Curvature instability of diblock copolymer bilayers

The curvature expansion of the free energy for diblock copolymers aggregated into bilayers is studied for strongly incompatible diblocks. It is shown that sufficient asymmetry in the di block composition leads to an instability of the flat bilayer with respect to spherical or saddle-splay deformations: when the bilayer consists of two (diblock copolymer) monolayers each having a strong tendency to curve convexly toward the solvent, i.e., when the outer block is much larger than the inner block, spherical vesicles become favored by the curvature elastic free energy over flat bilayers. In the opposite case, saddle-splay deformations are favored.