Shearing a Glassy Material: Numerical Tests of Nonequilibrium Mode-Coupling Approaches and Experimental Proposals

The predictions of a nonequilibrium schematic mode-coupling theory developed to describe the nonlinear rheology of soft glassy materials have been numerically challenged in a sheared binary Lennard-Jones mixture. The theory gives an excellent description of the stress/temperature `jamming phase diagram' of the system. In the present paper, we focus on the issue of an effective temperature Teff for the slow modes of the fluid, as defined from a generalized fluctuation-dissipation theorem. As predicted theoretically, many different observables are found to lead to the same value of Teff, suggesting several experimental procedures to measure Teff. New, simple experimental protocols to access Teff from a generalized equipartition theorem are also proposed, and one such experiment is numerically performed. These results give strong support to the thermodynamic interpretation of Teff and make it experimentally accessible in a very direct way.Comment: Version accepted for publication - Physical Review Letter

Characterizing dynamic length scales in glass-forming liquids

Reply to Comment by Flenner and Szamel on our paper in Nature Physics 8, 164 (2012).Comment: 1 pag

Fluctuation-dissipation relation in a sheared fluid

In a fluid out of equilibrium, the fluctuation dissipation theorem (FDT) is usually violated. Using molecular dynamics simulations, we study in detail the relationship between correlation and response functions in a fluid driven into a stationary non-equilibrium state. Both the high temperature fluid state and the low temperature glassy state are investigated. In the glassy state, the violation of the FDT is quantitatively identical to the one observed previously in an aging system in the absence of external drive. In the fluid state, violations of the FDT appear only when the fluid is driven beyond the linear response regime, and are then similar to those observed in the glassy state. These results are consistent with the picture obtained earlier from theoretical studies of driven mean-field disordered models, confirming the similarity between these models and real glasses.Comment: 4 pages, latex, 3 ps figure

Shear yielding of amorphous glassy solids: Effect of temperature and strain rate

We study shear yielding and steady state flow of glassy materials with molecular dynamics simulations of two standard models: amorphous polymers and bidisperse Lennard-Jones glasses. For a fixed strain rate, the maximum shear yield stress and the steady state flow stress in simple shear both drop linearly with increasing temperature. The dependence on strain rate can be described by a either a logarithm or a power-law added to a constant. In marked contrast to predictions of traditional thermal activation models, the rate dependence is nearly independent of temperature. The relation to more recent models of plastic deformation and glassy rheology is discussed, and the dynamics of particles and stress in small regions is examined in light of these findings

Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations

We study in detail the predictions of various theoretical approaches, in particular mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wavevector dependence of multi-point correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multi-point correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multi-point correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.Comment: 23 pages, 12 fig

Glassy dynamics of partially pinned fluids: an alternative mode-coupling approach

We use a simple mode-coupling approach to investigate glassy dynamics of partially pinned fluid systems. Our approach is different from the mode-coupling theory developed by Krakoviack [Phys. Rev. Lett. 94, 065703 (2005), Phys. Rev. E 84, 050501(R) (2011)]. In contrast to Krakoviack's theory, our approach predicts a random pinning glass transition scenario that is qualitatively the same as the scenario obtained using a mean-field analysis of the spherical p-spin model and a mean-field version of the random first-order transition theory. We use our approach to calculate quantities which are often considered to be indicators of growing dynamic correlations and static point-to-set correlations. We find that the so-called static overlap is dominated by the simple, low pinning fraction contribution. Thus, at least for randomly pinned fluid systems, only a careful quantitative analysis of simulation results can reveal genuine, many-body point-to-set correlations

Slow dynamics of a confined supercooled binary mixture II: Q space analysis

We report the analysis in the wavevector space of the density correlator of a Lennard Jones binary mixture confined in a disordered matrix of soft spheres upon supercooling. In spite of the strong confining medium the behavior of the mixture is consistent with the Mode Coupling Theory predictions for bulk supercooled liquids. The relaxation times extracted from the fit of the density correlator to the stretched exponential function follow a unique power law behavior as a function of wavevector and temperature. The von Schweidler scaling properties are valid for an extended wavevector range around the peak of the structure factor. The parameters extracted in the present work are compared with the bulk values obtained in literature.Comment: 8 pages with 8 figures. RevTeX. Accepted for publication in Phys. Rev.

Static and dynamic properties of a reversible gel

We study a microscopically realistic model of a physical gel and use computer simulations to investigate its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a critical point, a gelation line, and an equilibrium gel phase unrelated to phase separation. The global structure of the gel is homogeneous, but the stress is supported by a fractal network. Gelation results in a dramatic slowing down of the dynamics, which can be used to locate the transition, which otherwise shows no structural signatures. Moreover, the equilibrium gel dynamics is highly heterogeneous as a result of the presence of particle families with different mobilities. An analysis of gel dynamics in terms of mobile and arrested particles allows us to elucidate several differences between the dynamics of equilibrium gels and that of glass-formers.Comment: 9 pages, 7 figures, paper presented at the 10th Granada Seminar on Computational and Statistical Physic

Intermittent origin of the large violations of the fluctuation dissipation relations in an aging polymer glass

The fluctuation-dissipation relation (FDR) is measured on the dielectric properties of a polymer glass (polycarbonate)in the range $20mHz - 100Hz$. It is found that after a quench below the glass transition temperature the fluctuation dissipation theorem is strongly violated. The amplitude and the persistence time of this violation are decreasing functions of frequency. At frequencies larger than 1Hz it persists for about $3h$. The origin of this violation is a highly intermittent dynamics characterized by large fluctuations. The relevance of these results for recent models of aging dynamics are discussed.Comment: to be published in Europhysics Letter

Critical fluctuations and breakdown of Stokes-Einstein relation in the Mode-Coupling Theory of glasses

We argue that the critical dynamical fluctuations predicted by the mode-coupling theory (MCT) of glasses provide a natural mechanism to explain the breakdown of the Stokes-Einstein relation. This breakdown, observed numerically and experimentally in a region where MCT should hold, is one of the major difficulty of the theory, for which we propose a natural resolution based on the recent interpretation of the MCT transition as a bona fide critical point with a diverging length scale. We also show that the upper critical dimension of MCT is d_c=8.Comment: Proceedings of the workshop on non-equilibrium phenomena in supercooled fluids, glasses and amorphous materials (17-22 September, 2006, Pisa