Entropic approach curves of a polymer of fixed topology

We determine how the force needed to place a polymer close to a solid wall varies with the positioning of the chain origin, which is kept pinned. This force is purely entropic in origin as it arises from the loss of available structures close to the wall. We show that with present-day micromanipulation experiments it should be possible to determine whether an initially linear chain forms a loop, e.g. when its ends are rendered sticky, by measuring this entropic force. We discuss the possibility to characterise knot topology via the same procedure.