Phase separation in suspensions of colloids, polymers and nanoparticles : role of solvent quality, physical mesh, and nonlocal entropic repulsion

Abstract

Analytic and numerical microscopic integral equation theory for polymer particle suspensions is employed to investigate the dependence of fluid fluid phase separation on size asymmetry, solvent quality, and higher order polymer polymer interactions. For athermal good solvents, our prior novel prediction of enhanced miscibility with increasing (decreasing) polymer (particle) size is found not to be fundamentally tied to physical mesh formation or strong polymer-induced colloid clustering. Rather, the key is a proper treatment of the polymer second virial coefficient, which is sensitive to how chains organize in the empty space between particles. The origin of the qualitative error made by classic mean-field theories for the shifting of phase boundaries with size asymmetry is established. The phase separation behavior predicted by integral equation theory for ideal polymers is completely different than the athermal case for all size asymmetries and particle volume fractions, thereby establishing the remarkably large consequences of polymer polymer repulsions. For large polymers or small nanoparticles under ideal solvent conditions, the suspension miscibility worsens with increasing size asymmetry, opposite to the athermal solvent behavior. However, over a significant range of intermediate size asymmetries the spinodal curves are either nearly constant, or display a nonmonotonic shifting, as size asymmetry is varied. Higher order contributions in polymer concentration modestly stabilize the miscible phase in both athermal and ideal solvents.