Forces between surfaces with weakly end-adsorbed polymers

We study the interaction forces between two plates in a semi-dilute solution of polymers each having one weakly adsorbing end-group. We show that this system exhibits both repulsive and attractive interactions of comparable magnitude and well-separated length scales: when the plate separation is within a range of order the end-to-end distance of the end-adsorbed polymer, repulsion arises with a magnitude of ε_Na3^Φ where e is the end-adsorption energy, N is the degree of polymerization, a is the Kühn length and Φ the volume fraction of the polymer. This repulsion is due to desorption of the end-adsorbed chains. At plate separations of order the correlation length of the solution, a depletion attraction sets in with a magnitude that scales with the bulk osmotic pressure.