Crossover behavior and multi-step relaxation in a schematic model of the cut-off glass transition

We study a schematic mode-coupling model in which the ideal glass transition is cut off by a decay of the quadratic coupling constant in the memory function. (Such a decay, on a time scale tau_I, has been suggested as the likely consequence of activated processes.) If this decay is complete, so that only a linear coupling remains at late times, then the alpha relaxation shows a temporal crossover from a relaxation typical of the unmodified schematic model to a final strongly slower-than-exponential relaxation. This crossover, which differs somewhat in form from previous schematic models of the cut-off glass transition, resembles light-scattering experiments on colloidal systems, and can exhibit a `slower-than-alpha' relaxation feature hinted at there. We also consider what happens when a similar but incomplete decay occurs, so that a significant level of quadratic coupling remains for t>>tau_I. In this case the correlator acquires a third, weaker relaxation mode at intermediate times. This empirically resembles the beta process seen in many molecular glass formers. It disappears when the initial as well as the final quadratic coupling lies on the liquid side of the glass transition, but remains present even when the final coupling is only just inside the liquid (so that the alpha relaxation time is finite, but too long to measure). Our results are suggestive of how, in a cut-off glass, the underlying `ideal' glass transition predicted by mode-coupling theory can remain detectable through qualitative features in dynamics.Comment: 14 pages revtex inc 10 figs; submitted to pr

High order vibration modes of glass embedded AgAu nanoparticles

High resolution low frequency Raman scattering measurements from embedded AgAu nanoparticles unveil efficient scattering by harmonics of both the quadrupolar and the spherical modes. Comparing the experimental data with theoretical calculations that account for both the embedding medium and the resonant Raman process enables a very complete description of the observed multiple components in terms of harmonics of both the quadrupolar and spherical modes, with a dominating Raman response from the former ones. It is found that only selected harmonics of the quadrupolar mode contribute significantly to the Raman spectra in agreement with earlier theoretical predictions.Comment: 11 pages, 4 figure

Long-lived submicrometric bubbles in very diluted alkali halide water solutions

Solutions of LiCl and of NaCl in ultrapure water were studied through Rayleigh/Brillouin scattering as a function of the concentration (molarity, M) of dissolved salt from 0.2M to extremely low concentration (2.10^-17 M ). The Landau-Placzek ratio, R/B, of the Rayleigh scattering intensity over the total Brillouin, was measured thanks to the dynamically controlled stability of the used Fabry-Perot interferometer. It was observed that the R/B ratio follows two stages as a function of increasing dilution rate: after a strong decrease between 0.2M and 2.10^-5 M, it increases to reach a maximum between 10^-9 M and 10^-16 M. The first stage corresponds to the decrease of the Rayleigh scattering by the ion concentration fluctuations with the decrease of salt concentration. The second stage, at lower concentrations, is consistent with the increase of the Rayleigh scattering by long-lived sub-microscopic bubbles with the decrease of ion concentration. The origin of these sub-microscopic bubbles is the shaking of the solutions which was carried out after each centesimal dilution. The very long lifetime of the sub-microscopic bubbles and the effects of aging originate in the electric charge of bubbles. The increase of R/B with the decrease of the low salt concentration corresponds to the increase of the sub-microscopic bubble size with the decrease of concentration, that is imposed by the bubble stability due to the covering of the surface bubble by negative ions.Comment: 6 figures. To be published in Physical Chemistry and Chemical Physics (PCCP

Susceptibility functions for slow relaxation processes in supercooled liquids and the search for universal relaxation patterns

In order to describe the slow response of a glass former we discuss some distribution of correlation times, e.g., the generalized gamma distribution (GG) and an extension thereof (GGE), the latter allowing to reproduce a simple peak susceptibility such as of Cole-Davidson type as well as a susceptibility exhibiting an additional high frequency power law contribution (excess wing). Applying the GGE distribution to the dielectric spectra of glass formers exhibiting no beta-process peak (glycerol, propylene carbonate and picoline) we are able to reproduce the salient features of the slow response (1e-6 Hz - 1e9 Hz). A line shape analysis is carried out either in the time or frequency domain and in both cases an excess wing can be identified. The latter evolves in a universal way while cooling and shows up for correlation times tau_alpha > 1e-8 s. It appears that its first emergence marks the break down of the high temperature scenario of mode coupling theory. - In order to describe a glass former exhibiting a beta-process peak we have introduced a distribution function which is compatible with assuming a thermally activated process in contrast to some commonly used fit functions. Together with the GGE distribution this function allows in the frame of the Williams-Watts approach to completely interpolate the spectra, e.g. of fluoro aniline (1e-6 Hz - 1e9 Hz). The parameters obtained indicate an emergence of both the excess wing and the beta-process again at tau_alpha > 1e-8s.Comment: 22 pages, 12 figure

Glassy dynamics in mono-, di-, and tri-propylene glycol: From the alpha- to the fast beta-relaxation

We present a thorough characterization of the glassy dynamics of three propylene glycols (mono-, di- and trimer) by broadband dielectric spectroscopy. By covering a frequency range of more than 15 decades, we have access to the entire variety of dynamic processes typical for glassy dynamics. These results add three more molecular glass formers to the sparse list of materials for which real broadband spectra, including the region of the fast beta-process, are available. Some first analyses of the various observed dynamic processes are provided

Spectral Shape of Relaxations in Silica Glass

Precise low-frequency light scattering experiments on silica glass are presented, covering a broad temperature and frequency range (9 GHz < \nu < 2 THz). For the first time the spectral shape of relaxations is observed over more than one decade in frequency. The spectra show a power-law low-frequency wing of the relaxational part of the spectrum with an exponent $\alpha$ proportional to temperature in the range 30 K < T < 200 K. A comparison of our results with those from acoustic attenuation experiments performed at different frequencies shows that this power-law behaviour rather well describes relaxations in silica over 9 orders of magnitude in frequency. These findings can be explained by a model of thermally activated transitions in double well potentials.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Dielectric and thermal relaxation in the energy landscape

We derive an energy landscape interpretation of dielectric relaxation times in undercooled liquids, comparing it to the traditional Debye and Gemant-DiMarzio-Bishop pictures. The interaction between different local structural rearrangements in the energy landscape explains qualitatively the recently observed splitting of the flow process into an initial and a final stage. The initial mechanical relaxation stage is attributed to hopping processes, the final thermal or structural relaxation stage to the decay of the local double-well potentials. The energy landscape concept provides an explanation for the equality of thermal and dielectric relaxation times. The equality itself is once more demonstrated on the basis of literature data for salol.Comment: 7 pages, 3 figures, 41 references, Workshop Disordered Systems, Molveno 2006, submitted to Philosophical Magazin

Statistical mechanical approach to secondary processes and structural relaxation in glasses and glass formers

The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and structural relaxation. The study of the dynamics allows for predictions on the system relaxation above the temperature of dynamic arrest in the mean-field approximation, that are compared with the outcomes of the equations of motion directly derived within the Mode Coupling Theory (MCT) for under-cooled viscous liquids. Varying the external thermodynamic parameters a wide range of phenomenology can be represented, from a very clear separation of structural and secondary peak in the susceptibility loss to excess wing structures.Comment: 13 pages, 8 figure