Molecular dynamics of tethered membranes

Abstract

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 distantneighbor 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.PACS numbers: 64.60.-i, 82.65.-i In recent years there has been considerable interest in the large-scale properties of random surfaces in the context of both field theory x and condensed-matter theory. 2 Condensed-matter systems in which surfaces and interfaces play a significant role include microemulsions, lipid bilayers, vesicles, and suspensions of monolayers of exfoliated layered crystals. While much of the statistical mechanics of two-dimensional surfaces embedded in a higher-dimensional space remains to be understood, it is known that there is no single universality class which encompasses all such systems. 3 Recently, Kantor, Kardar, and Nelson 4 introduced an interesting model of random surfaces, namely, the tethered membrane. In this model, particles (hard spheres of diameter <r) are joined in a fixed pattern by flexible tethers of length /. For /<(3) 1/2 a, the membrane is self-avoiding in that it cannot intersect itself without the overlap of hard spheres. Without further parameters, the properties of this membrane are temperature independent and determined by the entropy. Kantor, Kardar, and Nelson 4 argued, on the basis of a Flory meanfield theory, that such membranes are crumpled; i.e., the radius of gyration scales as R g~~L v , where L is a characteristic size of the membrane, and the exponent v takes on the value 0.8 for two-dimensional membranes free to move in three-dimensional space. Monte Carlo simulations and renormalization-group arguments 4,5 seemed to support this conclusion.Recently, Plischke and Boal 6 have questioned this result on the basis of larger and more detailed simulations. By examining the shape of tethered self-avoiding membranes they reached the conclusion that these systems are asymptotically flat at large length scales. In particular, they found that the eigenvalues of the inertia tensor have the scaling behavior \\~-L Vl and A, 3~~L v \ where X\ and X3 are the smallest and largest eigenvalues, respectively. The exponents were consistent with the values vi«0.7 and V3« 1.0, corresponding in the limit of large size to a rough but flat object.These results are surprising when taken together with the fact that "phantom" membranes are crumpled 7 and undergo a finite-temperature transition to a flat phase if the membrane has explicit bending rigidity. In a phantom membrane the particles interact only with nearest neighbors on the network, and there is a gre...

Anomalous elasticity, fluctuations and disorder in elastic membranes

“…At first, a high-temperature crumpled phase has only been seen in computer simulations of the so-called "phantom" membranes, in the absence of self-avoiding interaction, with interactions between nearest neighbor monomers only [51,52,54]. The crumpled phase however has subsequently been seen in Monte Carlo simulations of self-avoiding tethered surfaces modeled by impenetrable flexible plaquette.…”

Statistical Mechanics of Thin Spherical Shells

“…The crumpling transition at high temperatures was in fact observed in Monte Carlo simulations of phantom membranes without self-avoidance [61,62]. However, a number of simulations with purely repulsive self-avoiding interactions find that the flat phase persists for arbitrarily high temperatures [63][64][65][66][67]. We note that a pair potential with an attractive as well as a repulsive part can produce a compact phase (D f ¼ 3) at low temperatures, which transitions to a flat phase with D f ¼ 2 at high temperatures [68,69].…”

Anomalous diffusion of a tethered membrane: A Monte Carlo investigation

“…Along with the experimental studies, self-avoiding polymerized membranes have also attracted remarkable interest from the point of view of basic research in recent years. Their static properties have been studied analytically and numerically [7,8,9,10,11,12,13,14,15,16,17,18,19].…”