Distribution functions in three liquid crystals from X-ray diffraction measurements

Abstract

The intensities of X-ray scattering from three compounds has been measured photographically at a number of temperatures. The substances studied were 4,4′di-n-octyloxyazoxybenzene (OOAB) and its di-n-heptyl homologue (HOAB) in their nematic and smectic C phases and ethyl-4-(4′acetoxybenzylidene)aminocinnamate (EABAC) in its nematic and smectic A phases. In all cases except the smectic C phase of HOAB the distribution function f _d(β) describing the orientation of the local director for clusters of ≳ 10 molecules relative to the average director has been determined. The form of f _d(β) is close to that predicted by simple mean field theory although the magnitude of the order parameters ⟨P ₂⟩ in general differ significantly. from the simple mean field values. The results suggest that f _d(β) is close to the true singlet distribution so that the dominant angular fluctuations are co-operative and involve several molecules. For the smectic phases properties of the density wave f(z) which is the smectic layer distribution function have been investigated and, in particular, values of the smectic order parameter τ₁ = ⟨cos 2πz/d⟩ and ⟨z ²⟩^1/2 have been obtained. For EABAC these are compared with recent theoretical predictions.