Anisotropic 23Na spin relaxation in liquid crystals. Determination of all nine spectral densities for a hexagonal lyotropic phase

The orientation dependence of three independent ²³Na relaxation rates is determined from measurements on the counterions in a magnetically aligned hexagonal lyotropic liquid crystal. The data allow us to determine the nine director-frame spectral densities that comprise the full information content of the spin-relaxation behavior of a quadrupolar nucleus in a uniaxial phase. The model-independent director-frame spectral densities provide important information about the time scale and rotational symmetry of the anisotropic motions in the phase. More detailed information is obtained by invoking a specific dynamic model that separates dynamic and structural factors. The six high-frequency spectral densities are quantitatively accounted for in terms of fast local motions and counterion surface diffusion around the cylindrical surfactant aggregates, while the three zero-frequency spectral densities contain large contributions from diffusion-modulated director fluctuations.