J. Phys. I France
Volume 7, Numéro 11, November 1997
Page(s) 1369 - 1390
DOI: 10.1051/jp1:1997136
J. Phys. I France 7 (1997) 1369-1390

The Freezing of Flexible Vesicles of Spherical Topology

G. Gompper1 and D.M. Kroll2

1  Max-Planck-Institut für Kolloid- und Grenzflächenforschung, Kantstrasse 55, 14513 Teltow, Germany
2  Department of Medicinal Chemistry and Minnesota Supercomputer Institute, University of Minnesota, 308 Harvard Street SE, Minneapolis, MN 55455, USA

(Received 20 March 1997, revised 19 June 1997, accepted 23 July 1997)

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 $\ell_0\simeq (1.53\pm 0.01)\sigma_0$, where $\sigma_0$ is the bead diameter. For flexible vesicles with bending rigidities $0.85k_{\rm B}T\leq k\leq \sqrt{3}k_{\rm B}T$, the reduced free energy of dislocations with Burgers vector $\langle\ell\rangle,\,F_{\rm dloc}/k$, is found to scale for small tether lengths with the scaling variable $k/(K_0\langle\ell\rangle^2)$, where K0 is the Young modulus of a crystalline membrane of the same tether length, and $\langle\ell\rangle$ 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.

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