2017/06/25 by Idan Niv, Niv, Idan, Efi Efrati +1 · 2 citations
Engineering · Materials Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Materials and Mechanics #FOS: Physical sciences #Liquid Crystal Research Advancements #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.1706.08187
openalex publication_date 2017/06/25 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The uniform director field obtained for the nematic ground state of the\nhard-rod model of liquid crystals in two dimensions reflects the high symmetry\nof the constituents of the liquid; It is a manifestation of the constituents'\nlocal tendency to avoid splaying and bending with respect to one another. In\ncontrast, bent-core (or banana shaped) liquid-crystal-forming-molecules locally\nfavor a state of zero splay and constant bend. However, such a structure cannot\nbe realized in the plane and the resulting liquid-crystalline phase is\nfrustrated and must exhibit some compromise of these two mutually contradicting\nlocal intrinsic tendencies. The generation of geometric frustration from the\nintrinsic geometry of the constituents of a material is not only natural and\nubiquitous but also leads to a striking variety of morphologies of ground\nstates and exotic response properties.\n In this work we establish the necessary and sufficient conditions for two\nscalar functions, s and b to describe the splay and bend of a director\nfield in the plane. We generalize these compatibility conditions for geometries\nwith non-vanishing constant Gaussian curvature, and provide a reconstruction\nformula for the director field depending only on the splay and bend fields and\ntheir derivatives. Last, we discuss optimal compromises for simple incompatible\ncases where the locally preferred values of the splay and bend cannot be\nglobally achieved.\n