Figure 3.

Examples of phase diagram showing the formation of curvature induced domains in vesicles. (a) AT high T or low $C_1$ , the liquid phase is homogeneous; numbered regions correspond to modulated phases with the number of the most stable ℓ-mode ( $\ell =1$ to 5 here; $\ell =1$ corresponds to the macrophase separation). The superscript corresponds to the sign of $C_1$ . The bending modulus $\kappa$ does not depend on the order parameter $\varphi$ in the model. In this case, $C_0=\mathsf{\Delta }p=0$ . Adapted from [104]. (b) Sketch of a quasi-spherical vesicle with two different types of lipids inducing either thicker (with a larger bending modulus ${\kappa }_0+{\kappa }_1$ ) or curved patches with a local spontaneous curvature $C_0+C_1$ . (c) Associated phase diagram in the $(C_{1}R,{\kappa }_1/{\kappa }_0)$ plane. The symbols have the same signification as in Figure 2a. (b) and (c) are reproduced from [85], with permission of The European Physical Journal (EPJ), Copyright 2014.