The Freezing of Flexible Vesicles of Spherical Topology

Abstract

The freezing transition of tensionless fluctuating vesicles is investigated by Monte Carlo simulations and scaling arguments for a simple tether-and-bead model of fluid membranes. In this model, a freezing transition is induced by reducing the tether length. In the case of planar membranes (with periodic boundary conditions), the model shows a fluid-to-crystalline transition at a tether length 0 ≃ (1.53 ± 0.01)σ 0 , where σ 0 is the bead diameter. For flexible vesicles with bending rigidities 0.85k B T ≤ κ ≤ √κ B T, the reduced free energy of dislocations with Burgers vector (), F dloc /κ, is found to scale for small tether lengths with the scaling variable κ/(K 0 () 2 ), where K 0 is the Young modulus of a crystalline membrane of the same tether length, and () is the average nearest-neighbor distance. This is a strong indication that free dislocations are present, so that the membrane is in a hexatic phase for small tether lengths. A hexatic-to-fluid transition occurs with increasing tether length. With decreasing bending rigidity, this transition moves to smaller tether lengths.