Universal density-force relations for polymers near a repulsive wall

The relation between the force exerted-by long flexible polymer chains on a repulsive wall and the corresponding monomer density close to the wall is shown to imply a universal amplitude ratio. This is calculated in an epsilon expansion, and its importance in various situations is pointed out. These include a single polymer trapped between two parallel walls and a solution of polymers inducing a depletion interaction between the wall and a mesoscopic particle. Dilute and semidilute solutions in the half space are also considered.