Experiments, theory, and simulation were used to study glass formation in a simple model system composed of hard spheres with short-range attraction ("sticky hard spheres"). The experiments, using well-characterized colloids, revealed a reentrant glass transition line. Mode-coupling theory calculations and molecular dynamics simulations suggest that the reentrance is due to the existence of two qualitatively different glassy states: one dominated by repulsion (with structural arrest due to caging) and the other by attraction (with structural arrest due to bonding). This picture is consistent with a study of the particle dynamics in the colloid using dynamic light scattering.Understanding the glass transition is an outstanding challenge for statistical and condensed-matter physics, with relevance throughout materials science as well as biology (1-3). In the multidisciplinary quest for understanding of glasses, the study of simple model systems occupies an important place. One of the simplest models amenable to theoretical study as well as experimentation is a collection of N hard spheres of radius R in volume V at density (volume fraction) ϭ (4/3)R 3 N/V. Although there have been speculations about a hardsphere glass at least since Bernal (4), substantial progress began in the 1980s with modecoupling theory (MCT) calculations (5) and experiments using colloids (6, 7). Further predictions from MCT have been substantially confirmed by colloid experiments and simulations (8), and novel features, such as spatially inhomogeneous particle dynamics, are still being revealed by new experimental probes (9). This close interplay between experiment, theory, and simulation has helped to give hard spheres the status of a reference system.In a system of hard spheres, particles are increasingly caged by their neighbors as increases. At a critical density, g , this caging becomes effectively permanent, stopping all long-range particle motion, and the system can be considered nonergodic, or glassy. MCT captures the essential nonlinear feedback in this mechanism. Each particle is both caged and forms part of the cage of its neighbors. We present a combined experimental, theoretical, and simulational study of how the hard-sphere glass transition is perturbed by a short-range interparticle attraction ("stickiness"). We find that such an attraction first "melts" the hardsphere glass, and then a second, qualitatively different, glassy state is formed (Fig. 1). Sticky hard spheres therefore represent perhaps the simplest system in which multiple glassy states occur.In our experiments, we used sterically stabilized polymethylmethacrylate (PMMA) particles (hard-sphere radius R ϭ 202 nm, polydispersity ϭ 7%) dispersed in cis-decalin. Computer simulations (10) predict that below ϭ 0.494, the lowest free energy state is an ergodic fluid consisting of amorphously arranged particles exploring all available space. For 0.494 Ͻ Ͻ 0.545, fluid and crystal coexist. Above ϭ 0.545, the system should fully crystallize. PMMA colloids follow this predi...

The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third-order bifurcation point, i.e., in a A 3 ͑cusp͒ singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourthorder A 4 ͑swallow-tail͒ singularity at a critical well width. Close to the A 3 and A 4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.

A first principles approach to the nonlinear flow of dense suspensions is presented which captures shear thinning of colloidal fluids and dynamical yielding of colloidal glasses. The advection of density fluctuations plays a central role, suppressing the caging of particles and speeding up structural relaxation. A mode coupling approach is developed to explore these effects.PACS numbers: 82.70. Dd, 83.60.Df, 83.50.Ax, 64.70.Pf, The properties of dispersions under flow are central to their processing and technological use [1,2]. But especially the non-linear rheology is not yet well understood. For the simplest case of steady shearing, the low density behavior is known [3], but upon increasing the density the growing importance of particle interactions requires theoretical approximation [4,5], hinders simulations [6], and calls for studies of model systems, e.g. [7,8]. Of major interest is the arrest of the structural relaxation when approaching solidification for higher densities, which raises the question of how the imposition of steady shearing might interfere with glass formation. The linear phenomenology is familiar: a colloidal fluid possesses a viscosity and flows, while a colloidal glass characterized by elastic constants, only distorts under strain [1,2]. But the nonlinear rheology of glassy colloids, which exhibit a continuous slowing down of the structural relaxation due to particle blocking (the "cage effect") [1], is less clear. While the mode coupling theory (MCT) recovers the linear phenomenology of this fluid-to-glass transition from microscopic starting points [9], a nonlinear external driving introduces new time scales whose influence on (non-)equilibration is not understood, and has been addressed only in minimal models [10] or mean-field approaches [11]. Moreover, as the true nature of the glass is still uncertain, its behavior under shearing may provide broader new insights (as suggested by recent simulation studies [12,13]).Here we develop a first-principles approach for the simplest case of a disordered colloidal suspension under steady imposed shear, neglecting both many-body hydrodynamics and the resulting velocity fluctuations. We first identify some generic features in the yield properties of glass; approximations suggested by the MCT are then introduced in order to derive quantitative predictions.The system consists of N spherical particles (diameter d) dispersed in a volume V of solvent with imposed flow profile v(r) = κ r, where for simple shear with velocity along the x-axis and its gradient along the y-axis, the shear rate tensor is κ ij =γ δ ix δ jy . The effect of the shear rateγ on the particle dynamics is measured by the Peclet number The system is taken to be in quiescent equilibrium (γ = 0) at t ≤ 0 when averages . . . (γ=0) are the canonical equilibrium ones. Then at t = 0 + , the velocity profile is switched on instantaneously, so that the steady state distribution function Ψ s , which satisfies Ω (γ) Ψ s = 0, will be approached at long times, t → ∞. If Ψ s was known the st...

Within the mode-coupling theory ͑MCT͒ for the dynamics of simple liquids, the leading corrections to the asymptotic solutions for the relaxation in the vicinity of an ideal glass transition are derived. The formulas are used to determine the range of validity of the scaling-law description of the MCT results for the ␣ and ␤ processes in glass-forming systems. Solutions of the MCT equations of motion are calculated for a hard-sphere colloidal suspension model and compared with the derived analytical results. The leading-order formulas are shown to describe the major qualitative features of the bifurcation scenario near the transition and the leadingplus-next-to-leading-order formulas are demonstrated to give a quantitative description of the evolution of structural relaxation for the model. ͓S1063-651X͑97͒06005-4͔

The colloidal gel and glass transitions are investigated using the idealized mode coupling theory (MCT) for model systems characterized by short-range attractive interactions. Results are presented for the adhesive hard sphere and hard core attractive Yukawa systems. According to MCT, the former system shows a critical glass transition concentration that increases significantly with introduction of a weak attraction. For the latter attractive Yukawa system, MCT predicts low temperature nonergodic states that extend to the critical and subcritical region. Several features of the MCT nonergodicity transition in this system agree qualitatively with experimental observations on the colloidal gel transition, suggesting that the gel transition is caused by a low temperature extension of the glass transition. The range of the attraction is shown to govern the way the glass transition line traverses the phase diagram relative to the critical point, analogous to findings for the fluid-solid freezing transition.

Abstract. 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.

The nonlinear rheological properties of dense suspensions are discussed within simplified models, suggested by a recent first principles approach to the model of Brownian particles in a constant-velocity-gradient solvent flow. Shear thinning of colloidal fluids and dynamical yielding of colloidal glasses arise from a competition between a slowing down of structural relaxation, because of particle interactions, and enhanced decorrelation of fluctuations, caused by the shear advection of density fluctuations. A mode coupling approach is developed to explore the shear-induced suppression of particle caging and the resulting speed-up of the structural relaxation.

Within 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 ␣-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 ͑1995͔͒. ͓S1063-651X͑98͒09609-3͔