Surface Anchoring and Elastic Properties of Confined Liquid Crystals.

The saddle-splay surface elastic constant, K _{24}, in a nematic liquid crystal material was measured in two independent deuterium nuclear magnetic resonance (^2H-NMR) experiments; this first determination of K_{24} comes fifty years after the pioneering work of Oseen and Zocher. The measurements were possible from observations of nematic director-field configurations and a unique configuration transition in submicrometer-size cylindrical cavities of Nuclepore membranes with various surface treatments and cavity sizes. The inherent difficulties in measuring both the surface elastic constant, K _{24}, and the molecular anchoring strength, W_{o}, were overcome by this unique use of NMR and the ability to predict stable nematic structures with elastic theory. The value of K_{24} compares in magnitude to the splay, twist and bend bulk elastic constants in the compound 4^'-pentyl -4-cyanobiphenyl (5CB-betad _2) at room temperature. Studies of nematic director-fields were extended further to supramicrometer capillary tubes using optical polarizing microscopy where the observed optical birefringence pattern is sensitive to the detailed bulk elastic properties of the nematic material. The bend-to-splay (K_{33 }/K_{11}) elastic constant ratio was estimated accurately by simulating the observed microscope textures. The sensitivity of the ^2H -NMR technique to the molecular ordering in submicrometer cavities of Nuclepore and Anopore membranes facilitates studies of surface induced order in the isotropic phase. The ^2H-NMR spectra reveal for the first time the existence of a weakly orientationally ordered molecular layer at the cavity wall in a 17 K interval above the nematic-isotropic transition. Such a behavior is expected when the ordering mechanisms are non-collective in nature. At elevated temperatures in the isotropic phase the measurements reveal the order of the first molecular layer at the cavity wall, while at temperatures near the isotropic-nematic transition the measurements are primarily sensitive to the order penetrating into the cavity in a manner described by Landau-de Gennes theory. Wide variations in the degree of order at the cavity wall, S_{o} , are possible, depending on the nature of the surface interactions controlled by preparation of the cavity wall. There is particular sensitivity to the dynamics of the first molecular layer where the molecular exchange rate with the bulk is estimated to be ~10 ^3 s^{-1} , substantially reduced from self-diffusion rates in the bulk of the cavity.