On the spontaneous symmetry breaking in the mesophases of achiral banana-shaped molecules

We propose that the natural tendency of banana-shaped mesogen molecules to induce a local bend of the nematic director can result in pathological elasticity, with negative bend elastic constant. Under this hypothesis, a simple Landau-like phenomenological model predicts a symmetry-breaking transition inside the nematic phase, from uniform textures toward spontaneous periodic distortion, either oscillating splay-bend or conical twist-bend helix. The predicted lower symmetry nematic phases are expected to show interesting polar properties, similar to those already reported for banana-shaped smectogens.