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

TL;DR

This paper investigates how embedding a self-interacting polymer into a flexible surface influences its nematic transition and can induce a tubulization transition of the surface, with implications for surface elasticity and morphology.

Contribution

It provides a mean-field analysis of the nematic transition of surface-embedded polymers and derives how this affects the elastic properties and morphology of the surface.

Findings

Surface tension and curvature modulus depend on polymer coverage in the disordered state.

Nematic ordering induces anisotropic elastic constants and symmetry breaking.

High nematic order can cause the surface to tubulize due to negative perpendicular surface tension.

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.