A simple many-body Hamiltonian for polymer-colloid mixtures: simulations and mean-field theory

We investigate depletion interactions between inert hard colloids in the presence of ideal polymers, with a focus on the case where the polymer radius of gyration (R-g) is equal to the radius of the colloids (R-c). We first establish structure and fluid-fluid phase equilibria of this model system as accurately as possible. To achieve this, we replace the ideal polymers by "effective spheres'', using the approach of Bolhuis and Louis [P. Bolhuis and A. A. Louis, Macromolecules, 2002, 35, 1860.] With this approach, we have been able to simulate (approximate) fluid-fluid phase diagrams in dispersions containing relatively long chains, up to 2401-mers (R-g = R-c = 20 bond lengths). We devote some effort to illustrate many-body effects, and demonstrate that, at least relatively close to the respective critical point, there is a much stronger tendency to form clusters in the low density phase when many-body interactions are taken into account. This is primarily due to the repulsive contributions from higher-order interactions in the liquid, enforcing a high critical polymer chemical potential. At such a high chemical potential, there is a significant tendency to form small clusters in the gas phase. The results of these "effective sphere'' simulations are compared with predictions by a polymer+colloid many-body theory that was recently proposed by us. Our results suggest that this theory, even at the mean-field level is surprisingly accurate.