SURFACELIKE-ELASTICITY-INDUCED SPONTANEOUS TWIST DEFORMATIONS AND LONG-WAVELENGTH STRIPE DOMAINS IN A HYBRID NEMATIC LAYER

We consider the effect of the divergence K24 term del[n(del n) + n X d el X n] in the nematic free energy, which has been ignored for a long time. The K24 term is shown to be able to cause spontaneous twist defo rmations. This mechanism is irrespective of the bulk Frank constant an isotropy in contrast to the well-known mechanism associated with the s mallness of the twist elastic constant K22. For geometries with suffic iently large surface-to-volume ratios, it can also be effective in oth er condensed media described by similar free-energy functionals, but w ith considerably less anisotropic constants than liquid crystals (e.g. , the B phase of liquid He-3 and ferromagnets). As a specific model we consider the formation of long-wavelength stripe domains in a usual b ut rather thin hybrid nematic layer. Degenerate boundary conditions ar e imposed on the surfaces of the latter. Recent experiments show the e xistence of such domains in a hybrid nematic layer whose state had alw ays been regarded as homogeneous in the layer plane. The theory worked out in the paper allows one to incorporate all the harmonics of the p eriodic domain structure in the vicinity of the critical point. The de pendence of the domain period on the layer thickness, obtained in the paper, makes it possible to find the value of the elastic constant K24 from the experimental data.