Modulated phases in multicomponent fluid membranes.

We investigate the behavior of flexible two-component bilayer and three-component monolayer membranes. The components are assumed to have different spontaneous curvatures, and to mutually phase separate in planar membranes. As a function of temperature, lateral tension and bending rigidity, a rich phase behavior is obtained. In particular, we find three different types of modulated phases. In symmetric bilayers, the excess component assembles at the boundary between oppositely curved domains; in sufficiently asymmetric bilayers, the excess component is found to preferentially assemble in a single layer, with no tendency for segregation to the domain boundaries. We show that the phase behavior of three-component monolayer strongly resembles the behavior of two-component bilayers. In fact, in a certain, restricted region of parameter space, the two models can be shown to be equivalent.