| In the first half of the thesis, we demonstrate the feasibility and utility of an augmented version of the Gibbs ensemble Monte Carlo (GEMC) method for computing the phase behavior of model colloidal systems with extremely short-ranged attractions as well as with an additional long-ranged repulsion. For generic potential shapes, this approach allows for the investigation of narrower attractive widths than those previously reported. In the purely attractive case, direct comparison to previous self-consistent Ornstein-Zernike approximation (SCOZA) calculations are made. A preliminary investigation of out-of-equilibrium behavior is also performed. The results suggest that the recent observations of stable cluster phases in systems without long-ranged repulsions are intimately related to gas-crystal and metastable gas-liquid phase separation. With the inclusion of an additional long-ranged repulsion, the first quantitative determination of the phase boundaries and microphase ground states in such systems is made. We demonstrate that gelation may occur in such systems as the result of arrested microphase separation.; In the second half of the thesis, we study the formation of dynamical hetero-geneities in two types of system. First, we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems via lattice simulations. We demonstrate that models of glassy behavior without quenched disorder display scalings of the probability of local two-time correlators that are qualitatively similar to that of supercooled liquids. The key ingredient for such scaling properties is shown to be the development of a critical-like dynamical correlation length, and not other microscopic details. We develop a theory to describe both the form and evolution of these distributions based on a effective sigma-model approach. Second, a comparison of measures of dynamical heterogeneity in repulsive and nearly attractive glass formers is made. Slow growing heterogeneities are observed near the attractive glass regime, which also shows a smaller dynamical lengthscale and a greater susceptibility to short-distance processes than in the repulsive glass forming regime. This is consistent with the results from a spin-glass model that shows similar dynamical arrest phenomenology. |
