What can be learned from the schematic mode-coupling approach to experimental data ?

We propose a detailed investigation of the schematic mode-coupling approach to experimental data, a method based on the use of simple mode-coupling equations to analyze the dynamics of supercooled liquids. Our aim here is to clarify different aspects of this approach that appeared so far uncontrolled or arbitrary, and to validate the results obtained from previous works. Analyzing the theoretical foundations of the approach, we first identify the parameters of the theory playing a key role and obtain simple requirements to be met by a schematic model for its use in this context. Then we compare the results obtained from the schematic analysis of a given set of experimental data with a variety of models and show that they are all perfectly consistent. A number of potential biases in the method are identified and ruled out by the choice of appropriate models. Finally, reference spectra computed from the mode-coupling theory for a model simple liquid are analyzed along the same lines as experimental data, allowing us to show that, despite the strong simplification in the description of the dynamics it involves, the method is free from spurious artifacts and provides accurate estimates of important parameters of the theory. The only exception is the exponent parameter, the evaluation of which is hindered, as for other methods, by corrections to the asymptotic laws of the theory present when the dynamics is known only in a limited time or frequency range.Comment: 13 pages, 5 figures, revtex4, to appear in J. Chem. Phy

Study of the Depolarized Light Scattering Spectra of Supercooled Liquids by a Simple Mode-Coupling Model

By using simple mode coupling equations, we investigate the depolarized light scattering spectra of two so-called "fragile" glassforming liquids, salol (phenylsalicylate) and CKN (Ca_{0.4}K_{0.6}(NO_3)_{1.4}), measured by Cummins and coworkers. Nonlinear integrodifferential equations for the time evolution of the density-fluctuations autocorrelation functions are the basic input of the mode coupling theory. Restricting ourselves to a small set of such equations, we fit the numerical solution to the experimental spectra. It leads to a good agreement between model and experiment, which allows us to determine how a real system explores the parameter space of the model, but it also leads to unrealistic effective vertices in a temperature range where the theory makes critical asymptotic predictions. We finally discuss the relevance and the range of validity of these universal asymptotic predictions when applied to experimental data on supercooled liquids.Comment: 31 LaTeX pages using overcite.sty, 10 postscript figures, accepted in J. Chem. Phy

Disentangling density and temperature effects in the viscous slowing down of glassforming liquids

We present a consistent picture of the respective role of density and temperature in the viscous slowing down of glassforming liquids and polymers. Specifically, based in part upon a new analysis of simulation and experimental data on liquid ortho-terphenyl, we conclude that a zeroth-order description of the approach to the glass transition should be formulated in terms of a temperature-driven super-Arrhenius activated behavior rather than a density-driven congestion or jamming phenomenon. The density plays a role at a quantitative level, but its effect on the viscosity and the structural relaxation time can be simply described via a single parameter, an effective interaction energy that is characteristic of the high temperature liquid regime; as a result, density does not affect the ``fragility'' of the glassforming system.Comment: RevTeX4, 8 pages, 8 eps figure

On the correlation between fragility and stretching in glassforming liquids

We study the pressure and temperature dependences of the dielectric relaxation of two molecular glassforming liquids, dibutyl phtalate and m-toluidine. We focus on two characteristics of the slowing down of relaxation, the fragility associated with the temperature dependence and the stretching characterizing the relaxation function. We combine our data with data from the literature to revisit the proposed correlation between these two quantities. We do this in light of constraints that we suggest to put on the search for empirical correlations among properties of glassformers. In particular, argue that a meaningful correlation is to be looked for between stretching and isochoric fragility, as both seem to be constant under isochronic conditions and thereby reflect the intrinsic effect of temperature

Connection between slow and fast dynamics of molecular liquids around the glass transition

The mean-square displacement (MSD) was measured by neutron scattering at various temperatures and pressures for a number of molecular glass-forming liquids. The MSD is invariant along the glass-transition line at the pressure studied, thus establishing an ``intrinsic'' Lindemann criterion for any given liquid. A one-to-one connection between the MSD's temperature dependence and the liquid's fragility is found when the MSD is evaluated on a time scale of approximately 4 nanoseconds, but does not hold when the MSD is evaluated at shorter times. The findings are discussed in terms of the elastic model and the role of relaxations, and the correlations between slow and fast dynamics are addressed.Comment: accepted by Phys Rev E (2010

Dynamical heterogeneity in glass-forming toluene: Comparison of bulk and confined conditions by quasielastic neutron scattering and molecular dynamics simulations

We investigate the presence of dynamical heterogeneities and their consequences on the incoherent intermediate scattering function Fs(Q,t) of a molecular glass-forming liquid, toluene, in bulk and confined conditions. We show that the dynamical heterogeneity deeply affects the shape (stretching and plateau height) of the function Fs(Q,t) and the mean square displacement when the slowest or the fastest populations are considered. Owing to the rigid character of the molecule and the remarkable agreement of the MD simulations with the quasielastic neutron scattering experiments, we extend our analysis to the interplay of translational and rotational motions in the relaxation processes. Since the existence of dynamical heterogeneities and a related cooperative length in the supercooled regime are postulated in many theoretical approaches of the glass transition phenomenon, the liquid is then confined into a pore of a few nano-meter diameter, where this characteristic length cannot extend beyond the pore size. The dynamics slow down when the size of the pore becomes smaller than the correlation length evaluated in the bulk with different methods (size effect on the diffusion coefficient, size of dynamical heterogeneities). An important increase of the stretching of the intermediate incoherent scattering function Fs(Q,t) also appears. We show that the heterogeneous character of the dynamics increases when the liquid is confined due to the presence of a rigid surface

Properties of a confined molecular glass-forming liquid

We use molecular dynamics (MD) simulations to investigate the modification of the dynamic and static properties of liquid toluene when confined in cylindrical mesopores a few molecular diameters across. Due to the strong influence of the substrate on the dynamics of the confined liquid, we choose a procedure where no additional thermal interactions between the wall and the liquid are taken into account. We observe the characteristic oscillations of molecular density profiles (layering) when temperature and pore size are changed. Mean square displacements and intermediate incoherent scattering functions of the centre of mass of the molecules are calculated as functions of different distances from the wall along the principal axis of the pore z and along the perpendicular x- and y-directions. At 200 K the relaxations of the two correlation functions slow down by one order of magnitude as compared to the bulk, with a slightly more pronounced slowing down in the x-direction. This slowing down increases strongly when the wall is approached. However, we do not observe any layer-specific dependence of the dynamics, but instead a continuous change. When the molecules are arrested near the wall in the time window (1 ns) of the simulations, we find hopping processes

Influence of density and temperature on the microscopic structure and the segmental relaxation of polybutadiene

We investigate the influence of temperature and density on the local structure and the dynamics of polybutadiene by controlling both hydrostatic pressure and temperature in polarized neutron diffraction experiments on deuterated polybutadiene and in inelastic incoherent scattering experiments on protonated polybutadiene. We observe that the static structure factor S(Q) does not change along macroscopic isochores. This behavior is contrary to the relaxations observed on the nanosecond and picosecond time scales and viewed by the dynamic incoherent scattering law S(Q,omega), which differ strongly along the same thermodynamic path. We conclude that the static behavior, i.e., S(Q), is dominated by macroscopic density changes, similar to the vibrational excitations in the meV range. However, the relaxation dynamics is more sensitive to thermal energy changes. This is confirmed by the finding that lines of identical relaxation behavior (in time, shape, and Q dependence), isochrones on the 10(-9) sec time scale, clearly cross the constant density lines in the (P,T) plane. Concerning S(Q), we can reasonably relate the variation of the main-peak position to the average neighbor chain distance and deduce crude microscopic thermal expansion and compressibility coefficients. In the low-Q regime, the observed pressure and temperature variation of S(Q) exceeds the compressibility contribution and suggests the existence of additional scattering, which might originate from structural correlations arising at higher temperature and low pressure