Bilayer membranes with 2D-nematic order of the surfactant polar heads

In this paper we review and discuss the possibility of having a 2D-nematic ordering of the surfactant polar heads in bilayer membranes. The coupling b etween the nematic order parameters and the curvature call yield instabilit ies in the shape of the membrane, generally leading to tubules with mesosco pic radiuses. The nematic directors in the two monolayers should present co upled disclinations with peculiar characteristics. Para-nematic membranes, i.e., nematic membranes that are in the isotropic phase when flat, should b ehave as the nematic membranes in the curved state.