Polymer-mediated entropic forces between scale-free objects

The number of configurations of a polymer is reduced in the presence of a
barrier or an obstacle. The resulting loss of entropy adds a repulsive
component to other forces generated by interaction potentials. When the
obstructions are scale invariant shapes (such as cones, wedges, lines or
planes) the only relevant length scales are the polymer size R_0 and
characteristic separations, severely constraining the functional form of
entropic forces. Specifically, we consider a polymer (single strand or star)
attached to the tip of a cone, at a separation h from a surface (or another
cone). At close proximity, such that h<