DISTORTIONS INDUCED BY THE K13 SURFACE-LIKE ELASTIC TERM IN A THIN NEMATIC LIQUID-CRYSTAL FILM

We have investigated some of the consequences of the inclusion of a nonzero (and fairly large) K13 term in the elastic free energy of a thin nematic liquid-crystal layer, where K13 is the splay-bend elastic constant. A sufficiently thin film is predicted to deform spontaneously in zero applied field, for large enough values of K13. 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 pi wall. The existence of this anomalous distortion mode leads to dramatic changes in the topology of the Freedericksz phase diagram: the onset of the Freedericksz 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 K13 no spontaneously deformed state occurs and the critical field of the Freedericksz transition is merely found to be shifted from its value for K13 = 0. The possibility of experimentally observing some of these effects is also briefly discussed.