Inhomogeneous model colloid-polymer mixtures: Adsorption at a hard wall - art. no. 041405

We study the equilibrium properties of inhomogeneous model colloid-polymer mixtures. By integrating out the degrees of freedom of the ideal polymer co ils, we derive a formal expression for the effective one-component Hamilton ian of the (hard sphere) colloids that is valid for arbitrary external pote ntials acting on both the colloids and the polymers. We show how one can re cover information about the distribution of polymer in the mixture given kn owledge of the colloid correlation functions calculated using the effective one-component Hamiltonian. This result is then used to furnish the connect ion between the free-volume and perturbation theory approaches to determini ng the bulk phase equilibria. For the special case of a planar hard wall th e effective Hamiltonian takes an explicit form, consisting of zero-, one-, and two-body, but no higher-body, contributions provided the size ratio q=s igma (p)/sigma (c)<0.1547, where <sigma>(c) and sigma (p) denote the diamet ers of colloid and polymer respectively. We employ a simple density functio nal theory to calculate colloid density profiles from this effective Hamilt onian for q=0.1. The resulting profiles are found to agree well with those from Monte Carlo simulations for the same Hamiltonian. Adding very small am ounts of polymer gives rise to strong depletion effects at the hard wall wh ich lead to pronounced enhancement of the colloid density profile (close to the wall) over what is found for hard spheres at a hard wall.