Periodic splay-twist Fréedericksz transition for nematics confined between two concentric cylinders

This paper derives theoretical results for the periodic splay-twist Fréedericksz transition in nematic liquid crystals confined between two infinite concentric cylinders. The calculation of Lonberg and Meyer [Phys. Rev. Lett. 55, 718 (1985)], for nematics sandwiched between two infinite planes, is extended to annular domains. The phase transition is triggered by an applied voltage between the outer and the inner delimiting walls. The critical threshold behavior is analyzed via the linearized Euler-Lagrange equations related to the Frank's free energy. It is found that, the threshold depends on both the ratio between the twist and the splay elastic constants, and the sample radii ratio. Results for planar samples are recovered in the thin cell limit. With respect to the planar geometry, our analysis predicts that for annular geometries the periodic Fréedericksz transition is also allowed for elastic anisotropies K2/K1>0.303.