Role of molecular structure on X-ray diffraction in uniaxial and biaxial phases of thermotropic liquid crystals

X-ray diffraction is one of the most definitive methods to determine the structure of condensed matter phases, and it has been applied to unequivocally infer the structures of conventional calamitic and lyotropic liquid crystals. With the advent of bent-core and tetrapodic mesogens and the discovery of the biaxial nematic phase in them, the experimental results require more careful interpretation and analysis. Here, we present ab-initio calculations of X-ray diffraction patterns in the isotropic, uniaxial nematic, and biaxial nematic phases of bent-core mesogens. A simple Meier-Saupe-like molecular distribution function is employed to describe both aligned and unaligned mesophases. The distribution function is decomposed into two, polar and azimuthal, distribution functions to calculate the effect of the evolution of uniaxial and biaxial nematic orientational order. The calculations provide satisfactory semiquantitative interpretations of experimental results. The calculations presented here should provide a pathway to more refined and quantitative analysis of X-ray diffraction data from the biaxial nematic phase.