Critical Splay-Bend Deformation of Nematic Films

I n t h i n nemat ic f i lms the d i rec tor field n may on ly depend on z, the n o r m a l to the film p lane. There are two stable conf igurat ions w i t h less than a l l three types of de fo rma t ion present, the pure tw is t and the pure splay-bend. Fo r the pure tw is t under the add i t i ona l in f luence of an ex te rna l field n o r m a l to the tw is t p lane the range of s tab i l i t y is w e l l k n o w n a l ready. For the pu re splaybend the c r i t i c a l equat ion is der ived here under the add i t i ona l in f luence of an ex terna l f ie ld no rma l to the splay-bend p lane. I t comes out as an eigenvalue p rob lem wh i ch can be solved us ing R i tz ' method. N u m e r i c a l solut ions are presented fo r K t = K 3 .