Fluid membranes - theory of vesicle conformations

Abstract

The theory of conformations of fluid membranes and vesicles presented in this treatise started from a continuum description based on two relevant degrees of freedom: the local shape, and the local density difference in the two monolayers. Energy minimization, taking into account the geometrical constraints, yields a variety of shapes of various topologies. These shapes are arranged into phase diagrams which separate phases of different symmetry. For vesicles of higher genus, this approach culminates in the prediction of conformal diffusion which amounts to a one-fold continuous degeneracy of the ground state. For bound vesicles and vesicles consisting of two components, an additional energy enters the minimization, which leads to the prediction of a curvature-driven adhesion transition and curvature-induced lateral phase segregation, respectively.