Theoretical Study of Fluid Membranes of Spherical Topology with Internal Degrees of Freedom

Abstract

A theoretical study of vesicles of topological genus zero is presented. The bilayer membranes forming the vesicles have various degrees of intrinsic (tangent-plane) orientational order, ranging from smectic to hexatic, frustrated by curvature and topology. The field-theoretical model for these `$n$-atic' surfaces has been studied before in the low temperature (mean-field) limit. Work presented here includes the effects of thermal fluctuations. Using the lowest Landau level approximation, the coupling between order and shape is cast in a simple form, facilitating insights into the behaviour of vesicles. The order parameter contains vortices, whose effective interaction potential is found, and renormalized by membrane fluctuations. The shape of the phase space has a counter-intuitive influence on this potential. A criterion is established whereby a vesicle of finite rigidity may be burst by its own in-plane order, and an analogy is drawn with flux exclusion from a type-I superconductor.