Inelastic X-ray scattering studies of phonons propagating along the axial direction of a DNA molecule having different counter-ion atmosphere

Shear-aligned 40 wt% calf-thymus Na-DNA molecules in aqueous solutions are prepared in their liquid crystalline phases and studied by high resolution inelastic X-ray scattering (IXS). Measured IXS spectra are analyzed with the generalized three effective eignmode (GTEE) theory. The phonon dispersion relations along the axial direction of DNA molecules with different MgCl2 concentrations are constructed and compared. It is found that the sound speed along the axial direction of DNA molecules varies only slightly, but the phonon dampening is greatly affected with the increase amount of MgCl2 concentration. Using the GTEE theory, we are able to extract the longitudinal viscosity in the hydrodynamic limit from the Q-dependence of a fitted parameter. We make a comprehensive review of the GTEE theory and discuss detailed analyses of IXS spectra taking into account finite energy resolution of the instrument.