Distortions induced by the K13 surfacelike elastic term in a thin nematic liquid-crystal film.

Abstract

We have investigated some of the consequences of the inclusion of a nonzero (and fairly large) ${\mathit{K}}_{13}$ term in the elastic free energy of a thin nematic liquid-crystal layer, where ${\mathit{K}}_{13}$ is the splay-bend elastic constant. A sufficiently thin film is predicted to deform spontaneously in zero applied field, for large enough values of ${\mathit{K}}_{13}$. This deformation breaks the mirror symmetry of the film around its midplane and disappears at a critical value of the applied field which is a function of sample thickness. In the particular case where the boundaries favor parallel anchoring, the midplane of the spontaneously deformed layer will contain a nonsingular \ensuremath{\pi} wall. The existence of this anomalous distortion mode leads to dramatic changes in the topology of the Fr\'eedericksz phase diagram: the onset of the Fr\'eedericksz transition is predicted to occur at the critical field for infinitely strong anchoring, and the distorted state eventually becomes unstable with respect to the undistorted configuration as the strength of the applied field is further increased. For small ${\mathit{K}}_{13}$ no spontaneously deformed state occurs and the critical field of the Fr\'eedericksz transition is merely found to be shifted from its value for ${\mathit{K}}_{13}$=0. The possibility of experimentally observing some of these effects is also briefly discussed.