Entropic depletion in colloidal suspensions and polymer liquids: role of nanoparticle surface topography

We employ a hybrid Monte Carlo plus integral equation theory approach to study how dense fluids of small nanoparticles or polymer chains mediate entropic depletion interactions between topographically rough particles where all interaction potentials are hard core repulsion. The corrugated particle surfaces are composed of densely packed beads which present variable degrees of controlled topographic roughness and free volume associated with their geometric crevices. This pure entropy problem is characterized by competing ideal translational and (favorable and unfavorable) excess entropic contributions. Surface roughness generically reduces particle depletion aggregation relative to the smooth hard sphere case. However, the competition between ideal and excess packing entropy effects in the bulk, near the particle surface and in the crevices, results in a non-monotonic variation of the particle-monomer packing correlation function as a function of the two dimensionless length scale ratios that quantify the effective surface roughness. As a result, the inter-particle potential of mean force (PMF), second virial coefficient, and spinodal miscibility volume fraction vary non-monotonically with the surface bead to monomer diameter and particle core to surface bead diameter ratios. A miscibility window is predicted corresponding to an optimum degree of surface roughness that completely destroys depletion attraction resulting in a repulsive PMF. Variation of the (dense) matrix packing fraction can enhance or suppress particle miscibility depending upon the amount of surface roughness. Connecting the monomers into polymer chains destabilizes the system via enhanced contact depletion attraction, but the non-monotonic variations with surface roughness metrics persist.