By molecular-dynamics simulation, we investigate the possible existence of a crumpling transition for a model of tethered membranes, where the particles are tethered by a continuous potential. For distant-neighbor interactions, the potential is repulsive and contains a variable hard-core diameter parameter. By varying this parameter, we are able to study in detail the effect of self-avoidance. Our results suggest the interpretation that self-avoiding two-dimensional tethered membranes are asymptotically flat, even without an explicit bending rigidity, and that there is no crumpling transition except for "phantom" membranes.
Flexible polymerized membranes in a good solvent are expected to exhibit a remarkable low-temperature hat phase, characterized by a diverging bending rigidity, vanishing elastic constants, and large fluctuations both parallel and perpendicular to the surface. A theory of the equilibrium structure factor provides a good fit to extensive molecular dynamics simulations of simplified "tethered surface" models of these materials. These results show how information about the size, thickness, and internal structure of polymerized membranes can be extracted from diffraction experiments.
Fluctuations in polymerized membranes are explored via extensive molecular dynamics simulations of simplified "tethered surface" models. The entropic rigidity associated with repulsive second-nearest-neighbor interactions leads to a flattening of "phantom surfaces". An attractive interaction in the presence of distant self-avoidance leads to a collapsed membrane with fractal dimension three at sufficiently low temperatures. When the attractive interaction is turned off, the surface returns to the flat phase found in earlier simulations. A study of density profiles and hexatic internal order allows a simple physical interpretation of results for the structure function of oriented membranes.
Molecular dynamics simulations of tethered membranes indicate that an attraction between the monomers leads to a well-defined sequence of folding transitions with decreasing temperature. With insights gained from Landau theory and simulations of bimembranes, the folding transitions are found to be intimately linked to the unbinding of membranes. Finite-size effects, mainly due to the loss of entropy from edge fluctuations, play an important role in hindering folding transitions.