Nuclear Magnetic Resonance Studies of Bicontinuous Liquid Crystalline Phases of Cubic Symmetry: Transport Properties from ²H Nuclear Magnetic Resonance Relaxation Rates

Abstract

The ternary system didodecyltrimethylammonium bromide, 1-decanol, and water forms an extended reversed continuous phase of cubic symmetry at 25 °C. The cubic phase belongs to the space group Im3m, as shown by small-angle X-ray experiments. We present extensive deuterium NMR relaxation data from this cubic phase for 1-decanol, deuterated at the carbon adjacent to the hydroxyl carbon position. 2H spin-lattice (R 1) and spin–spin (R 2) relaxation rates were measured over the existence region of the cubic phase, which extends from 0.2 to 0.6 in volume fraction of the dividing bilayer surface of the cubic phase. The data are interpreted with an existing theoretical framework for NMR spin relaxation in bicontinuous cubic phases, which takes its starting point in the description of bicontinuous phases using periodic minimal surfaces. Specifically, we obtain the self-diffusion coefficient over the minimal surface in one unit cell for 1-decanol. We also present pulsed field gradient NMR-derived self-diffusion data for didodecyltrimethylammonium bromide and compare the two sets of data. The diffusion data for both components show a mild, if any, dependence on the volume fraction of the bilayer surface. Furthermore, we present diffusion data for the water component in the cubic phase. Finally, we discuss the influences of the choice of the value of the product of the deuterium quadrupole constant and the order parameter S. Within the framework of the model used to analyze the relaxation data, a value for this parameter is required. As an initial value, we rely on measurements of deuterium quadrupolar splittings from deuterated decanol in an anisotropic phase.