Orientational ordering in liquid crystals: isotope labelling neutron diffraction experiments

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Abstract
Orientational order parameters for nematogens have been determined using the neutron diffraction isotope labelling technique, where the single molecule component of the scattering from mixtures of protonated and perdeuteriated molecules is extracted at low Q. Experiments were performed on the relatively rigid nematogens 4-methoxy-4′-cyanobiphenyl (1-OCB) and 4,4′-dimethoxyazoxybenzene (PAA). Legendre polynomial orientational order parameters -PL were extracted from the anisotropy of the single molecule scattering, without assumptions regarding the form of the singlet orientational distribution function. Only knowledge of a molecular structure is required. For these molecules, values of ¯P 2 in good agreement with nuclear magnetic resonance (NMR) studies were obtained. ¯P 4 can also be determined and for 1-OCB it is found to be near zero, in accord with earlier Raman spectroscopy results for other cyanobiphenyl liquid crystals. Given order parameters as input constraints, the maximum entropy method is used to construct singlet orientational distribution functions to provide a visualisation of the significance of particular combinations of order parameters. The form of these functions is found to be very sensitive to the number and magnitudes of the constraints. The results of Richardson, Allman and McIntyre (1990, Liq. Cryst. 7, 701) on the ordering of 4-n-pentyloxybenzylidene-4′-n-heptylaniline (5O.7) in nematic and smectic B phases are reanalysed to investigate the validity of their approach in which they use models for scattering from uniform cylinders with assumed orientational distribution functions. For 5O.7 order parameters up to ¯P 8 were obtained; however the values of ¯P 2 and ¯P 4 are not in good agreement with previous NMR and Raman experiments. It is believed that an imperfect monodomain of the smectic B phase resulted in apparently reduced orientational ordering. Our results are comparable to those obtained by Richardson et al. for the nematic phase, but significant differences are found for the smectic B phase.