Static periodic distortion above bend Freedericksz transition in nematics

The linearized mathematical model developed by Allender, Hornreich and Johnson [1987, Phys. Rev. Lett., 59, 2654], for explaining the appearance of the magnetic field induced stripe phase (SP) above the bend Freedericksz threshold in a nematic close to the smectic transition, is generalized to the case of uniform tilt θ₁ of the nematic director n₀ away from the homeotropic with the field H acting normal to n₀. Calculations of SP threshold and domain wave vector Q are presented for different elastic ratios and tilts θ₁, by exact computation of the ground state homogeneous deformation (HD) under the rigid anchoring hypothesis. Approximate estimates based on energetics, explicitly taking into account the modal symmetry of perturbations, agree well with the results of exact calculations based on the solution of torque equations. For homeotropic alignment (θ₁ = 0) calculations predict that the SP domain width should decrease when the sample is heated away from the smectic transition point; at a given temperature when H is rotated through a small angle with respect to the sample planes the domains should grow wider. These points can be verified experimentally. It is also shown that for sufficiently high initial tilt θ₁ away from the homeotropic director alignment, SP may be quenched. Materials, such as nematic polymers, which exhibit static periodic domains (PD) in splay geometry (of the kind discovered by Lonberg and Meyer, 1985, Phys. Rev. Lett., 55, 718) may also show SP for director tilts θ₁ close to the homeotropic. It appears possible to make tentative predictions regarding the effects of weak anchoring and oblique magnetic fields on the SP threshold and domain wave vector.