Models of traps and glass phenomenology

Trap models and slow dynamics in supercooled liquids

The predictions of a class of phenomenological trap models of supercooled liquids are tested via computer simulation of a model glass-forming liquid. It is found that a model with a Gaussian distribution of trap energies provides a good description of the landscape dynamics, even at temperatures above T(c), the critical temperature of mode-coupling theory. A scenario is discussed whereby deep traps are composed of collections of inherent structures above T(c) and single inherent structures below T(c). Deviations from the simple Gaussian trap picture are quantified and discussed.

Equivalence of driven and aging fluctuation-dissipation relations in the trap model

We study the nonequilibrium version of the fluctuation-dissipation (FD) relation in the glass phase of a trap model that is driven into a nonequilibrium steady state by external "shear." This extends our recent study of aging FD relations in the same model, where we found limiting, observable independent FD relations for "neutral" observables that are uncorrelated with the system's average energy. In this work, for such neutral observables, we find the FD relation for a stationary weakly driven system to be the same, to within small corrections, as for an infinitely aged system. We analyze the robustness of this correspondence with respect to non-neutrality of the observable, and with respect to changes in the driving mechanism.

Slow relaxation and solvent effects in the collapse of a polymer

Using molecular dynamic simulations we study the quench of a homopolymer chain into a poor solvent at finite temperature. We show that, depending on the quench depth, there are different relaxation pathways to the collapsed state. Solvent effects are introduced through an effective Lennard-Jones potential depending on the local monomer density. The various relaxation regimes are characterized by the contact correlation function. As the quench depth increases, the system evolves towards a glassy state, and the relaxation dynamics continuously changes from an exponential to a stretched exponential law. The characteristic relaxation time diverges at low temperature following an Arrhenius law, like in the case of strong glasses. We found that the stretching exponent depends on aging in a nonuniversal way. The solvent modifies the globular state by diminishing the effects of frustration and glassy behavior.

Rejuvenation and overaging in a colloidal glass under shear

We report the modifications of the microscopic dynamics of a colloidal glass submitted to shear. We use multispeckle diffusing wave spectroscopy to monitor the evolution of the spontaneous slow relaxation processes after the samples have been submitted to various straining. We show that high shear rejuvenates the system and accelerates its dynamics, whereas moderate shear over-ages the system. We analyze these phenomena within the frame of the Bouchaud's trap model.

Interrupted coarsening in a driven kinetically constrained Ising chain

We introduce a driven version of the one-dimensional kinetically constrained spin chain [J. Jackle and S. Eisinger, Zeitschr. Phys. B 84, 115 (1991)]. In its original undriven version, this model shows anomalous coarsening following a quench to a low temperature, with an equilibration time that diverges as approximately exp(1/T(2)) for T-->0. We show that driving of constant rate gamma; interrupts coarsening and stabilizes the chain in a state analogous to that of a coarsening chain of age 1/gamma;. We present an analytical theory for this steady state, and demonstrate it to be in excellent agreement with our simulation results.

Disordered backgammon model

In this paper we consider an exactly solvable model that displays glassy behavior at zero temperature due to entropic barriers. The new ingredient of the model is the existence of different energy scales or modes associated with different relaxational time scales. Low-temperature relaxation takes place by partial equilibration of successive lower-energy modes. An adiabatic scaling solution, defined in terms of a threshold energy scale epsilon*, is proposed. For such a solution, modes with energy epsilon>>epsilon* are equilibrated at the bath temperature, modes with epsilon<<epsilon* remain out of equilibrium, and relaxation occurs in the neighborhood of the threshold epsilon approximately epsilon*. The model is presented as a toy example to investigate the conditions related to the existence of an effective temperature in glassy systems and its possible dependence on the energy sector is probed by the corresponding observable.

Aging in the random energy model

The random energy model (REM) has become a key reference model for glassy systems. In particular, it is expected to provide a prime example of a system whose dynamics shows aging, a universal phenomenon characterizing the dynamics of complex systems. The analysis of its activated dynamics is based on so-called trap models, introduced by Bouchaud, that are also used to mimic the dynamics of more complex disordered systems. In this Letter we report the first results that justify rigorously the trap model predictions in the REM.

Observable dependence of fluctuation-dissipation relations and effective temperatures

We study the nonequilibrium fluctuation-dissipation theorem (FDT) in the glass phase of Bouchaud's trap model. We incorporate an arbitrary observable m and obtain its correlation and response functions in closed form. A limiting nonequilibrium FDT plot is approached at long times for most choices of m. In contrast to standard mean field models, however, the shape of the plot depends nontrivially on the observable, and its slope varies continuously even though there is a single scaling of relaxation times with age. Nonequilibrium FDT plots can therefore not be used to define a meaningful effective temperature T(eff) in this model. Consequences for the wider applicability of an FDT-derived T(eff) are discussed.

Jamming, hysteresis, and oscillation in scalar models for shear thickening

We investigate shear thickening and jamming within the framework of a family of spatially homogeneous, scalar rheological models. These are based on the "soft glassy rheology" model of Sollich et al. [Phys. Rev. Lett. 78, 2020 (1997)], but with an effective temperature x that is a decreasing function of either the global stress sigma or the local strain l. For appropriate x=x(sigma), it is shown that the flow curves include a region of negative slope, around which the stress exhibits hysteresis under a cyclically varying imposed strain rate (.)gamma.A subclass of these x(sigma) have flow curves that touch the (.)gamma=0 axis for a finite range of stresses; imposing a stress from this range jams the system, in the sense that the strain gamma creeps only logarithmically with time t, gamma(t) approximately ln t. These same systems may produce a finite asymptotic yield stress under an imposed strain, in a manner that depends on the entire stress history of the sample, a phenomenon we refer to as history-dependent jamming. In contrast, when x=x(l) the flow curves are always monotonic, but we show that some x(l) generate an oscillatory strain response for a range of steady imposed stresses. Similar spontaneous oscillations are observed in a simplified model with fewer degrees of freedom. We discuss this result in relation to the temporal instabilities observed in rheological experiments and stick-slip behavior found in other contexts, and comment on the possible relationship with "delay differential equations" that are known to produce oscillations and chaos.

Microscopic theory of heterogeneity and nonexponential relaxations in supercooled liquids

Recent experiments show that supercooled liquids around the glass transition temperature are "dynamically heterogeneous" [H. Sillescu, J. Non-Cryst. Solids 243, 81 (1999)]. 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.

Viscous flow and jump dynamics in molecular supercooled liquids. I. Translations

The transport and relaxation properties of a molecular supercooled liquid on an isobar are studied by molecular dynamics. The molecule is a rigid heteronuclear biatomic system. The diffusivity is fitted over four orders of magnitude by the power law D proportional to (T-T(c))(gamma(D)), with gamma(D)=1.93+/-0.02 and T(c)=0.458+/-0.002. The self-part of the intermediate scattering function F(s)(k(max),t) exhibits a steplike behavior at the lowest temperatures. On cooling, the increase of the related relaxation time tau(alpha) tracks the diffusivity, i.e., tau(alpha) proportional to (k(2)(max)D)(-1). At the lowest temperatures, fractions of highly mobile and trapped molecules are also evidenced. Translational jumps are also evidenced. The duration of the jumps exhibits a distribution. The distribution of the waiting times before a jump takes place, psi(t), is exponential at higher temperatures. At lower temperatures a power-law divergence is evidenced at short times, psi(t) proportional to t(xi-1) with 0<xi<or=1, which is ascribed to intermittency. The shear viscosity is fitted by the power law eta proportional to (T-T(c))(gamma(eta)), with gamma(eta)=-2.20+/-0.03 at the lowest temperatures. At higher temperatures the Stokes-Einstein relation fits the data if stick boundary conditions are assumed. The product D eta/T increases at lower temperatures, and the Stokes-Einstein relation breaks down at a temperature which is close to the one where the intermittency is evidenced by psi(t). A precursor effect of the breakdown is observed, which manifests itself as an apparent stick-slip transition.

Viscous flow and jump dynamics in molecular supercooled liquids. II. Rotations

The rotational dynamics of a supercooled model liquid of rigid A-B dumbbells interacting via a Lennard-Jones potential is investigated along one single isobar. The time-temperature superposition principle, one key prediction of mode-coupling theory (MCT), was studied for the orientational correlation functions C(l). In agreement with previous studies we found that the scaling of C(l) in a narrow region at long times is better at high-l values. However, on a wider time interval the scaling works fairly better at low-l values. Consistently, we observed the remarkable temperature dependence of the rotational correlation time tau(1) as a power law in T-T(c) over more than three orders of magnitude and the increasing deviations from that law on increasing l (T(c) is the MCT critical temperature). For 0.7<T<2, good agreement with the diffusion model is found. For lower temperatures the agreement becomes poorer, and the results are also only partially accounted for by the jump-rotation model. The angular Van Hove function shows that in this region a meaningful fraction of the sample reorientates by jumps of about 180 degrees. The distribution of the waiting times in the angular sites cuts exponentially at long times. At lower temperatures it decays at short times as t(xi-1), with xi=0.34+/-0.04 at T=0.5, in analogy with the translational case. The breakdown of the Debye-Stokes-Einstein relation is observed at lower temperatures, where the rotational correlation times diverge more weakly than the viscosity.

Phenomenological glass model for vibratory granular compaction

A model for weakly excited granular media is derived by combining the free volume argument of Nowak et al. [Phys. Rev. E 57, 1971 (1998)] and the phenomenological model for supercooled liquids of Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)]. This is made possible by relating the granular excitation parameter Gamma, defined as the peak acceleration of the driving pulse scaled by gravity, to a temperaturelike parameter eta(Gamma). The resulting master equation is formally identical to that of Bouchaud's trap model for glasses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results are shown to compare favorably with a range of known experimental behavior. This includes the logarithmic densification and power spectrum of fluctuations under constant eta, the annealing curve when eta is varied cyclically in time, and memory effects observed for a discontinuous shift in eta. Finally, we discuss the physical interpretation of the model parameters and suggest further experiments for this class of systems.

Multiple scaling regimes in simple aging models

We investigate aging in glassy systems based on a simple model, where a point in configuration space performs thermally activated jumps between the minima of a random energy landscape. The model allows us to show explicitly a subaging behavior and multiple scaling regimes for the correlation function. Both the exponents characterizing the scaling of the different relaxation times with the waiting time and those characterizing the asymptotic decay of the scaling functions are obtained analytically by invoking a "partial equilibrium" concept.

Ergodicity-breaking transition and high-frequency response in a simple free-energy landscape

We present a simple dynamical model described by a Langevin equation in a piecewise parabolic free-energy landscape, modulated by a temperature-dependent overall curvature. The zero-curvature point marks a transition to a phase with broken ergodicity. The frequency-dependent response near this transition is reminiscent of observations near the glass transition.