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.

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 mode coupling theory (MCT) of glasses, while offering an incomplete description of glass transition physics, represents the only established route to first-principles prediction of rheological behavior in nonergodic materials such as colloidal glasses. However, the constitutive equations derivable from MCT are somewhat intractable, hindering their practical use and also their interpretation. Here, we present a schematic (single-mode) MCT model which incorporates the tensorial structure of the full theory. Using it, we calculate the dynamic yield surface for a large class of flows.arrest | solidification | plasticity T he 20th Century saw formidable advances in the subject known as theoretical rheology-whose aim is to predict or explain the nonlinear flow behavior of materials. Ideally, for each class of material, one wishes to gain a "constitutive equation" that predicts the stress tensor at time t as a functional of the strain tensor at all earlier times (or vice versa). There are two broad approaches to this task. The more traditional one focuses on symmetry, conservation, and invariance principles (often of some subtlety) and then proposes empirical equations that respect these principles (1). In the second approach, the goal is to start from a first-principles analysis of molecular motion and, then, by judicious (though possibly uncontrolled) approximation, arrive at a continuum-level constitutive model. This is clearly far more ambitious, and success has so far been restricted to relatively few classes of material. Perhaps the most striking success has been the Doi-Edwards theory for solutions and melts of entangled linear polymers (2, 3) [extended later to branched (4) or breakable (5) chains]. In their resting state, such polymers are ergodic and therefore attain the Boltzmann distribution: Moreover their local structure is weakly perturbed from this, even under flow.Glasses at rest, in contrast, are nonergodic on experimental time scales. This poses major obstacles to the rheological theory of glasses and is responsible for aging and other phenomena that have been partially addressed by using mesoscopic models (6). The onset of arrest at the glass transition is, familiarly, accompanied by the onset of an elastic modulus. Window glass is a brittle solid: it deforms elastically for low stresses but shatters under large ones. However, some other glasses-most notably in colloidal suspensions (whose glass transition, for hard spheres, is found experimentally at ≈58% volume fraction) are not brittle solids but show continuous yielding behavior. Although experiments suggest a more complex picture (7,8), the simplest explanation is that, above some yield stress, the glass melts. If a steady stress above the yield level is maintained, the resulting fluid can be expected to attain an ergodic (though non-Boltzmann) steady state.This restoration of ergodicity under steady flow offers one motivation for an approach to glass rheology based on mode-coupling theory (MCT). In particular, it mitigates a well-known sho...