Dynamics, vitrification, and gelation of colloidal mixtures

Naive mode coupling theory (NMCT) and the nonlinear stochastic Langevin equation (NLE) theory of activated dynamics have been generalized to biphasic mixtures of spherical particles. The NMCT transition signals a dynamical crossover to activated barrier hopping dynamics. For binary mixtures of equal diameter hard and attractive spheres, a mixture composition sensitive "glass-melting" type of phenomenon is predicted at high total packing fractions and weak attractions. As the total packing fraction decreases, a transition to partial localization occurs corresponding to the coexistence of a tightly localized sticky species in a gel-like state with a fluid of hard spheres. Complex behavior of the localization lengths and shear moduli exist because of the competition between excluded volume caging forces and attraction-induced physical bond formation between sticky particles.;The coupled activated dynamics in dense mixtures of repulsive and sticky hard spheres also has been studied using NLE theory. The effective free energy surface, barriers, saddle point trajectories, and mean first passage times depend in a rich manner on mixture composition, (high) total volume fraction, and attractive particle interaction strength. The mean first passage, or hopping, times are computed using multidimensional Kramers theory. In most cases, the hopping time trends reflect the behavior of the barrier height, especially as the sticky particle attraction strengths become large. However, there are dramatic exceptions associated with cooperative repulsive and attractive particle trajectories where the barriers are high but a greatly enhanced number of such trajectories near the saddle point exist.;An ideal kinetic arrest diagram has also been determined in the tracer particle limit and predicts increasing matrix attractions enhances matrix particle clustering, which induces extra free volume for tracer motion and shifts the onset of tracer localization to higher volume fractions. The barriers for transport and mean first passage, or hopping, times are rich functions of matrix attraction strength and volume fraction. An excellent zeroth order collapse of the dependence of these quantities on the latter two variables is obtained based on the mean-square force exerted on the tracer by the matrix.;A Brownian simulation solution of the stochastic NLE has been used to study repulsive particle dynamics in biphasic mixtures with large dynamical asymmetry. Quantities such as the mean square displacement, the non-Gaussian parameter, the incoherent dynamic structure factor, and displacement distributions (van Hove function) are examined.