Abstract
We study the effects of the saddle-splay constant K24 on the periodic splay-twist Fréedericksz transition in nematic liquid crystals. The nematic is confined between two parallel infinite plates with weak planar anchoring boundary conditions. The transition is triggered by a uniform magnetic field orthogonal to the delimiting plates. The analysis, performed within the framework of the Oseen-Zocher-Frank theory, reveals that the periodic splay-twist Fréedericksz transition occurs only for a ratio between the twist and the splay constant ϱ below a critical value ϱc. The critical threshold ϱc depends in turn on the anchoring strength and on the saddle-splay constant. In particular, we prove that the influence of K24 on the stripe thickness becomes very important whenever ϱ is just below ϱc. The adjustability of ϱc through surface treatments furnishes a useful method to measure K24 by using the periodic Fréedericksz transition.