Static and Dynamic Anomalies in a Repulsive Spherical Ramp Liquid: Theory and Simulation

We compare theoretical and simulation results for static and dynamic properties for a model of particles interacting via a spherically symmetric repulsive ramp potential. The model displays anomalies similar to those found in liquid water, namely, expansion upon cooling and an increase of diffusivity upon compression. In particular, we calculate the phase diagram from the simulation and successfully compare it with the phase diagram obtained using the Rogers-Young (RY) closure for the Ornstein-Zernike equation. Both the theoretical and the numerical calculations confirm the presence of a line of isobaric density maxima, and lines of compressibility minima and maxima. Indirect evidence of a liquid-liquid critical point is found. Dynamic properties also show anomalies. Along constant temperature paths, as the density increases, the dynamics alternates several times between slowing down and speeding up, and we associate this behavior with the progressive structuring and de-structuring of the liquid. Finally we confirm that mode coupling theory successfully predicts the non-monotonic behavior of dynamics and the presence of multiple glass phases, providing strong evidence that structure (the only input of mode coupling theory) controls dynamics.Comment: Static and Dynamic Anomalies in a Repulsive Spherical Ramp Liquid: Theory and Simulatio

How does the relaxation of a supercooled liquid depend on its microscopic dynamics?

Using molecular dynamics computer simulations we investigate how the relaxation dynamics of a simple supercooled liquid with Newtonian dynamics differs from the one with a stochastic dynamics. We find that, apart from the early beta-relaxation regime, the two dynamics give rise to the same relaxation behavior. The increase of the relaxation times of the system upon cooling, the details of the alpha-relaxation, as well as the wave vector dependence of the Edwards-Anderson-parameters are independent of the microscopic dynamics.Comment: 6 pages of Latex, 4 figure

Dynamics of supercooled liquids: density fluctuations and Mode Coupling Theory

We write equations of motion for density variables that are equivalent to Newtons equations. We then propose a set of trial equations parameterised by two unknown functions to describe the exact equations. These are chosen to best fit the exact Newtonian equations. Following established ideas, we choose to separate these trial functions into a set representing integrable motions of density waves, and a set containing all effects of non-integrability. It transpires that the static structure factor is fixed by this minimum condition to be the solution of the Yvon-Born-Green (YBG) equation. The residual interactions between density waves are explicitly isolated in their Newtonian representation and expanded by choosing the dominant objects in the phase space of the system, that can be represented by a dissipative term with memory and a random noise. This provides a mapping between deterministic and stochastic dynamics. Imposing the Fluctuation-Dissipation Theorem (FDT) allows us to calculate the memory kernel. We write exactly the expression for it, following two different routes, i.e. using explicitly Newtons equations, or instead, their implicit form, that must be projected onto density pairs, as in the development of the well-established Mode Coupling Theory (MCT). We compare these two ways of proceeding, showing the necessity to enforce a new equation of constraint for the two schemes to be consistent. Thus, while in the first `Newtonian' representation a simple gaussian approximation for the random process leads easily to the Mean Spherical Approximation (MSA) for the statics and to MCT for the dynamics of the system, in the second case higher levels of approximation are required to have a fully consistent theory

Inherent Structures, Configurational Entropy and Slow Glassy Dynamics

We give a short introduction to the inherent structure approach, with particular emphasis on the Stillinger and Weber decomposition, of glassy systems. We present some of the results obtained in the framework of spin-glass models and Lennard-Jones glasses. We discuss how to generalize the standard Stillinger and Weber approach by including the entropy of inherent structures. Finally we discuss why this approach is probably insufficient to describe the behavior of some kinetically constrained models.Comment: 16 pages, 8 figures, Contribution to the ESF SPHINX meeting `Glassy behaviour of kinetically constrained models' (Barcelona, March 22-25, 2001

Dynamical heterogeneities close to a colloidal gel

Dynamical heterogeneities in a colloidal fluid close to gelation are studied by means of computer simulations. A clear distinction between some fast particles and the rest, slow ones, is observed, yielding a picture of the gel composed by two populations with different mobilities. Analyzing the statics and dynamics of both sets of particles, it is shown that the slow particles form a network of stuck particles, whereas the fast ones are able to move over long distances. Correlation functions show that the environment of the fast particles relaxes much faster than that of the slow ones, but at short times the bonds between fast particles are longer lived due to the flexibility of their structure. No string-like motion is observed for the fast particles, but they occupy preferential sites in the surface of the structure formed by the slow ones

Confirmation of Anomalous Dynamical Arrest in attractive colloids: a molecular dynamics study

Previous theoretical, along with early simulation and experimental, studies have indicated that particles with a short-ranged attraction exhibit a range of new dynamical arrest phenomena. These include very pronounced reentrance in the dynamical arrest curve, a logarithmic singularity in the density correlation functions, and the existence of `attractive' and `repulsive' glasses. Here we carry out extensive molecular dynamics calculations on dense systems interacting via a square-well potential. This is one of the simplest systems with the required properties, and may be regarded as canonical for interpreting the phase diagram, and now also the dynamical arrest. We confirm the theoretical predictions for re-entrance, logarithmic singularity, and give the first direct evidence of the coexistence, independent of theory, of the two coexisting glasses. We now regard the previous predictions of these phenomena as having been established.Comment: 15 pages,15 figures; submitted to Phys. Rev.

Fast relaxation in a fragile liquid under pressure

The incoherent dynamic structure factor of ortho-terphenyl has been measured by neutron time-of-flight and backscattering technique in the pressure range from 0.1 MPa to 240 MPa for temperatures between 301 K and 335 K. Tagged-particle correlations in the compressed liquid decay in two steps. The alpha-relaxation lineshape is independent of pressure, and the relaxation time proportional to viscosity. A kink in the amplitude f_Q(P) reveals the onset of beta relaxation. The beta-relaxation regime can be described by the mode-coupling scaling function; amplitudes and time scales allow a consistent determination of the critical pressure P_c(T). alpha and beta relaxation depend in the same way on the thermodynamic state; close to the mode-coupling cross-over, this dependence can be parametrised by an effective coupling Gamma ~ n*T**{-1/4}.Comment: 4 Pages of RevTeX, 4 figures (submitted to Physical Review Letters

Supercooled Water and the Kinetic Glass Transition II: Collective Dynamics

In this article we study in detail the Q-vector dependence of the collective dynamics in simulated deeply supercooled SPC/E water. The evolution of the system has been followed for 250 ns at low T, allowing a clear identification of a two step relaxation process. We present evidence in favor of the use of the mode coupling theory for supercooled liquid as framework for the description of the slow alpha-relaxation dynamics in SPC/E water, notwithstanding the fact that the cage formation in this system is controlled by the formation of an open network of hydrogen bonds as opposed to packing constraints, as in the case of simple liquids.Comment: rev-tex + 9 figure

A mode-coupling theory for the glassy dynamics of a diatomic probe molecule immersed in a simple liquid

Generalizing the mode-coupling theory for ideal liquid-glass transitions, equations of motion are derived for the correlation functions describing the glassy dynamics of a diatomic probe molecule immersed in a simple glass-forming system. The molecule is described in the interaction-site representation and the equations are solved for a dumbbell molecule consisting of two fused hard spheres in a hard-sphere system. The results for the molecule's arrested position in the glass state and the reorientational correlators for angular-momentum index $\ell = 1$ and $\ell = 2$ near the glass transition are compared with those obtained previously within a theory based on a tensor-density description of the molecule in order to demonstrate that the two approaches yield equivalent results. For strongly hindered reorientational motion, the dipole-relaxation spectra for the $\alpha$-process can be mapped on the dielectric-loss spectra of glycerol if a rescaling is performed according to a suggestion by Dixon et al. [Phys. Rev. Lett. {\bf 65}, 1108 (1990)]. It is demonstrated that the glassy dynamics is independent of the molecule's inertia parameters.Comment: 19 pages, 10 figures, Phys. Rev. E, in prin

Asymptotic laws for tagged-particle motion in glassy systems

Within the mode-coupling theory for structural relaxation in simple systems the asymptotic laws and their leading-asymptotic correction formulas are derived for the motion of a tagged particle near a glass-transition singularity. These analytic results are compared with numerical ones of the equations of motion evaluated for a tagged hard sphere moving in a hard-sphere system. It is found that the long-time part of the two-step relaxation process for the mean-squared displacement can be characterized by the $\alpha$-relaxation-scaling law and von Schweidler's power-law decay while the critical-decay regime is dominated by the corrections to the leading power-law behavior. For parameters of interest for the interpretations of experimental data, the corrections to the leading asymptotic laws for the non-Gaussian parameter are found to be so large that the leading asymptotic results are altered qualitatively by the corrections. Results for the non-Gaussian parameter are shown to follow qualitatively the findings reported in the molecular-dynamics-simulations work by Kob and Andersen [Phys. Rev. E 51, 4626 (1995)]