Critical Decay at Higher-Order Glass-Transition Singularities

Within the mode-coupling theory for the evolution of structural relaxation in glass-forming systems, it is shown that the correlation functions for density fluctuations for states at A_3- and A_4-glass-transition singularities can be presented as an asymptotic series in increasing inverse powers of the logarithm of the time t: $\phi(t)-f\propto \sum_i g_i(x)$, where $g_n(x)=p_n(\ln x)/x^n$ with p_n denoting some polynomial and x=ln (t/t_0). The results are demonstrated for schematic models describing the system by solely one or two correlators and also for a colloid model with a square-well-interaction potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in Colloidal Systems with Short-Range Attractions", Messina, Italy, December 2003 (submitted

Vitrification of a monatomic 2D simple liquid

A monatomic simple liquid in two dimensions, where atoms interact isotropically through the Lennard-Jones-Gauss potential [M. Engel and H.-R. Trebin, Phys. Rev. Lett. 98, 225505 (2007)], is vitrified by the use of a rapid cooling technique in a molecular dynamics simulation. Transformation to a crystalline state is investigated at various temperatures and the time-temperature-transformation (TTT) curve is determined. It is found that the transformation time to a crystalline state is the shortest at a temerature 14% below the melting temperature Tm and that at temperatures below Tv = 0.6 Tm the transformation time is much longer than the available CPU time. This indicates that a long-lived glassy state is realized for T < Tv.Comment: 5pages,5figures,accepted for publication in CEJ

Relaxation in glassforming liquids and amorphous solids

The field of viscousliquid and glassysolid dynamics is reviewed by a process of posing the key questions that need to be answered, and then providing the best answers available to the authors and their advisors at this time. The subject is divided into four parts, three of them dealing with behavior in different domains of temperature with respect to the glass transition temperature, Tg,and a fourth dealing with “short time processes.” The first part tackles the high temperature regime T\u3eTg, in which the system is ergodic and the evolution of the viscousliquid toward the condition at Tg is in focus. The second part deals with the regime T∼Tg, where the system is nonergodic except for very long annealing times, hence has time-dependent properties (aging and annealing). The third part discusses behavior when the system is completely frozen with respect to the primary relaxation process but in which secondary processes, particularly those responsible for “superionic” conductivity, and dopart mobility in amorphous silicon, remain active. In the fourth part we focus on the behavior of the system at the crossover between the low frequency vibrational components of the molecular motion and its high frequency relaxational components, paying particular attention to very recent developments in the short time dielectric response and the high Qmechanical response

Structural Relaxation and Mode Coupling in a Simple Liquid: Depolarized Light Scattering in Benzene

We have measured depolarized light scattering in liquid benzene over the whole accessible temperature range and over four decades in frequency. Between 40 and 180 GHz we find a susceptibility peak due to structural relaxation. This peak shows stretching and time-temperature scaling as known from $\alpha$ relaxation in glass-forming materials. A simple mode-coupling model provides consistent fits of the entire data set. We conclude that structural relaxation in simple liquids and $\alpha$ relaxation in glass-forming materials are physically the same. A deeper understanding of simple liquids is reached by applying concepts that were originally developed in the context of glass-transition research.Comment: submitted to New J. Phy

Time Scales for transitions between free energy minima of a hard sphere system

Time scales associated with activated transitions between glassy metastable states of a free energy functional appropriate for a dense hard sphere system are calculated by using a new Monte Carlo method for the local density variables. We calculate the time the system,initially placed in a shallow glassy minimum of the free energy, spends in the neighborhood of this minimum before making a transition to the basin of attarction of another free energy minimum. This time scale is found to increase with the average density. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This scale shows no evidence of dependence on sample size.Comment: 25 pages, Revtex, 6 postscript figures. Will appear in Phys Rev E, March 1996 or s

Universal and non-universal features of glassy relaxation in propylene carbonate

It is demonstrated that the susceptibility spectra of supercooled propylene carbonate as measured by depolarized-light-scattering, dielectric-loss, and incoherent quasi-elastic neutron-scattering spectroscopy within the GHz window are simultaneously described by the solutions of a two-component schematic model of the mode-coupling theory (MCT) for the evolution of glassy dynamics. It is shown that the universal beta-relaxation-scaling laws, dealing with the asymptotic behavior of the MCT solutions, describe the qualitative features of the calculated spectra. But the non-universal corrections to the scaling laws render it impossible to achieve a complete quantitative description using only the leading-order-asymptotic results.Comment: 37 pages, 16 figures, to be published in Phys. Rev.

Microscopic Theory of Heterogeneity and Non-Exponential Relaxations in Supercooled Liquids

Recent experiments and computer simulations show that supercooled liquids around the glass transition temperature are "dynamically heterogeneous" [1]. Such heterogeneity is expected from the random first order transition theory of the glass transition. Using a microscopic approach based on this theory, we derive a relation between the departure from Debye relaxation as characterized by the $\beta$ value of a stretched exponential response function $\phi(t) =e^{-(t/ \tau_{KWW})^{\beta}}$, and the fragility of the liquid. The $\beta$ value is also predicted to depend on temperature and to vanish as the ideal glass transition is approached at the Kauzmann temperature.Comment: 4 pages including 3 eps figure

Mode-coupling theory of the stress-tensor autocorrelation function of a dense binary fluid mixture

We present a generalized mode-coupling theory for a dense binary fluid mixture. The theory is used to calculate molecular-scale renormalizations to the stress-tensor autocorrelation function (STAF) and to the long-wavelength zero-frequency shear viscosity. As in the case of a dense simple fluid, we find that the STAF appears to decay as $t^{-3/2}$ over an intermediate range of time. The coefficient of this long-time tail is more than two orders of magnitude larger than that obtained from conventional mode-coupling theory. Our study focuses on the effect of compositional disorder on the decay of the STAF in a dense mixture.Comment: Published; withdrawn since ordering in the archive gives misleading impression of new publicatio

Metastable Dynamics of the Hard-Sphere System

The reformulation of the mode-coupling theory (MCT) of the liquid-glass transition which incorporates the element of metastability is applied to the hard-sphere system. It is shown that the glass transition in this system is not a sharp one at the special value of the density or the packing fraction, which is in contrast to the prediction by the conventional MCT. Instead we find that the slowing down of the dynamics occurs over a range of values of the packing fraction. Consequently, the exponents governing the sequence of time relaxations in the intermediate time regime are given as functions of packing fraction with one additional parameter which describes the overall scale of the metastable potential energy for defects in the hard-sphere system. Implications of the present model on the recent experiments on colloidal systems are also discussed.Comment: 21 pages, 5 figures (available upon request), RevTEX3.0, JFI Preprint

The evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wave length and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wave length with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by X-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.Comment: 50 pages, 17 postscript files including 18 figures, to be published in Phys. Rev.