Direct visualization and measurement of the extrapolation length on cooling toward the nematic-smectic-A phase transition temperature

A herringbone "easy axis" pattern is scribed into a polyimide alignment layer for liquid-crystal orientation using the stylus of an atomic force microscope. Owing to the liquid crystal's bend elasticity K-33, the nematic director is unable to follow the sharp turn in the scribed easy axis, but instead relaxes over an extrapolation length L=K-33/W-2(phi), where W-2(phi) is the quadratic azimuthal anchoring strength coefficient. By immersing a tapered optical fiber into the liquid crystal, illuminating the fiber with polarized light, and scanning the fiber close to the substrate, a visualization and direct measurement of L are obtained on approaching the nematic-smectic-A phase transition temperature T-NA from above. L is found to exhibit a sharp pretransitional increase near T-NA, consistent with a diverging bend elastic constant.