Phase transitions and shapes of two component membranes and vesicles II : weak segregation limit

We investigate equilibrium Shapes of vesicles composed of a mixture of partially miscible amphiphiles embedded in twoand three-dimensional Space. The amphiphilic molecules can diffuse within the membrane and undergo an intramembrane phase separation below a critical temperature. We assume a simple phenomenological coupling between the local relative composition of the amphiphiles and the local curvature of the membrane shape. A linear stability analysis in the vicinity of the critical temperature indicates that a shape instability is induced by the coupling. Using a single mode approximation, we obtained phase diagrams for (I) twodimensional vesicles and (iii three-dimensional axisymmetric vesicles. The equilibrium shape deformations are shown to depend on the phenomenological parameters of our model yielding highly non-trivial vesicle shapes which deviate from spherical-like objects.