Intrinsic bending force in anisotropic membranes made of chiral molecules

Abstract

A linear term linked to molecular chirality occurs in the bending energy of membranes with ${C}_{2}$ or ${D}_{2}$ symmetry. We find it to alternate in sign, depending on the direction of a cylindrical curvature, and discuss consequences for anisotropic solid membranes, tilted fluid bilayers, and ferroelectric smectic liquid crystals.