Nearly logarithmic decay of correlations in glass-forming 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.

The dynamic susceptibility in glass forming molecular liquids: The search for universal relaxation patterns II

The susceptibility spectra of ten molecular glass formers are completely interpolated by an extension of the generalized gamma distribution of correlation times. The data cover at least 15 decades in frequency and the interpolation includes both alpha peak and excess wing. It is shown that the line shape parameters and the time constant of the alpha relaxation are related to each other. Master curves are identified by a scaling procedure that involves only three parameters, namely, the glass transition temperature T(g), the fragility m, and the excess wing exponent at T(g). This holds independent of whether a further secondary relaxation peak is present or not. Above a crossover temperature T(x) this unique evolution of the line shape parameters breaks down, and a crossover to a simple peak susceptibility without excess wing is observed. Here, the frequency-temperature superposition principle holds in good approximation up to temperatures well above the melting point. It turns out that the crossover coincides with the temperature at which the low-temperature Vogel-Fulcher law starts to fail upon heating. Thus, the so-called Stickel temperature gets a more physical meaning as it marks a qualitative change in the evolution of the susceptibility spectra of glass formers. Moreover, the interrelation of the line shape parameters can explain why the "Nagel scaling" works in some approximation. Our study demonstrates that the excess wing in molecular glass formers is a secondary relaxation, which is linked to the alpha process in a unique way.

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.

Universal power law in the orientational relaxation in thermotropic liquid crystals

We observe a surprisingly general power law decay at short to intermediate times in orientational relaxation in a variety of model systems (both calamitic and discotic, and also lattice) for thermotropic liquid crystals. As all these systems transit across the isotropic-nematic phase boundary, two power law relaxation regimes, separated by a plateau, emerge, giving rise to a steplike feature (well known in glassy liquids) in the single-particle second-rank orientational time correlation function. In contrast to its probable dynamical origin in supercooled liquids, we show that the power law here can originate from the thermodynamic fluctuations of the orientational order parameter, driven by the rapid growth in the second-rank orientational correlation length.

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.

Numerical Study of a Fragile Three-Dimensional Kinetically Constrained Model

We numerically study the three-dimensional generalization of the kinetically constrained east model, the north-or-east-or-front (NEF) model. We characterize the equilibrium behavior of the NEF model in detail, measuring the temperature dependence of several quantities: alpha-relaxation time, distributions of relaxation times, dynamic susceptibility, dynamic correlation length, and four-point susceptibility. We show that the NEF model describes quantitatively experimental observations over an exceptionally wide range of time scales. We illustrate this by fitting experimental data obtained both in the mildly supercooled regime by optical Kerr effect and close to the glass transition by dielectric spectroscopy.

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.

Structural relaxation in liquid water by inelastic UV scattering

Using the novel synchrotron radiation based inelastic ultraviolet scattering technique, the dynamic structure factor of normal and supercooled liquid water has been measured at a momentum transfer Q approximately equal to 0.1 nm(-1), in the temperature range 260-340 K. The structural (alpha) relaxation has been observed in the supercooled temperature region (T< or =273 K), where the inverse relaxation time matches the frequency of the probed sound modes. The T dependence of the relaxation time shows a diverging behavior with a critical temperature T approximately equal to 220 K. These results provide a unique experimental opportunity to frame the dynamics of water in the mode-coupling theory.