We determined the phase boundaries of aqueous mixtures containing colloidal rod-like fd-viruses and polystyrene spheres using diffusing-wave spectroscopy and compared the results with free volume theory predictions. Excluded volume interactions in mixtures of colloidal rods and spheres lead to mediated depletion interactions. The strength and range of this attractive interaction depend on the concentrations of the particles, the length L and diameter D of the rods and the radius R of the spheres. At strong enough attraction, this depletion interaction leads to phase separation. We experimentally determined the rod and sphere concentrations where these phase transitions occur by systematically varying the size ratios L/R and D/R and the aspect ratio L/D. This was done by using spheres with different radii and modifying the effective diameter of the rods through either the ionic strength of the buffer or anchoring a polymeric brush to the surface of the rods. The observed phase transitions were from a binary fluid to a colloidal gas/liquid phase coexistence which occurred already at very low concentrations due to the depletion efficiency of highly anisotropic rods. The experimentally measured phase transitions were compared to phase boundaries obtained using free volume theory (FVT), a well established theory for calculating the phase behaviour of colloidal particles mixed with depletants. We find good correspondence between the experimental phase transitions and the theoretical FVT model where the excluded volume of the rod-like depletants was explicitly accounted for in both the reservoir and the system.
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In mixtures of colloids and nonadsorbing polyelectrolytes, a Donnan potential arises across the region between surfaces that are depleted of the polyelectrolyte and the rest of the system. This Donnan potential tends to shift the polyelectrolyte density profile toward the colloidal surface and leads to the local accumulation of polyelectrolytes. We derive a zero-field theory for the disjoining pressure between two parallel flat plates. The polyelectrolyte is allowed to enter the confined interplate region at the cost of a conformational free energy penalty. The resulting disjoining pressure shows a crossover to a repulsive regime when the interplate separation gets smaller than the size of the polyelectrolyte chain, followed by an attractive part. We find a quantitative match between the model and self-consistent field computations that take into account the full Poisson–Boltzmann electrostatics.
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