From Equilibrium to Steady State: The Transient Dynamics of Colloidal Liquids under Shear

We investigate stresses and particle motion during the start up of flow in a colloidal dispersion close to arrest into a glassy state. A combination of molecular dynamics simulation, mode coupling theory and confocal microscopy experiment is used to investigate the origins of the widely observed stress overshoot and (previously not reported) super-diffusive motion in the transient dynamics. A link between the macro-rheological stress versus strain curves and the microscopic particle motion is established. Negative correlations in the transient auto-correlation function of the potential stresses are found responsible for both phenomena, and arise even for homogeneous flows and almost Gaussian particle displacements.Comment: 24 pages, 14 figures, J. Phys.: Condens. Matter, in pres

Tension and stiffness of the hard sphere crystal-fluid interface

A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of 0.66 kT/\sigma^2 with a small anisotropy of about 0.025 kT and stiffnesses with e.g. 0.53 kT/\sigma^2 for the (001) orientation and 1.03 kT/\sigma^2 for the (111) orientation. Here kT is denoting the thermal energy and \sigma the hard sphere diameter. We compare our results with existing experimental findings

Residual Stresses in Glasses

The history dependence of the glasses formed from flow-melted steady states by a sudden cessation of the shear rate $\dot\gamma$ is studied in colloidal suspensions, by molecular dynamics simulations, and mode-coupling theory. In an ideal glass, stresses relax only partially, leaving behind a finite persistent residual stress. For intermediate times, relaxation curves scale as a function of $\dot\gamma t$, even though no flow is present. The macroscopic stress evolution is connected to a length scale of residual liquefaction displayed by microscopic mean-squared displacements. The theory describes this history dependence of glasses sharing the same thermodynamic state variables, but differing static properties.Comment: submitted to Physical Revie

Aging in a simple glassformer

Using molecular dynamics computer simulations we investigate the out-of-equilibrium dynamics of a Lennard-Jones system after a quench from a high temperature to one below the glass transition temperature. By studying the radial distribution function we give evidence that during the aging the system is very close to the critical surface of mode-coupling theory. Furthermore we show that two-time correlation functions show a strong dependence on the waiting time since the quench and that their shape is very different from the one in equilibrium. By investigating the temperature and time dependence of the frequency distribution of the normal modes we show that the energy of the inherent structures can be used to define an effective (time dependent) temperature of the aging system.Comment: Talk presented at ``Unifying Concepts in Glass Physics'', ICTP, Trieste 15 - 18 September 1999; 12 pages of Late

Some Finite Size Effects in Simulations of Glass Dynamics

We present the results of a molecular dynamics computer simulation in which we investigate the dynamics of silica. By considering different system sizes, we show that in simulations of the dynamics of this strong glass former surprisingly large finite size effects are present. In particular we demonstrate that the relaxation times of the incoherent intermediate scattering function and the time dependence of the mean squared displacement are affected by such finite size effects. By compressing the system to high densities, we transform it to a fragile glass former and find that for that system these types of finite size effects are much weaker.Comment: 12 pages of RevTex, 4 postscript figures available from W. Ko

Static and Dynamic Properties of a Viscous Silica Melt Molecular Dynamics Computer Simulations

We present the results of a large scale molecular dynamics computer simulation in which we investigated the static and dynamic properties of a silica melt in the temperature range in which the viscosity of the system changes from O(10^-2) Poise to O(10^2) Poise. We show that even at temperatures as high as 4000 K the structure of this system is very similar to the random tetrahedral network found in silica at lower temperatures. The temperature dependence of the concentration of the defects in this network shows an Arrhenius law. From the partial structure factors we calculate the neutron scattering function and find that it agrees very well with experimental neutron scattering data. At low temperatures the temperature dependence of the diffusion constants $D$ shows an Arrhenius law with activation energies which are in very good agreement with the experimental values. With increasing temperature we find that this dependence shows a cross-over to one which can be described well by a power-law, D\propto (T-T_c)^gamma. The critical temperature T_c is 3330 K and the exponent gamma is close to 2.1. Since we find a similar cross-over in the viscosity we have evidence that the relaxation dynamics of the system changes from a flow-like motion of the particles, as described by the ideal version of mode-coupling theory, to a hopping like motion. We show that such a change of the transport mechanism is also observed in the product of the diffusion constant and the life time of a Si-O bond, or the space and time dependence of the van Hove correlation functions.Comment: 30 pages of Latex, 14 figure

Computer Simulations of Supercooled Liquids and Glasses

After a brief introduction to the dynamics of supercooled liquids, we discuss some of the advantages and drawbacks of computer simulations of such systems. Subsequently we present the results of computer simulations in which the dynamics of a fragile glass former, a binary Lennard-Jones system, is compared to the one of a strong glass former, SiO_2. This comparison gives evidence that the reason for the different temperature dependence of these two types of glass formers lies in the transport mechanism for the particles in the vicinity of T_c, the critical temperature of mode-coupling theory. Whereas the one of the fragile glass former is described very well by the ideal version of mode-coupling theory, the one for the strong glass former is dominated by activated processes. In the last part of the article we review some simulations of glass formers in which the dynamics below the glass transition temperature was investigated. We show that such simulations might help to establish a connection between systems with self generated disorder (e.g. structural glasses) and quenched disorder (e.g. spin glasses).Comment: 37 pages of Latex, 11 figures, to appear as a Topical Review article in J. Phys.: Condens. Matte

Quantum correction to the Kubo formula in closed mesoscopic systems

We study the energy dissipation rate in a mesoscopic system described by the parametrically-driven random-matrix Hamiltonian H[\phi(t)] for the case of linear bias \phi=vt. Evolution of the field \phi(t) causes interlevel transitions leading to energy pumping, and also smears the discrete spectrum of the Hamiltonian. For sufficiently fast perturbation this smearing exceeds the mean level spacing and the dissipation rate is given by the Kubo formula. We calculate the quantum correction to the Kubo result that reveals the original discreteness of the energy spectrum. The first correction to the system viscosity scales proportional to v^{-2/3} in the orthogonal case and vanishes in the unitary case.Comment: 4 pages, 3 eps figures, REVTeX

Apparent finite-size effects in the dynamics of supercooled liquids

Molecular dynamics simulations are performed for a supercooled simple liquid with changing the system size from N=108 to $10^4$ to examine possible finite-size effects. Although almost no systematic deviation is detected in the static pair correlation functions, it is demonstrated that the structural $\alpha$ relaxation in a small system becomes considerably slower than that in larger systems for temperatures below $T_c$ at which the size of the cooperative particle motions becomes comparable to the unit cell length of the small system. The discrepancy increases with decreasing temperature.Comment: 4 pages 5 figure

Complex lithium ion dynamics in simulated LiPO3 glass studied by means of multi-time correlation functions

Molecular dynamics simulations are performed to study the lithium jumps in LiPO3 glass. In particular, we calculate higher-order correlation functions that probe the positions of single lithium ions at several times. Three-time correlation functions show that the non-exponential relaxation of the lithium ions results from both correlated back-and-forth jumps and the existence of dynamical heterogeneities, i.e., the presence of a broad distribution of jump rates. A quantitative analysis yields that the contribution of the dynamical heterogeneities to the non-exponential depopulation of the lithium sites increases upon cooling. Further, correlated back-and-forth jumps between neighboring sites are observed for the fast ions of the distribution, but not for the slow ions and, hence, the back-jump probability depends on the dynamical state. Four-time correlation functions indicate that an exchange between fast and slow ions takes place on the timescale of the jumps themselves, i.e., the dynamical heterogeneities are short-lived. Hence, sites featuring fast and slow lithium dynamics, respectively, are intimately mixed. In addition, a backward correlation beyond the first neighbor shell for highly mobile ions and the presence of long-range dynamical heterogeneities suggest that fast ion migration occurs along preferential pathways in the glassy matrix. In the melt, we find no evidence for correlated back-and-forth motions and dynamical heterogeneities on the length scale of the next-neighbor distance.Comment: 12 pages, 13 figure