Repulsive surfaces reduce the number of available configurations of long polymers, leading to entropic forces between the polymers and the surfaces. This interaction modifies the monomer density and mean end-to-end distance of the polymer.

Scale-free (SF), or scale-invariant surfaces have no characteristic length scale. We show that when one end of a long ideal polymer is held near a SF surface, its density can be related to the electrostatic potential of a point charge, placed at the point where the polymer end is held, near a conducting surface of the same geometry. The detailed (entropic) pressure distribution of the polymer on the surface can be related to the electric field of the electrostatic problem. We demonstrate the relation for a 2- and 3-dimensional wedge and a 3-dimensional cone. We prove a Gauss-like law that relates the pressure on the surface to the force applied to the end of a polymer.