Glassy relaxation and excess wing in mode-coupling theory: the dynamic susceptibility of propylene carbonate above and below T(c)

We explore the possibility of describing experimental susceptibility spectra of the glass former propylene carbonate with a two-component schematic model of mode-coupling theory (MCT) from above the melting point down to temperatures far below the critical temperature of MCT. By introducing a phenomenological time-dependent hopping rate, the spectra are reproduced in the full frequency and temperature range available. Literature data of dielectric susceptibilities and depolarized Brillouin light-scattering spectra are combined with our measurements of photon correlation spectroscopy to cover up to 18 decades in frequency of spectra for two different dynamical variables. A consistent description of all data sets is obtained by adjusting only a few physically motivated parameters. In particular the excess wing or slow β-relaxation commonly observed in the susceptibility spectra can consistently be modeled as originating from a coupling of the individual experimental probe correlator to the collective density fluctuations.

Facilitation, complexity growth, mode coupling, and activated dynamics in supercooled liquids

In low-temperature-supercooled liquids, below the ideal mode-coupling theory transition temperature, hopping and continuous diffusion are seen to coexist. Here, we present a theory that shows explicitly the interplay between the two processes and shows that activated hopping facilitates continuous diffusion in the otherwise frozen liquid. Several universal features arise from nonlinear interactions between the continuous diffusive dynamics described here by the mode coupling theory (MCT)] and the activated hopping (described here by the random first-order transition theory). We apply the theory to a specific system, Salol, to show that the theory correctly predicts the temperature dependence of the nonexponential stretching parameter, beta, and the primary alpha relaxation timescale, tau. The study explains why, even below the mean field ergodic to nonergodic transition, the dynamics is well described by MCT. The nonlinear coupling between the two dynamical processes modifies the relaxation behavior of the structural relaxation from what would be predicted by a theory with a complete static Gaussian barrier distribution in a manner that may be described as a facilitation effect. Furthermore, the theory correctly predicts the observed variation of the stretching exponent beta with the fragility parameter, D. These two predictions also allow the complexity growth to be predicted, in good agreement with the results of Capaccioli et al. [Capaccioli S, Ruocco G, Zamponi F (2008) J Phys Chem B 112:10652-10658].

Intermolecular forces and the glass transition

Random first-order transition theory is used to determine the role of attractive and repulsive interactions in the dynamics of supercooled liquids. Self-consistent phonon theory, an approximate mean field treatment consistent with random first-order transition theory, is used to treat individual glassy configurations, whereas the liquid phase is treated using common liquid-state approximations. Free energies are calculated using liquid-state perturbation theory. The transition temperature, T*A, the temperature where the onset of activated behavior is predicted by mean field theory; the lower crossover temperature, T*C, where barrierless motions actually occur through fractal or stringy motions (corresponding to the phenomenological mode coupling transition temperature); and T*K, the Kauzmann temperature (corresponding to an extrapolated entropy crisis), are calculated in addition to T*g, the glass transition temperature that corresponds to laboratory cooling rates. Relationships between these quantities agree well with existing experimental and simulation data on van der Waals liquids. Both the isobaric and isochoric behavior in the supercooled regime are studied, providing results for DeltaCV and DeltaCp that can be used to calculate the fragility as a function of density and pressure, respectively. The predicted variations in the alpha-relaxation time with temperature and density conform to the empirical density-temperature scaling relations found by Casalini and Roland. We thereby demonstrate the microscopic origin of their observations. Finally, the relationship first suggested by Sastry between the spinodal temperature and the Kauzmann temperatures, as a function of density, is examined. The present microscopic calculations support the existence of an intersection of these two temperatures at sufficiently low temperatures.

Spatial correlations in the dynamics of glassforming liquids: experimental determination of their temperature dependence

We use recently introduced three-point dynamic susceptibilities to obtain an experimental determination of the temperature evolution of the number of molecules Ncorr that are dynamically correlated during the structural relaxation of supercooled liquids. We first discuss in detail the physical content of three-point functions that relate the sensitivity of the averaged two-time dynamics to external control parameters (such as temperature or density), as well as their connection to the more standard four-point dynamic susceptibility associated with dynamical heterogeneities. We then demonstrate that these functions can be experimentally determined with good precision. We gather available data to obtain the temperature dependence of Ncorr for a large number of supercooled liquids over a wide range of relaxation time scales from the glass transition up to the onset of slow dynamics. We find that Ncorr systematically grows when approaching the glass transition. It does so in a modest manner close to the glass transition, which is consistent with an activation-based picture of the dynamics in glassforming materials. For higher temperatures, there appears to be a regime where Ncorr behaves as a power-law of the relaxation time. Finally, we find that the dynamic response to density, while being smaller than the dynamic response to temperature, behaves similarly, in agreement with theoretical expectations.

Depolarized light scattering versus optical Kerr effect. II. Insight into the dynamic susceptibility of molecular liquids

We have previously discussed [J. Chem. Phys. 125, 114502 (2006)] that optical Kerr effect (OKE) and depolarized light scattering (DLS) data of molecular liquids reveal, each in their native domain, the same characteristic signatures of the glass transition dynamics; in particular, the intermediate power law of OKE is equivalent with the excess wing of the frequency-domain data, long since known in dielectric spectroscopy. We now extend the discussion to show that the excess wing is an equally common feature in DLS. We further discuss the time-temperature superposition property of OKE data in relation to our DLS and literature dielectric-spectroscopic results, and the merits of their mode coupling theory analyses. Spectroscopic signatures of a liquid-crystal-forming system (nematogen) are discussed in the same frame.

Dynamics of a discotic liquid crystal in the isotropic phase

Optically heterodyne-detected optical Kerr effect (OHD-OKE) experiments are conducted to study the orientational dynamics of a discotic liquid crystal 2,3,6,7,10,11-hexakis(pentyloxy)triphenylene (HPT) in the isotropic phase near the columnar-isotropic (C-I) phase transition. The OHD-OKE signal of HPT is characterized by an intermediate power law t(-0.76+/-0.02) at short times (a few picoseconds), a von Schweidler power law t(-0.26+/-0.01) at intermediate times (hundreds of picoseconds), and an exponential decay at long times (tens of nanoseconds). The exponential decay has Arrhenius temperature dependence. The functional form of the total time dependent decay is identical to the one observed previously for a large number of molecular supercooled liquids. The mode coupling theory schematic model based on the Sjogren [Phys. Rev. A 33, 1254 (1986)] model is able to reproduce the HPT data over a wide range of times from <1 ps to tens of nanoseconds. The studies indicate that the HPT C-I phase transition is a strong first order transition, and the dynamics in the isotropic phase display a complex time dependent profile that is common to other molecular liquids that lack mesoscopic structure.

Depolarized light scattering versus optical Kerr effect spectroscopy of supercooled liquids: Comparative analysis

Recently, heterodyne-detected optical Kerr effect (HD-OKE) spectroscopy was used to study dynamics of supercooled molecular liquids. The studies revealed an apparently new physical phenomenon that had not been reported before from the related depolarized light scattering (DLS), namely, an intermediate power law (nearly logarithmic decay) of the response functions [H. Cang et al., J. Chem. Phys. 118, 2800 (2003)]. Conceptually, HD-OKE and DLS data reflect optical anisotropy fluctuations mainly due to molecular reorientation dynamics in time and frequency domains, respectively. The above-mentioned effects are revealed in the mesoscopic range less, similar1 GHz ( greater, similar100 ps), where no direct comparison of the techniques was reported. In this Communication, we attempt such a comparison of exemplifying HD-OKE literature data of the glass-forming salol (phenyl salicylate), benzophenone, and liquid-crystal forming 4-cyano-4(')-pentylbiphenyl with DLS data of the same systems that we measured down to ca. 200 MHz by a combined tandem Fabry-Perot interferometer plus tandem-grating-monochromator technique. Generally, we find a satisfactory agreement, albeit in some cases with subtle differences at frequencies greater, similar10 GHz. We conclude that, in the mesoscopic dynamic range, HD-OKE and DLS studies provide consistent and comparable information, and therefore their conclusions must agree. We argue that the intermediate power law of HD-OKE is in essence a manifestation of the excess wing of the corresponding frequency-domain data, known long since from broadband dielectric spectroscopy and anticipated from DLS studies of supercooled liquids.

Dynamics in Supercooled Ionic Organic Liquids and Mode Coupling Theory Analysis

Optically heterodyne-detected optical Kerr effect experiments are applied to study the orientational dynamics of the supercooled ionic organic liquids N-propyl-3-methylpyridinium bis(trifluoromethylsulfonyl)imide (PMPIm) and 1-ethyl-3-methylimidazolium tosylate (EMImTOS). The orientational dynamics are complex with relaxation involving several power law decays followed by a final exponential decay. A mode coupling theory (MCT) schematic model, the Sjögren model, was able to reproduce the PMPIm data very successfully over a wide range of times from 1 ps to hundreds of ns for all temperatures studied. Over the temperature range from room temperature down to the critical temperature Tc of 231 K, the OHD-OKE signal of PMPIm is characterized by the intermediate power law t(-1.00+/-0.04) at short times, a von Schweidler power law t(-0.51+/-0.03) at intermediate times, and a highly temperature-dependent exponential (alpha relaxation) at long times. This form of the decay is identical to the form observed previously for a large number of organic van der Waals liquids. MCT analysis indicates that the theory can explain the experimental data very well for a range of temperatures above Tc, but as might be expected, there are some deviations from the theoretical modeling at temperatures close to Tc. For EMImTOS, the orientational dynamics were studied on the ps time scale in the deeply supercooled region near its glass transition temperature. The orientational relaxation of EMImTOS clearly displays the feature associated with the boson peak at approximately 2 ps, which is the first time domain evidence of the boson peak in ionic organic liquids. Overall, all the dynamical features observed earlier for organic van der Waals liquids using the same experimental technique are also observed for organic ionic liquids.

Cole-Cole law for critical dynamics in glass-forming liquids

Within the mode-coupling theory (MCT) for glassy dynamics, the asymptotic low-frequency expansions for the dynamical susceptibilities at critical points are compared to the expansions for the dynamic moduli; this shows that the convergence properties of the two expansions can be quite different. In some parameter regions, the leading-order expansion formula for the modulus describes the solutions of the MCT equations of motion outside the transient regime successfully; at the same time, the leading- and next-to-leading-order expansion formulas for the susceptibility fail. In these cases, one can derive a Cole-Cole law for the susceptibilities; and this law accounts for the dynamics for frequencies below the band of microscopic excitations and above the high-frequency part of the alpha peak. It is shown that this scenario explains the optical-Kerr-effect data measured for salol and benzophenone (BZP). For BZP it is inferred that the depolarized light-scattering spectra exhibit a wing for the alpha peak within the Gigahertz band. This wing results from the crossover of the von Schweidler law part of the alpha peak to the high-frequency part of the Cole-Cole peak; and this crossover can be described quantitatively by the leading-order formulas of MCT for the modulus.

A mode coupling theory description of the short- and long-time dynamics of nematogens in the isotropic phase

Optical heterodyne-detected optical Kerr effect (OHD-OKE) experimental data are pre-sented on nematogens 4-(trans-4-n-octylcyclohexyl)isothiocyanatobenzene (8-CHBT), and 4-(4-pentyl-cyclohexyl)-benzonitrile (5-PCH) in the isotropic phase. The 8-CHBT and 5-PCH data and previously published data on 4-pentyl-4-biphenylcarbonitrile (5-CB) are analyzed using a modification of a schematic mode coupling theory (MCT) that has been successful in describing the dynamics of supercooled liquids. At long time, the OHD-OKE data (orientational relaxation) are well described with the standard Landau-de Gennes (LdG) theory. The data decay as a single exponential. The decay time diverges as the isotropic to nematic phase transition is approached from above. Previously there has been no theory that can describe the complex dynamics that occur at times short compared to the LdG exponential decay. Earlier, it has been noted that the short-time nematogen dynamics, which consist of several power laws, have a functional form identical to that observed for the short time behavior of the orientational relaxation of supercooled liquids. The temperature-dependent orientational dynamics of supercooled liquids have recently been successfully described using a schematic mode coupling theory. The schematic MCT theory that fits the supercooled liquid data does not reproduce the nematogen data within experimental error. The similarities of the nematogen data to the supercooled liquid data are the motivation for applying a modification of the successful MCT theory to nematogen dynamics in the isotropic phase. The results presented below show that the new schematic MCT theory does an excellent job of reproducing the nematogen isotropic phase OHD-OKE data on all time scales and at all temperatures.

Bridging the gap between the mode coupling and the random first order transition theories of structural relaxation in liquids

A unified treatment of structural relaxation in a deeply supercooled glassy liquid is developed which extends the existing mode coupling theory (MCT) by incorporating, in a self-consistent way, the effects of activated events by using the concepts from the random first order transition (RFOT) theory. We show how the decay of the dynamic structure factor is modified by localized activated hopping events called instantons. The instanton vertex added to the usual MCT depicts the probability and consequences of such an event. In the vertex, the probability is proportional to exp(-A/s(c)) where s(c) is the configurational entropy. Close to the glass transition temperature, Tg, since s(c) is diminishing, the activated process slows beyond the time window and this eventually leads to an arrest of the structural relaxation as expected for glasses. The combined treatment describes the dynamic structure factor, phi(t), in deeply supercooled liquid fairly well. We show that below the mode coupling transition temperature, T(c), phi(t) not only decays via the hopping channel but the otherwise frozen MCT part of phi(t) also shows a hopping induced decay. This decay is primarily due to the relaxation of the longitudinal viscosity which is otherwise divergent in the idealized MCT. We further show that although hopping motion induces a decay in the MCT part of phi(t), due to the self-consistent calculation, this effect is nonlinear in nature.

Boson peak in supercooled liquids: Time domain observations and mode coupling theory

Optical heterodyne-detected optical Kerr effect (OHD-OKE) experiments are presented for the supercooled liquid acetylsalicylic acid (aspirin - ASP). The ASP data and previously published OHD-OKE data on supercooled dibutylphthalate (DBP) display highly damped oscillations with a periods of approximately 2 ps as the temperature is reduced to and below the mode coupling theory (MCT) temperature T(C). The oscillations become more pronounced below T(C). The oscillations can be interpreted as the time domain signature of the boson peak. Recently a schematic MCT model, the Sjogren model, was used to describe the OHD-OKE data for a number of supercooled liquids by Gotze and Sperl [W. Gotze and M. Sperl, Phys. Rev. E 92, 105701 (2004)] , but the short-time and low-temperature behaviors were not addressed. Franosch et al. [T. Franosch, W. Gotze, M. R. Mayr, and A. P. Singh, Phys. Rev. E 55, 3183 (1997)] found that the Sjogren model could describe the boson peak observed by depolarized light-scattering (DLS) experiments on glycerol. The OHD-OKE experiment measures a susceptibility that is a time domain equivalent of the spectrum measured in DLS. Here we present a detailed analysis of the ASP and DBP data over a broad range of times and temperatures using the Sjogren model. The MCT schematic model is able to describe the data very well at all temperatures and relevant time scales. The trajectory of MCT parameters that fit the high-temperature data (no short-time oscillations) when continued below T(C) results in calculations that reproduce the oscillations seen in the data. The results indicate that increasing translational-rotational coupling is responsible for the appearance of the boson peak as the temperature approaches and drops below T(C).

Nearly logarithmic decay in the colloidal hard-sphere system

Nearly logarithmic decay is identified in the data for the mean-squared displacement of the colloidal hard-sphere system at the liquid-glass transition [W. van Megen, Phys. Rev. E 58, 6073 (1998)]. The solutions of the mode-coupling theory for the microscopic equations of motion fit the experimental data well. Based on these equations, the nearly logarithmic decay is explained as the equivalent of a beta-peak phenomenon, a manifestation of the critical relaxation when the coupling between of the probe variable and the density fluctuations is strong. In an asymptotic expansion, a Cole-Cole formula including corrections is derived from the microscopic equations of motion, which describes the experimental data for three decades in time.

Mode coupling behavior in glass-forming liquid crystalline isopentylcyanobiphenyl

Linear and nonlinear dielectric measurements of liquid crystalline chiral isopentylcyanobiphenyl (5*CB) and n -pentylcyanobiphenyl (5CB), combined with viscosity eta (T) data, are presented. The 5*CB compound glassifies on cooling in the cholesteric phase whereas 5CB crystallizes in the nematic phase. In both compounds the temperature evolution of dielectric relaxation times, the dc conductivity, and the viscosity are well described by the "critical-like" description from mode coupling theory (MCT). However, for 5*CB a unique coincidence of the MCT "critical" temperature and extrapolated temperature of the hypothetical continuous isotropic-cholesteric (T*) phase transition was found. The temperature dependence of the strong electric-field-induced changes of the dielectric permittivity exhibits a strong anomaly in the direction of negative values on approaching T* , not observed up to now. The anomaly is described by the susceptibility-related critical exponent gamma=1 . The divergence of the "nonlinear" dielectric relaxation follows a power dependence described by the exponent y=1 . This paper recalls the recent discussions on the glassy dynamics of a "hard-ellipsoid" liquid and the possible relationship between the glass transition, critical phenomena, and isotropic-nematic transition.

Ultrafast to Slow Orientational Dynamics of a Homeotropically Aligned Nematic Liquid Crystal

The orientational dynamics of a homeotropically aligned nematic liquid crystal, 4'-pentyl-4-biphenylcarbonitrile (5-CB), is studied over more than six decades of time (500 fs to 2 mus) using optical heterodyne detected optical Kerr effect experiments. In contrast to the dynamics of nematogens in the isotropic phase, the data do not decay as a highly temperature-dependent exponential on the longest time scale, but rather, a temperature-independent power law spanning more than two decades of time, the final power law, is observed. On short time scales (approximately 3 ps to approximately 1 ns) another power law, the intermediate power law, is observed that is temperature dependent. The power law exponent of the correlation function associated with the intermediate power law displays a linear dependence on the change in the nematic order parameter with temperature. Between the intermediate power law and the final power law, there is a crossover region that displays an inflection point. The temperature-dependent orientational dynamics in the nematic phase are shown to be very different than those observed in the isotropic phase.

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.

Nearly logarithmic decay of correlations in glass-forming liquids

Nearly logarithmic decay of correlations, which was observed for several supercooled liquids in optical-Kerr-effect experiments [Phys. Rev. Lett. 84, 2437 (2000)]; Phys. Rev. Lett. 90, 197401 (2003)]], is explained within the mode-coupling theory for ideal glass transitions as a manifestation of the beta-peak phenomenon. A schematic model, which describes the dynamics by only two correlators, one referring to density fluctuations and the other to the reorientational fluctuations of the molecules, yields for strong rotation-translation coupling response functions in agreement with those measured for benzophenone and Salol for the time interval extending from 2 ps to about 20 and 200 ns, respectively.

Experimental observation of a nearly logarithmic decay of the orientational correlation function in supercooled liquids on the picosecond-to-nanosecond time scales

Dynamics of five supercooled molecular liquids have been studied using optical heterodyne detected optical Kerr effect experiments. "Intermediate" time scale power law decays (approximately 2 ps to 1-10 ns) with temperature independent exponents close to -1 have been observed in all five samples from high temperature to approximately T(c), the mode-coupling theory (MCT) critical temperature. The amplitude of the intermediate power law increases with temperature as [(T-T(c))/T(c)](1/2). The results cannot be explained by standard MCT, and one possible explanation within MCT would require the higher order singularity scenario, thought to be highly improbable, to be virtually universal.

Diffusion and viscosity in a supercooled polydisperse system

We have carried out extensive molecular dynamics simulations of a supercooled polydisperse Lennard-Jones liquid with large variations in temperature at a fixed pressure. The particles in the system are considered to be polydisperse in both size and mass. The temperature dependence of dynamical properties such as the viscosity (eta) and the self-diffusion coefficients (D(i)) of different size particles is studied. Both viscosity and diffusion coefficients show super-Arrhenius temperature dependence and fit well to the well-known Vogel-Fulcher-Tammann equation. Within the temperature range investigated, the value of Angell's fragility parameter (D approximately 1.4) classifies the present system as a very fragile liquid. The critical temperature for diffusion (T(D(i))(o)) increases with the size of the particles. The critical temperature for viscosity (T(eta)(o)) is larger than that for diffusion, and sizable deviations appear for the smaller size particles, implying a decoupling of translational diffusion from viscosity in deeply supercooled liquids. Indeed, the diffusion shows markedly non-Stokesian behavior at low temperatures where a highly nonlinear dependence on size is observed. An inspection of the trajectories of the particles shows that at low temperatures the motions of both the smallest and largest size particles are discontinuous (jump type). However, the crossover from continuous Brownian to large length hopping motion takes place at shorter time scales for the smaller size particles.