PHYSICAL JOURNAL E Periodic saddle-splay Freedericksz transition in nematic liquid crystals

Abstract. By use of a local stability criterion recently introduced, we predict the existence of a periodic saddle-splay Freedericksz (PSSF) transition that adds to the existing class of classical Freedericksz transi-tions driven in a nematic cell by an external ¯eld. Occurrence of the PSSF transition requires a saddle-splay elastic constant with a large enough magnitude and di®erent anchoring strengths at the plates con¯ning the nematic cell. Otherwise, either the PSSF transition does not occur at all, or it requires a ¯eld higher than that associated with the classical aperiodic splay Freedericksz (ASF) transition, in which case it is not observable. Here, we determine the threshold ¯eld for which the PSSF precedes the ASF transition, as well as the structure of the destabilizing mode. PACS. 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layer-ing, surface-induced ordering, wetting, prewetting transitions, and wetting transitions { 61.30.Dk Contin-uum models and theories of liquid crystal structure