Surface elastic and molecular-anchoring properties of nematic liquid crystals confined to cylindrical cavities

The measurement of the saddle-splay surface elastic constant ${\mathit{K}}_{24}$ in a nematic liquid crystal is reported based on two independent deuterium nuclear-magnetic-resonance ${(}^2$H-NMR) experiments. Fifty years after the pioneering work of Oseen and Zocher, these measurements were made from observations of nematic director-field configurations and a configuration transition discovered in submicrometer-sized cylindrical cavities of Nuclepore membranes under selected surface preparations and wall curvatures. The experimental difficulties in separating the effect of anchoring energy from surface elastic energy (inherent in small confining volumes) were overcome by a unique use of NMR and the ability to predict stable nematic structures with elastic theory. Direct comparison of calculated ${}_{}{}^2{}_{}{}^{}\mathrm{NMR}$ spectral patterns to experiment is very sensitive to the details of the stable nematic director-field configuration in cylindrical cavities. Small differences in the director configuration imposed by the curvature or elastic properties of the nematic liquid crystal are strongly reflected in the shape of the spectral pattern. Different nematic structures with preferred perpendicular anchoring conditions such as the escaped radial and planar polar show markedly different patterns. Theoretical analysis reveals that a planar-polar structure is preferred in cavities with a high degree of curvature or sufficiently weak anchoring conditions at the cavity boundary.