SPONGES, TUBULES AND MODULATED PHASES OF PARA-ANTINEMATIC MEMBRANES

We theoretically analyze the behavior of membranes presenting a nemati c susceptibility, induced by the presence of anisotropic phospholipids having a quadrupolar nematic symmetry. This kind of anisotropic phosp holipids is either naturally found in some biological membranes, or ca n be chemically tailored by linking pairs of single surfactants at the level of their polar heads, giving rise to so-called ''gemini'' surfa ctants. We predict that such membranes can acquire a non-zero paranema tic order induced by the membrane curvature, which in turn produces cu rvature instabilities. We call the resulting paranematic order para-an tinematic, since it is opposite on opposite sides of the membrane. We find phase transitions toward sponges (L-3), tubules, or modulated ''e gg-carton'' phases.