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.

Using computer simulations, we identify the mechanisms causing aggregation and structural arrest of colloidal suspensions interacting with a short-ranged attraction at moderate and high densities. Two different nonergodicity transitions are observed. As the density is increased, a glass transition takes place, driven by excluded volume effects. In contrast, at moderate densities, gelation is approached as the strength of the attraction increases. At high density and interaction strength, both transitions merge, and a logarithmic decay in the correlation function is observed. All of these features are correctly predicted by mode coupling theory.

We present a first-principles theory for the active nonlinear microrheology of colloidal model system; for a constant external force on a spherical probe particle embedded in a dense host dispersion, neglecting hydrodynamic interactions, we derive an exact expression for the friction. Within mode-coupling theory, we discuss the threshold external force needed to delocalize the probe from a host glass, and its relation to strong nonlinear velocity-force curves in a host fluid. Experimental microrheology data and simulations, which we performed, are explained with a simplified model.

We analyze the slow glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory (MCT) of the glass transition. Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multicomponent calculation, but qualitative disagreement at small $q$ when the system is treated as effectively monodisperse. The origin of the different small-$q$ behavior is attributed to the interplay between interdiffusion processes and structural relaxation. Numerical solutions of the MCT equations are obtained taking properly binned partial static structure factors from the simulations as input. Accounting for a shift in the critical density, the collective density correlation functions are well described by the theory at all densities investigated in the simulations, with quantitative agreement best around the maxima of the static structure factor and worst around its minima. A parameter-free comparison of the tagged-particle dynamics however reveals large quantitative errors for small wave numbers that are connected to the well-known decoupling of self-diffusion from structural relaxation and to dynamical heterogeneities. While deviations from MCT behavior are clearly seen in the tagged-particle quantities for densities close to and on the liquid side of the MCT glass transition, no such deviations are seen in the collective dynamics.

Computer simulations were used to study the gel transition occurring in colloidal systems with short-range attractions. A colloid-polymer mixture was modeled and the results were compared with mode coupling theory (MCT) expectations and with the results for other systems (hard-spheres system and Lennard-Jones system). The self-intermediate scattering function and the mean squared displacement were used as the main dynamical quantities. Two different colloid packing fractions have been studied. For the lower packing fraction, $\alpha$-scaling holds and the wave-vector analysis of the correlation function shows that gelation is a regular nonergodicity transition within MCT. The leading mechanism for the novel nonergodicity transition is identified as the bond formation caused by the short-range attraction. The time scale and diffusion coefficient also show qualitatively the expected behavior, although different exponents are found for the power-law divergences of these two quantities. The non-Gaussian parameter was also studied and a very large correction to Gaussian behavior was found. The system with higher colloid packing fraction shows indications of a nearby high-order singularity, causing $\alpha$ scaling to fail, but the general expectations for nonergodicity transitions still hold.

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 of 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 stringlike motion is observed for the fast particles, but they occupy preferential sites in the surface of the structure formed by the slow ones.