Topology changes in fluid membranes

Abstract

Shape changes of a fluid membrane with fixed area modeled by a curvature Hamiltonian and a boundary line tension are investigated. The zero-temperature energetics are studied using a variational principle in the space of axisymmetric shapes. For zero spontaneous curvature, the only energy minimizing shapes are the disk and the sphere. The energy barrier heights between these configurations are determined as a function of the Hamiltonian parameters. Thermal fluctuations of the shape are studied by means of a Monte Carlo simulation. The "phase transition" from open to closed topology is determined as a function of the rigidity and line tension at nonzero temperature. The transition is found to persist even at zero membrane rigidity. The energetics of the transition are shown to be related to the branched polymer scaling behavior of the fluid membrane.