Orientational Ordering of Polymers on a Fluctuating Flexible Surface

Arguments are presented to the effect that embedding semi-flexible (wormlike) ideal polymers into a fluctuating, flexible surface leads to an effective attractive orientational interaction between polymer segments that precipitates an orientational ordering transition of the polymer chains on the surface even in the case of otherwise ideal (non-interacting) chains. The orientational interaction is analogous to the (zero order) Casimir force and is due to the energy change in surface conformational fluctuations in the presence of embedded semi-flexible chains.