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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 ɛ 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.
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