Topological instabilities and phase behavior of fluid membranes

A phenomenological model of membrane phase behavior is presented in which the lamellar (${\mathit{L}}_{\mathrm{\alpha }}$) phase is subject to two instabilities, one towards the formation of multiply connected, nearly minimal surfaces, and the other toward the formation of disconnected, nearly spherical surfaces. It is shown that upon dilution, fluctuations generally drive the system through one of these instabilities at a lamellar spacing ${\mathit{d}}_{\mathit{c}}$ less than the persistence length ${\xi }_{\mathrm{\kappa }}$ beyond which they destroy its mean rigidity, resulting when ${\mathit{d}}_{\mathit{c}}$≪${\xi }_{\mathrm{\kappa }}$ in isotropic phases of quasirigid membranes with well-defined preferred topologies.