Statistical mechanics of inhomogeneous model colloid—polymer mixtures

Abstract

We describe two strategies for tackling the equilibrium statistical mechanics of inhomogeneous colloid—polymer mixtures treated in terms of the simple Asakura—Oosawa—Vrij (AO) model, in which colloid—colloid and colloid—polymer interactions are hard-sphere like, whereas the polymer—polymer interaction is zero (perfectly interpenetrating polymer spheres). The first strategy is based upon integrating out the degrees of freedom of the polymer spheres to obtain an effective one-component Hamiltonian for the colloids. This is particularly effective for small size ratios q = σp/σc < 0.1547, where σp and σc are the diameters of colloid and polymer spheres, respectively, since in this regime three and higher body contributions to the effective Hamiltonian vanish. In the second strategy we employ a geometry based density functional theory (DFT), specifically designed for the AO model but based on Rosenfeld's fundamental measure DFT for additive mixtures of hard-spheres, that treats colloid and polymer on an equal footing and which accounts for the fluid-fluid phase separation occurring for larger values of q. Using the DFT we investigate the properties of the ‘free’ interface between colloid-rich (liquid) and colloid-poor (gas) fluid phases and adsorption phenomena at the interface between the AO mixture and a hard-wall, for a wide range of size ratios. In particular, for q = 0.6 to 1.0, we find rich interfacial phenomena, including oscillatory density profiles at the free interface and novel wetting and layering phase transitions at the hard-wall-colloid gas interface. Where appropriate we compare our DFT results with those from computer simulations and experiment. We outline several very recent extensions of the basic AO model for which geometry based DFTs have also been developed. These include a model in which the effective polymer sphere—polymer sphere interaction is treated as a repulsive step function rather than ideal and one in which the depletant is a fluid of infinitely thin rods (needles) with orientational degrees of freedom rather than (non-interacting) polymer spheres. We comment on the differences between results obtained from these extensions and those of the basic AO model. Whilst the interfacial properties of the AO model share features in common with the those of simple (atomic) fluids, with the polymer reservoir density replacing the inverse temperature, we emphasize that there are important differences which are related to the many-body character of the effective one-component Hamiltonian.