Smectic layering at the free surface of liquid crystals in the nematic phase: X-ray reflectivity

Smectic layering at the surface and smectic fluctuations in the bulk can be studied simultaneously by x-ray specular reflectivity and scattering measurements. There is a peak in the angular dependence of the specular reflectivity due to surface-induced smectic layering that penetrates into the bulk as exp(-z/${\xi }_{?}$) where ${\xi }_{?}$ is one of the nematic critical correlation lengths. This is illustrated by measurements of the liquid-crystal materials octyloxycyanobiphenyl (8OCB) and butyloxybenzyl- idene octylaniline (4O.8). In both cases the critical divergence of the intensity of the peak in the specular reflectivity is weaker than ${\xi }_{?}^2$, suggesting unexpected surface physics. The absolute value of the critical part of the density pair correlation function is determined by comparison to the Fresnel reflected intensity. Different geometries of the x-ray spectrometer are also discussed.