Predictions Of Mode-coupling Theory Research Articles

Testing of mode-coupling theory through impulsive stimulated thermal scattering

Abstract Impulsive stimulated thermal scattering, a time-domain light scattering technique spanning ps-ms time scales, allows a number of experimental tests of mode-coupling theory (MCT) predictions. Time-dependent acoustic responses and also slower relaxational responses to sudden heating are observed. From the acoustic responses, mechanical modulus spectra are deduced which permit testing of MCT predictions for α and β relaxation dynamics. From the relative intensities of acoustic and relaxational signals, the prediction of a cusp in the temperature-dependence of the nonergodicity parameter (Debye-Waller factor) can be tested. ISTS results from a concentrated (13 m%) aqueous LiCl solution, the molten salt [Ca(NO3)2]0.4[KNO3]0.6, and salol are reviewed.

Computer simulations of long-time tails: What's new?

Abstract Twenty five years ago Alder and Wainwright discovered, by simulation, the ‘long-time tails’ in the velocity autocorrelation function of a single particle in fluid [1]. Since then, few qualitatively new results on long-time tails have been obtained by computer simulations. However, within the framework of a lattice gas simulation, we recently developed a technique that makes it possible to ‘measure’ such velocity autocorrelation functions with an efficiency that is at least a factor 106 higher than can be achieved with conventional techniques. This method opens the way for making comparisons with the predictions of mode-coupling theory of long-time tails, to an accuracy which was hitherto not possible. In this paper we describe this method, and review the results on long-time tails that have been obtained. In particular, we present evidence that the functional form of the long-time tail in a two-dimensional fluid is qualitatively different from the simple power law observed by Alder-Wainwright. Su...

Tc of the mode coupling theory evaluated from impulsive stimulated light scattering on salol.

Time-domain light scattering on ns--ms time scales has been performed on salol to probe the dynamics in the glass transition range and evaluate through a novel method the nonergodicity parameter ${f}_{q}(T)$ of mode coupling theory (MCT) in the wave vector limit $q\ensuremath{\rightarrow}0$. Stretched-exponential structural relaxation dynamics were observed. In addition, a cusp in ${f}_{0}(T)$ was observed at a temperature ${T}_{c}$ of $\ensuremath{\sim}266$ K, consistent with earlier observations at high $q$. This supports the MCT prediction of a cusp at a $q$-independent temperature.

Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function.

We report the results of a large scale computer simulation of a binary supercooled Lennard-Jones liquid. We find that at low temperatures the curves for the mean squared displacement of a tagged particle for different temperatures fall onto a master curve when they are plotted versus rescaled time $tD(T)$, where $D(T)$ is the diffusion constant. The time range for which these curves follow the master curve is identified with the $\alpha$-relaxation regime of mode-coupling theory (MCT). This master curve is fitted well by a functional form suggested by MCT. In accordance with idealized MCT, $D(T)$ shows a power-law behavior at low temperatures. The critical temperature of this power-law is the same for both types of particle and also the critical exponents are very similar. However, contrary to a prediction of MCT, these exponents are not equal to the ones determined previously for the divergence of the relaxation times of the intermediate scattering function [Phys. Rev. Lett. {\bf 73}, 1376 (1994)]. At low temperatures the van Hove correlation function (self as well as distinct part) shows hardly any sign of relaxation in a time interval that extends over about three decades in time. This time interval can be interpreted as the $\beta$-relaxation regime of MCT. From the investigation of these correlation functions we conclude that hopping processes are not important on the time scale of the $\beta$-relaxation for this system and for the temperature range investigated. We test whether the factorization property predicted by MCT holds and find that this is indeed the case for all correlation functions investigated. The distance dependence of the critical amplitudes are in qualitative accordance with the ones predicted by MCT for some other mixtures. The non-gaussian parameter for the self part of the van

Dynamics of glasslike transitions in a quasi-two-dimensional system.

Transverse self-diffusion of field-induced magnetic colloidal chains is measured using real-space imaging. It has been found that the mean-square displacement $〈\ensuremath{\Delta}{r}^{2}〉$ depends on the aligning field $H$ and displays two different behaviors. In short times $〈\ensuremath{\Delta}{r}^{2}〉$ is subdiffusive, whereas in long times $〈\ensuremath{\Delta}{r}^{2}〉$ exhibits normal diffusion. The characteristic time separating the two time regimes diverges exponentially with $H$, indicating fast frozen-in density fluctuations in the system. Our experimental results deviate significantly from the predictions of mode-coupling theory.

Relaxational Dynamics and Strength in Supercooled Liquids from Impulsive Stimulated Thermal Scattering

ABSTRACTImpulsive stimulated thermal scattering (ISTS), a time-domain light scattering technique, provides a more than 6-decade time range from sub-ns to many ms. It permits characterization of the structural relaxation dynamics and determination of the relaxation strength or Debye-Waller factor in supercooled liquids, and thus allows testing of the mode coupling theory of the liquidglass transition. ISTS experiments were performed on glass formers salol, butylbenzene, and the molten salt [Ca(N03)]0.4[KNO3]0.6. The relaxational dynamics and the Debye-Waller factorfq=0 were obtained. A square-root anomaly was observed in fq=0 (T) at a crossover temperature Tc for all three materials, consistent with the prediction of mode coupling theory.

The dynamics of strong and fragile glass formers: vibrational and relaxation contributions

There are two contributions to the low-frequency excitation spectra (Raman and neutron scattering, specific heat, etc.) of glass formers: relaxations and vibrations. It is shown from the analysis of low-frequency Raman spectra that the relative weight of vibrational over relaxational excitations is larger for less fragile (in Angell's classification) glass formers. The spectra are compared with predictions of mode coupling theory (MCT) for relaxation processes. Qualitatively the predicted behaviour is observed in all analyzed systems. However, some quantitative disagreement due to significant vibrational contribution to the spectra is found for intermediate glass formers. The spectra are also analyzed using a model of vibrations coupled with relaxations. It is found that the temperature at which overdamping of the low-frequency vibrations happens is essentially the critical temperature of MCT. New details of a scenario for the liquid-glass transition are suggested.

Time-resolved measurements of scaling behavior in LiCl/H 2O near the liquid-glass transition

Time-domain light scattering experiments on ps-μs timescales permit determination of the complex compressibility modulus in liquids and glasses in the MHz-GHz frequency window. Analysis of mechanical and electrical modulus spectra for a concentrated aqueous LiCl solution yields results consistent with some predictions of mode-coupling theory: simple scaling for α-relaxation peaks and property-independent power-law functional forms for the spectra which are independent of the property described. Preliminary data from salol, recorded with an improved experimental system, are also presented.

Low-frequency Raman scattering on different types of glass formers used to test predictions of mode-coupling theory.

We have measured low-frequency Raman scattering (RS) spectra of the glass formers ${\mathrm{B}}_{2}$${\mathrm{O}}_{3}$, glycerol, m-tricresyl phosphate (m-TCP), and ${\mathrm{K}}_{3}$${\mathrm{Ca}}_{2}$(${\mathrm{NO}}_{3}$${)}_{7}$ in a broad temperature range above the glass transition temperature. The basic difference between the spectra is the ratio of relaxational to vibrational contributions: the more fragile the glass, the smaller is the vibrational contribution. Features of the relaxational contributions are quite similar. Testing predictions of mode-coupling theory (MCT) for m-TCP, we find that the dynamics is well described, and as the critical temperature we find ${\mathit{T}}_{\mathit{c}}$\ensuremath{\sim}260 K. In the case of glycerol, due to the strong vibrational contribution to the RS spectrum, a consistent interpolation of the rescaled data is only possible if other exponents than those predicted by MCT are applied; however, the MCT exponents are obtained in a narrow frequency range, provided the contribution of the \ensuremath{\alpha} process is subtracted first. Thus, MCT describes the dynamics for \ensuremath{\nu}300 GHz even in the nonfragile glass former glycerol. We extract ${\mathit{T}}_{\mathit{c}}$\ensuremath{\sim}310 K. Combining the RS results with those of NMR in the case of m-TCP, we further find (i) a change of stretching parameter close to ${\mathit{T}}_{\mathit{c}}$ and (ii) a change of the temperature dependence of the Debye-Waller factor at T\ensuremath{\sim}280 K which is close to ${\mathit{T}}_{\mathit{c}}$ for this system.

Neutron and light scattering study of supercooled glycerol.

Relaxation dynamics was investigated in the hydrogen-bonded glass former glycerol using incoherent neutron scattering and depolarized light scattering. The neutron data have a q-independent form in the intermediate \ensuremath{\beta}-relaxation regime implying factoratization of the q and \ensuremath{\omega} dependences. Similar susceptibility spectra obtained from both data sets qualitatively resembling the mode coupling theory scenario. Quantitative fits indicate apparent deviations of the exponents from mode coupling theory predictions suggesting that the influence of vibrational modes is severe in network glass formers.

Dynamical phase transition in simple supercooled liquids and polymers - an NMR approach

We present NMR investigations on m-tricresyl phosphate (m-TCP; 31P NMR) and on polybutadiene (PB; 2H NMR). Relaxation studies have been combined with the analysis of the stimulated echo, and a reorientational correlation function is probed over the entire supercooled regime providing correlation times in the range 10 -11 s-10 s. Furthermore, we have performed Raman scattering (RS) experiments on m-TCP and glycerol. Testing predictions of mode coupling theory (MCT), the scaling behaviour observed by RS on m-TCP is well described by MCT for T > T c with T c ∼ 260 K. The idea of a change of dynamics at T ∼ T c is further supported by phenomena which - although not yet emerging from MCT - are revealed by combining results from NMR, RS and neutron scattering. (i) The time scale of reorientational and translational motion separates below T c (m-TCP). (ii) The stretching parameter of the α-relaxation changes significantly near T c (m-TCP). (iii) NMR and dielectric relaxation probe a third process which exists only below T c. This process has all properties of the secondary relaxation discussed by Johari, however, it is well distinguished from the fast β-process analyzed within MCT and observed by RS. Thus, above T c the dynamics are described by a two-step correlation function with all the features predicted by MCT, whereas below T c a three-step function holds. As a consequence, a second order parameter appears, and the third process is described in terms of an activated process with a distribution of local environments.

Relaxational and vibrational contributions to the dynamics of the glass transition

The low-frequency Raman spectra of a few glass forming liquids were analysed. It is shown that the main difference of the spectra for strong and fragile glass formers is the ratio of vibrational to relaxation contributions: the stronger the glass former, the higher is the vibrational contribution. It is shown that this difference correlates with the difference in the low-temperature anomalies of glasses. The spectra are compared with the mode coupling theory predictions. Qualitatively the predicted behavior is observed in all cases, however, some quantitative disagreement is found.

Kinetic lattice-gas model of cage effects in high-density liquids and a test of mode-coupling theory of the ideal-glass transition

We have devised a kinetic lattice-gas model of an atomic liquid that incorporates the physical features associated with the formation of cages around a particle at high density. The model has simple equilibrium statistics, with a maximum of one particle per lattice site, and simple dynamical rules, so that it is feasible to perform dynamical calculations of the fluctuations about equilibrium over very long time scales. The cages inhibit the motion of the particles and cause the self-diffusion coefficient to fall rapidly with increasing density. Simulation results indicate that as the density \ensuremath{\rho}, defined as the number of particles per lattice site, approaches 0.881, the self-diffusion constant behaves in a critical way as (0.881-\ensuremath{\rho}${)}^{3.2}$. The time dependence of density-density correlation functions is calculated from the simulation results, and relaxation times extracted from these functions show a similar critical behavior. These results suggest that the model undergoes a dynamical transition from ergodic to nonergodic behavior. By investigating different system sizes we exclude the possibility that the observed transition is just a finite-size effect related to the bootstrap percolation problem. The mode-coupling theory (MCT) of ergodic-nonergodic transitions in the absence of activated hopping processes is tested for this model by comparing the behavior of the density correlation functions with the predictions of MCT. Surprisingly few of the MCT predictions hold for the system, depsite the fact that the model was devised to incorporate, in a schematic way, the dynamical cage effects that the MCT is usually regarded as describing. Thus the MCT does not provide a correct description of the cage-induced ideal-glass transition of this model.

Dynamic anomalies at the glass transition of organic van der Waals liquids

Abstract The paper discusses the question of whether there is a characteristic temperature T c above the calorimetric glass transition temperature T g . Mode-coupling theory (MCT) predicts a crossover from liquid- to solid-like dynamics at T c . Neutron scattering and gradient NMR experiments have been carried out to test MCT using the molecular van der Waals liquid ortho -terphenyl as a model system. A significant anomaly of the Debye—Waller factor and a “decoupling” of self-diffusion from viscosity support the MCT predictions. A critical discussion of the relevance of such tests and of the limitations of neutron scattering is presented.

Dynamic-light-scattering study of glasses of hard colloidal spheres.

Dynamic light scattering is applied to the glass phase of nonaqueous suspensions of sterically stabilized colloidal spheres. The short-ranged steric repulsion ensures that the particle interactions are close to hard sphere. This is supported by the observation that the equilibrium phase behavior of these suspensions agrees with that predicted for the hard-sphere atomic system. We verify a model for a nonergodic medium, which assumes that the particles are localized during an experiment and which allows the intermediate scattering function to be calculated from a single measurement of the time-averaged intensity autocorrelation function. Intermediate scattering functions are obtained for several concentrations over a range of wave vectors around the main diffraction peak. The measured nonergodicity parameters are in good agreement with the predictions of mode-coupling theory for the hard-sphere glass. The comparison involves no adjustable parameters. At long times the intermediate scattering functions can be scaled to a single curve for over 2.5 decades in time. This, combined with the results that the nonergodicity parameters and critical amplitudes required for the scaling are in quantitative agreement with mode-coupling theory, provides a convincing verification of the predicted factorization property of the \ensuremath{\beta} process in the glass phase.

The liquid–glass transition in LiCl/H2O: Impulsive stimulated light scattering experiments and mode-coupling analysis

Impulsive stimulated light scattering (ISS) experiments have been conducted on aqueous LiCl solutions to characterize the structural relaxation dynamics at temperatures above, near and below the glass transition temperature Tg. The data provide acoustic velocities, attenuation and thermal diffusion rates over wide ranges of temperature and wave vector. At temperatures in the glass transition region, the dynamics of thermal expansion and subsequent contraction (not due to thermal diffusion) are observed as well. The acoustic information from ISS as well as from earlier Brillouin scattering results is used to determine the frequency-dependent elastic modulus in the MHz–GHz range. Analysis in terms of an empirical (stretched exponential) relaxation function is carried out and shown to be inadequate. The main analysis is inspired by predictions of mode-coupling theory concerning susceptibility spectra. Simple scaling for the α-peak and identical power law dependencies on frequency for both electrical and mechanical moduli, as predicted by theory, were confirmed.

Dynamic structure factor near the glass transition : specific features

The dynamic structure factor in the supercooled liquid state just above the glass transition temperature reveals a number of characteristic universal features in the so-called "fragile" class of glassy systems. A theory independent, unbiased analysis shows that, compared to the behaviour expected in the ordinary liquid state, one can observe : (a) a two-step pattern in the time relaxation of the liquid structure factor, the slower of these steps scaling with the bulk viscosity, (b) a relatively small, oscillatory wavenumber dependence of the relaxation dynamics, and (c) approximate master functions of unconventional shapes for both relaxation steps. These qualitative features are in agreement with predictions of recent mode coupling theories and, in addition, the quantitative behaviour is also compatible with the theoretically predicted scaling properties.

Nonergodicity parameters of colloidal glasses.

Nonergodicity parameters, the nondecaying components of the coherent intermediate scattering functions, of ``hard-sphere'' colloidal glasses were measured by dynamic light scattering. These agree reasonably well with the predictions of mode-coupling theory for hard-sphere atoms, with no adjustable parameters in the comparison. In addition, we provide further verification of the recently developed theory of dynamic light scattering by nonergodic media.

THE GLASS TRANSITION ANOMALIES OF MYOGLOBIN IN THE LIGHT OF MODE COUPLING THEORY

The physics and some predictions of recent mode coupling theories concerning the liquid to glass instability are reviewed with the scope to explore its potential to explain the dynamics of non-simple liquids. It is proposed that the dynamics scaling behaviour observed in the neutron scattering spectra of myoglobin reveal a critical temperature which is associated with the arrest of density fluctuations.

Dynamic anomaly in the glass transition region of orthoterphenyl

We report on incoherent and coherent neutron scattering results in the supercooled liquid and the glassy regime of the van der Waals fluido-terphenyl using the backscattering and spin echo technique, respectively. A critical comparison of both techniques is presented. The data are analysed in the time domain assuming that microscopic correlation times (τ) scale with the viscosity η according to τ(T)∼η(T)/T. With this assumption we obtain an agreement with several predictions of mode coupling theory: the existence of a critical temperatureT c is shown, independently for both incoherent and coherent data, by a cusp in the temperature dependence of the Debye-Waller factorf Q (T). BelowT c fQ(T) follows the predicted $$\sqrt {T_c - T} $$ behaviour yielding also theQ-dependence of the critical parametersf Q c andh Q . AboveT c the α-process or structural relaxation can be well parametrized by a stretched exponential function. In accordance with theory the structural relaxation curves can also be described by a power law with a critical (von Schweidler) exponentb=0.525±0.10.