Ordered and curved meso-structures in membranes and amphiphilic films

Abstract

Curvature-induced instabilities in membranes and amphiphilic films are investigated by introducing a general coupling between a shape variable (such as curvature) and «internal» degrees of freedom (such as area per molecule, tilt angle, or local composition). A mean-field treatment of the Ginzburg-Landau free energy expansion shows the existence of various undulated phases (on a mesoscopic scale) that can appear between condensed (solid-like) and dilute (fluid-like) homogeneous phases of the membrane. These undulated phases are characterized by undulations in their local composition as well as in their local curvature. We find two types of undulated phases - stripe and hexagonal — and calculate the phase diagram for the system.