A splay-twist nematic phase of bent-shaped mesogens

This work investigates the significance of linear terms related to splay, twist and bend deformations in a newly proposed elastic energy density model, to understand spontaneous periodic distortions in nematic liquid crystals. Our analysis reveals that these terms play a crucial role in the emergence of spontaneous deformations. We focus on the simplified case of a nematic sample in slab geometry, where the confining surfaces induce planar orientation with finite anchoring energy. Within this framework, we demonstrate that twist and splay deformations, which depend solely on the distance from the confining surfaces, can occur as long as the elastic constants associated with the linear terms in the spatial derivatives are non-zero. Under appropriate conditions, we show that periodic deformations or modulations involving splay, twist or a combined splay-twist configuration can be stabilised. The sign of the coupling constant between the nematic and torsional fields determines whether the system undergoes a localised deformation close to the surfaces or a bulk modulation. Finally, we determine the stability range for splay, twist or splay-twist modulated nematics.