Nuclear spin relaxation in a hexagonal lyotropic liquid crystal

The hexagonal (E) phase in the sodium dodecyl sulphate (SDS)/decanol/water system is investigated by 2H and 23Na nuclear magnetic resonance (NMR) of the selectively deuterated SDS and the sodium counterion. Using macroscopically oriented E phase samples, prepared from the magnetically aligned nematic (NC) phase, we measure the orientation-dependent relaxation rates R1Z and R1Q as well as the line shape of both nuclei. The orientation dependence of the lab-frame spectral densities, determined from the relaxation rates, allow us to separate contributions from different types of molecular motion. In particular, we find a dominant contribution from molecular diffusion around the cylindrical aggregate. From this contribution we determine the lateral diffusion coefficient of SDS to (1.4±0.2)×10−10 m2 s−1 at 25 °C (activation energy 26±2 kJ mol−1 ) and the counterion surface diffusion coefficient to (4.8±0.9)×10−10 m2 s−1 at 25 °C (a factor 2.8 smaller than in an infinitely dilute aqueous electrolyte solution). Furthermore, the flexibility of the cylindrical aggregates in the investigated E phase (aggregate volume fraction 0.27) is quantified in terms of an orientational order parameter SDC≊0.9.