Phase transitions in flexible polymeric surfaces

Abstract

The statistical mechanics of polymerized surfaces with a finite bending rigidity \ensuremath{\kappa}' is studied via the Monte Carlo method. The model system consists of a hexagon, L atoms across, excised from a triangular lattice embedded in three-dimensional space. Nearest-neighbor atoms interact via an infinite-square-well potential, while the bending energy is proportional to the (negative) scalar product of unit normals to adjacent triangles. Self-avoiding interactions are not included. The largest hexagon considered (L=19) consists of 271 atoms. Unlike linear polymers or liquid membranes, these surfaces undergo a remarkable finite-temperature crumpling transition, with a diverging specific heat. For small \ensuremath{\kappa}=\ensuremath{\kappa}'/${k}_{B}$T, the surface is crumpled, and the radius of gyration ${R}_{g}$ grows as \ensuremath{\surd}lnL . For large \ensuremath{\kappa} we find that the surface remains flat, i.e., ${R}_{g}$\ensuremath{\sim}L. Our results demonstrate the presence of a finite-temperature (second-order) crumpling transition, and provide a lower bound on a related transition in real self-avoiding membranes.