Considerations in the determination of orientational order parameters from X-ray scattering experiments

An assessment of the data processing and analysis methods used to obtain the second- and fourth-rank orientational order parameters of liquid crystals from X-ray scattering experiments has been carried out, using experimental data from four extensively studied alkyl-cyanobiphenyls and calculated data generated from two general types of theoretical orientational distribution function. The application of a background subtraction and two different baseline correction methods to the scattering profiles is assessed, along with three different methods to analyse the processed data. The choice of baseline correction method is shown to have a significant effect: an offset to zero overestimates the order parameters from the experimental and calculated data sets, particularly for lower order parameters arising from broad distributions, whereas an offset to a value estimated from regions of low scattering intensity provides experimental values close to those reported from other experimental techniques. By contrast, the three different analysis methods are shown generally to result in relatively small absolute differences between the order parameters. We outline a straightforward general approach to experimental X-ray scattering data processing and analysis for uniaxial phases that results in order parameters that match well with those reported using other experimental techniques.