![FIG. 21 Schematic phase diagram for the vesicle unbinding transition (thick solid lines and thick dashed line) as calculated by Seifert and Lipowsky [47, 48] as a function of the reduced volume, v, and reduced substrate adhesion energy, w. In the solid region, nonaxisymmetric vesicle shapes are relevant. The solid lines are shape transitions of the vesicle within the bound or unbound region. (See Ref. 48 for further details.)](https://images.tandf.co.uk/common/jackets/crclarge/978036739/9780367394493.jpg "FIG. 21 Schematic phase diagram for the vesicle unbinding transition (thick solid lines and thick dashed line) as calculated by Seifert and Lipowsky [47, 48] as a function of the reduced volume, v, and reduced substrate adhesion energy, w. In the solid region, nonaxisymmetric vesicle shapes are relevant. The solid lines are shape transitions of the vesicle within the bound or unbound region. (See Ref. 48 for further details.)")
ABSTRACT
In the absence of bending rigidity, the minimization of the free energy is done in two steps. First, we note that when k=0 the solution of the shape equation in Eq. (49) is that of a spherical cap (see inset, Fig. 22). We know this to be the case when also k/R0 is taken to be zero so that the shape equation reduces to the well-known Laplace equation, but also with the spontaneous radius of curvature term present, the shape is that of a spherical cap. Second, we insert the spherical-cap profile, which is fully described by the radius R and contact angle θ, into the expression for the free energy, and then minimize with respect to R and θ.
