Thermal diffuse x-ray scattering in a model columnar liquid crystal

The fluctuation correlation functions and the density-density correlation functions for a realistic model of a columnar liquid crystal in its helically ordered phase are derived. The influence of positional and orientational molecular fluctuations on the thermal diffuse x-ray scattering is studied within a three-dimensional model of columns inscribed on a triangular lattice. Resulting from quasi-long-range ordering, very anisotropic long-tail scattered intensities are predicted, giving a nonuniversal signature for the helically ordered columnar liquid crystal phase. Scattered intensities both near the Bragg maxima at the inverse lattice vectors and at the Bragg condition due to periodic orientational ordering are treated. The percolation of the long-range behavior for a screw variable composed of two quantities having only quasi-long-range behavior is predicted.