| For two-dimensional geometries, computer simulations on a lattice based on the grand canonical Monte Carlo method, in combination with histogram reweighting and finite-size scaling, are used to determine the phase diagrams of colloid-polymer systems in which the colloids are modeled as hard spheres and the polymers as hard chains, and where an effective attractive interaction arises due to depletion effects. In contrast to the predictions of previous mean-field and other approximate theories, the nature of the coexistence phases is found to depend not solely on the polymer-to-colloid size ratio, but on the colloid diameter, the polymer radius of gyration, and the polymer monomer size. The threshold values of the polymer-to-colloid size ratio for the onset of liquid-liquid phase separation differ significantly from earlier predictions and from those of the corresponding three-dimensional systems. Extrapolation to the "protein limit" of very small colloid and very long polymer indicates that, in contrast to the case of three dimensions, immiscibility does not persist at this limit. The pair correlation functions, both positional and orientational, of the liquid and solid phases are determined experimentally by video microscopy and image analysis for aqueous suspensions of colloids with nonadsorbing polymer. Finally the diffusion of colloids and polymer (bacteriophage lambda-DNA) is studied experimentally by the same technique. The diffusivity of colloids as a function of polymer concentration exhibits a change of slope in the neighborhood of the overlap polymer concentrations.; For systems confined in one-dimensional channels, the colloid pair correlation function is determined experimentally as above. The diffusion of the colloidal particles is obtained by tracking individual colloidal particle and by determining their mean square displacement. For short times, the diffusion is of Brownian motion, Fickian type, with mean square displacement varying linearly with time. For long times, however, the mean square displacement is found to increase more slowly with time than linearly, in agreement with the theoretical prediction that diffusion in one dimension, in which mutual crossing of the particles is not possible, is non-Fickian and the mean square displacement increases as the square root of time. A crossover between short-time and long-time diffusion is observed, and is found to depend on the colloid and polymer concentrations. |
