Colloidal glass transition: Beyond mode-coupling theory

A new theory for dynamics of concentrated colloidal suspensions and the colloidal glass transition is proposed. The starting point is the memory function representation of the density correlation function. The memory function can be expressed in terms of a time-dependent pair-density correlation function. An exact, formal equation of motion for this function is derived and a factorization approximation is applied to its evolution operator. In this way a closed set of equations for the density correlation function and the memory function is obtained. The theory predicts an ergodicity breaking transition similar to that predicted by the mode-coupling theory, but at a higher density.Comment: to be published in PR

Mode Coupling relaxation scenario in a confined glass former

Molecular dynamics simulations of a Lennard-Jones binary mixture confined in a disordered array of soft spheres are presented. The single particle dynamical behavior of the glass former is examined upon supercooling. Predictions of mode coupling theory are satisfied by the confined liquid. Estimates of the crossover temperature are obtained by power law fit to the diffusion coefficients and relaxation times of the late $\alpha$ region. The $b$ exponent of the von Schweidler law is also evaluated. Similarly to the bulk, different values of the exponent $\gamma$ are extracted from the power law fit to the diffusion coefficients and relaxation times.Comment: 5 pages, 4 figures, changes in the text, accepted for publication on Europhysics Letter

Vibrational origin of the fast relaxation processes in molecular glass-formers

We study the interaction of the relaxation processes with the density fluctuations by molecular dynamics simulation of a flexible molecule model for o-terphenyl (oTP) in the liquid and supercooled phases. We find evidence, besides the structural relaxation, of a secondary vibrational relaxation whose characteristic time, few ps, is slightly temperature dependent. This i) confirms the result by Monaco et al. [Phys. Rev, E 62, 7595 (2000)] of the vibrational nature of the fast relaxation observed in Brillouin Light Scattering (BLS) experiments in oTP; and ii) poses a caveat on the interpretation of the BLS spectra of molecular systems in terms of a purely center of mass dynamics.Comment: RevTeX, 5 pages, 4 eps figure

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

Structural relaxation in orthoterphenyl: a schematic mode coupling theory model analysis

Depolarized light scattering spectra of orthoterphenyl showing the emergence of the structural relaxation below the oscillatory microscopic excitations are described by solutions of a schematic mode--coupling--theory model

Dynamics in Colloidal Liquids near a Crossing of Glass- and Gel-Transition Lines

Within the mode-coupling theory for ideal glass-transitions, the mean-squared displacement and the correlation function for density fluctuations are evaluated for a colloidal liquid of particles interacting with a square-well potential for states near the crossing of the line for transitions to a gel with the line for transitions to a glass. It is demonstrated how the dynamics is ruled by the interplay of the mechanisms of arrest due to hard-core repulsion and due to attraction-induced bond formation as well as by a nearby higher-order glass-transition singularity. Application of the universal relaxation laws for the slow dynamics near glass-transition singularities explains the qualitative features of the calculated time dependence of the mean-squared displacement, which are in accord with the findings obtained in molecular-dynamics simulation studies by Zaccarelli et. al [Phys. Rev. E 66, 041402 (2002)]. Correlation functions found by photon-correlation spectroscopy in a micellar system by Mallamace et. al [Phys. Rev. Lett. 84, 5431 2000)] can be interpreted qualitatively as a crossover from gel to glass dynamics.Comment: 13 pages, 12 figure

The mean-squared displacement of a molecule moving in a glassy system

The mean-squared displacement (MSD) of a hard sphere and of a dumbbell molecule consisting of two fused hard spheres immersed in a dense hard-sphere system is calculated within the mode-coupling theory for ideal liquid-glass transitions. It is proven that the velocity correlator, which is the second time derivative of the MSD, is the negative of a completely monotone function for times within the structural-relaxation regime. The MSD is found to exhibit a large time interval for structural relaxation prior to the onset of the $\alpha$-process which cannot be described by the asymptotic formulas for the mode-coupling-theory-bifurcation dynamics. The $\alpha$-process for molecules with a large elongation is shown to exhibit an anomalously wide cross-over interval between the end of the von-Schweidler decay and the beginning of normal diffusion. The diffusivity of the molecule is predicted to vary non-monotonically as function of its elongation.Comment: 18 pages, 12 figures, Phys. Rev. E, in prin

Activated events in glasses: the structure of entropic droplets

Using an effective potential approach, we present a replica instanton theory for the dynamics of entropic droplets in glassy systems. Replica symmetry breaking in the droplet interface leads to a length scale dependent reduction of the droplet surface tension and changes the character of the dynamical heterogeneity and activated dynamics in glasses.Comment: 4 pages, 2 figure

Flow curves of colloidal dispersions close to the glass transition: Asymptotic scaling laws in a schematic model of mode coupling theory

The flow curves, viz. the curves of stationary stress under steady shearing, are obtained close to the glass transition in dense colloidal dispersions using asymptotic expansions in a schematic model of mode coupling theory. The shear thinning of the viscosity in fluid states and the yielding of glassy states is discussed. At the transition between fluid and shear-molten glass, simple and generalized Herschel-Bulkley laws are derived with power law exponents that can be computed for different particle interactions from the equilibrium structure factor.Comment: 14 pages, 14 figures, 4 tables, Eur. Phys. J. E (submitted

Memory-Controlled Diffusion

Memory effects require for their incorporation into random-walk models an extension of the conventional equations. The linear Fokker-Planck equation for the probability density $p(\vec r, t)$ is generalized to include non-linear and non-local spatial-temporal memory effects. The realization of the memory kernels are restricted due the conservation of the basic quantity $p$. A general criteria is given for the existence of stationary solutions. In case the memory kernel depends on $p$ polynomially the transport is prevented. Owing to the delay effects a finite amount of particles remains localized and the further transport is terminated. For diffusion with non-linear memory effects we find an exact solution in the long-time limit. Although the mean square displacement shows diffusive behavior, higher order cumulants exhibits differences to diffusion and they depend on the memory strength