Orientational order, topology, and vesicle shapes

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Abstract
While ideal fluid membranes are characterized solely by curvature elasticity, many structural (‘‘external’’) properties of real membranes are strongly influenced by internal degrees of freedom. Here, we consider, within mean-field theory, the effect of in-plane vector order (such as the molecular tilt in surfactant bilayers) on the shapes of closed vesicles with the topology of a sphere. We find that coupling between in-plane order and Gaussian curvature causes continuous shape changes from spherical to cylindrical vesicles as the degree of in-plane order increases.