Isotropic - Nematic Transition of Surface Embedded Polymers and the Associated Tubulization Transition of the Embedding Surface

Abstract

A self-interacting polymer can undergo an orientational ordering transition, depending on the magnitude of the nematic interaction. The effect of embedding such a polymer into a flexible surface on this transition is studied on the mean-field level. Renormalized values of the elastic constants of the ``dressed'' surface are derived as functions of the orientational order parameter of the polymer chain. In the disordered state the surface tension and curvature modulus remain scalars but depend on the surface coverage of the embedded polymer. In the nematic state there is a symmetry breaking transition leading to anisotropic elastic constants. At a sufficiently large nematic order parameter the effective surface tension in the direction perpendicular to the nematic axis can become negative, leading to tubulization of the embedding surface.