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

Abstract

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.