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 no nzero (and fairly large) K13 term in the elastic free energy of a thin nematic liquid-crystal layer, where K13 is the splay-bend elastic con stant. A sufficiently thin film is predicted to deform spontaneously i n zero applied field, for large enough values of K13. This deformation breaks the mirror symmetry of the film around its midplane and disapp ears at a critical value of the applied field which is a function of s ample thickness. In the particular case where the boundaries favor par allel anchoring, the midplane of the spontaneously deformed layer will contain a nonsingular pi wall. The existence of this anomalous distor tion mode leads to dramatic changes in the topology of the Freedericks z phase diagram: the onset of the Freedericksz transition is predicted to occur at the critical field for infinitely strong anchoring, and t he distorted state eventually becomes unstable with respect to the und istorted configuration as the strength of the applied field is further increased. For small K13 no spontaneously deformed state occurs and t he 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.