Microscopic theory of polymer-mediated interactions between spherical particles

We develop an analytic integral equation theory for treating polymer-induced effects on the structure and thermodynamics of dilute suspensions of hard spheres. Results are presented for the potential of mean force, free energy of insertion per particle into a polymer solution, and the second virial coefficient between spheres. The theory makes predictions for all size ratios between the spheres and the polymer coil dimension. Based on the Percus–Yevick (PY) closure, the attractive polymer-induced depletion interaction is predicted to be too weak under athermal conditions to induce a negative value for the second virial coefficient, $B_2^{\mathrm{cc}},$ between spheres in the colloidal limit when the spheres are much larger than the coil size. A nonmonotonic dependence of the second virial coefficient on polymer concentration occurs for small enough particles, with the largest polymer-mediated attractions and most negative $B_2^{\mathrm{cc}}$ occurring near the dilute–semidilute crossover concentration. Predictions for the polymer-mediated force between spheres are compared to the results of computer simulations and scaling theory.