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The measurement of the saddle-splay surface elastic constant K~4 in a nernatic liquid crystal is reported based on two independent deuterium nuclear-magnetic-resonance ( 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 H-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 rejected 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. The features of the planar-polar structure are described in terms of the dimensionless parameter R 8'0/K, where R is the radius, 8'o is the molecular anchoring strength, and K is the bulk elastic constant in the one-constant approximation. At a sufficiently large radius or substantially strong anchoring conditions, the escaped-radial structure is favored and sensitive to the dimensionless surface parameter O. =R Wo/K+K24/K -1. The H-NMR technique unambiguously distinguishes between these two stable nematic director-field configurations and is sensitive to the surface parameters e and R8'0/K. Theoretical analysis also reveals that the relative magnitude of the bend (K33) and splay (K») bulk elastic constants plays a vital role in determining the molecular anchoring angle at the cavity wall of the escaped-radial configuration. As K33/K» increases, the molecular anchoring angle is shown to deviate further from its preferred perpendicular orientation in the presence of finite molecular anchoring to alleviate the expensive bend deformation. Experimentally, point defects occur in the escapedradial configuration where the direction of bend is changed, resulting is a series of alternating hyperbolic and radial defects. An analytical trial function is constructed that describes these defect structures in the region of interest. PACS number(s): 64.70.Md, 61.30. By, 61.30.Jf, 68.10.Cr I. INTRODUCTION Despite the successful application of elastic theory to uniaxial liquid crystals pioneered by Oseen [l] and Zocher [2] more than 50 years ago, the importance of the surface elastic contributions has...

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