Depletion Force in Polydisperse Systems

Abstract

The entropic depletion force, in colloids, arises when large particles are placed in a solution of smaller ones, and sterically constrained to avoid them. We calculate the interaction between two flat plates or large hard spheres (of radius R) in a solution of small and polydisperse hard spheres (of average diameter $\bar{\sigma} \ll R$) to second order in small sphere concentration. We find that the effect of polydispersity is to generally smoothen out the depletion force while maintaining the recently predicted repulsive barrier; but for high polydispersities, the repulsion could be eventually wiped out.