  In columnar assemblies of helical bio-molecules the azimuthal degrees of
freedom, i.e. rotations about the long axes of molecules, may be important in
determining the structure of the assemblies especially when the interaction
energy between neighbouring molecules explicitly depends on their relative
azimuthal orientations. For DNA this leads to a rich variety of mesophases for
columnar assemblies, each categorized by a specific azimuthal ordering. In a
preceding paper [A. Wynveen, D. J. Lee, and A. A. Kornyshev, Eur. Phys. J. E,
16, 303 (2005)] a statistical mechanical theory was developed for the
assemblies of torsionally rigid molecues in order to determine how thermal
fluctuations influence the structure of these mesophases. Here we extend this
theory by including torsional fluctuations of the molecules, where a DNA
molecule may twist about its long axis at the cost of torsional elastic energy.
Comparing this with the previous study, we find that inclusion of torsional
fluctuations further increases the density at which the transition between the
hexagonal structure and the predicted rhombic phase occurs and reduces the
level of distortion in the rhombic phase. As X-ray diffraction may probe the
2-D lattice structure of such assemblies and provide information concerning the
underlying interaction between molecules, we have also calculated correlation
functions for the azimuthal ordering which are manifest in an x-ray scattering
intensity profiles.
