Critical values of the elastic-constant ratio for the periodic twist-splay distortion in nematic liquid crystals.

Abstract

The occurrence of Fr\'eedericksz transitions giving rise to initially splay-twist distortions is theoretically investigated. We consider an experimental situation where a homogeneous nematic-liquid-crystal layer is placed in crossed electric and magnetic fields, which are orthogonal to the undistorted director. The electric field E and the magnetic field H couple, respectively, with the splay and twist components of the initial distortion. Both fields are destabilizing. Four types of distortions are considered: initially pure splay; pure twist; periodic splay-twist (PST), predominantly splay; and periodic twist-splay (PTS), predominantly twist. It is shown that the occurrence of the various types of deformations depends on the ratio r=${k}_{2}$/${k}_{1}$ between the twist and splay elastic constants and on the field strengths. For fixed H, between zero and the threshold field ${H}_{c2}$ for twist distortion, an increase of E gives rise to a PST transition for r${r}_{c}$(H), and to a splay transition for r>${r}_{c}$(H). A simple analytic expression for ${r}_{c}$(H) in strong-anchoring conditions is given. The limiting values of ${r}_{c}$(H) are 0.303 25. . . for H=0, as already found by F. Lonberg and R. B. Meyer [Phys. Rev. Lett. 55, 718 (1985)], and (1/3 for H=${H}_{c2}$. For r3 similar phenomena occur, involving twist and PTS distortions. In this case the distortions are induced by an increase of H, whereas E plays the role of a control parameter. For r within the interval ((1/3, 3) only aperiodic splay and twist distortions are allowed.