Many amphiphilic molecules self-assemble into cylindrical tubules, helical ribbons, and other twisted microstructures in solution. Here, we suggest a new mechanism for the formation of these structures based on the flexoelectric effect. The basic physical concept is that whenever there is order in the transverse axis of the molecules, there should be a favored bend in the nematic director. If the molecules are in a membrane, the favored bend should lead to a curvature of the membrane. This is a new mechanism to induce curvature, which is different from the favored twist associated with chirality, or the favored splay (spontaneous curvature) associated with asymmetry between the two sides of the bilayer. We apply this concept to bilayer membranes, using analytic calculations and numerical simulations of a tethered membrane. Our results show that this mechanism leads to both the formation of curved microstructures and a spontaneous chiral symmetry-breaking transition, even if molecular chirality is absent. We also discuss how similar twisted structures can form through quite different symmetry-breaking mechanisms in liquid-crystalline elastomers.
* Work carried out with Zhao Lu, Jawad Naciri, B. R. Ratna, Robin Selinger, Christopher Spillmann, Kenji Urayama, and Fangfu Ye; supported by NSF-DMR-0605889.