Determining a ‘diffusion-averaged’ characteristic ratio for aligned lyotropic hexagonal phases using PGSE NMR self-diffusion measurements, random walk simulations and obstruction models

Lyotropic liquid crystal (LLC) materials are promising for a wide range of applications from templating nanomaterials to drug delivery and separations technologies. Hexagonal phases of LLCs are made of cylindrical aggregates arranged on a hexagonal lattice. Small angle neutron scattering (SANS) or small angle X-ray scattering (SAXS) are typically used to measure the cylinder radius and hexagonal lattice parameter and hence a characteristic dimension ratio, e.g., ratio of hexagonal lattice parameter to the cylinder radius. Unlike SAXS or SANS, pulsed gradient spin-echo nuclear magnetic resonance (PGSE NMR) diffusion measurements probe much larger length scales. Probing porous systems via restricted diffusion (i.e., diffusion diffraction) is limited to μm dimensions by available gradient strengths, but analysis of diffusion obstruction and anisotropy permit probing smaller dimensions. PGSE NMR measurements of self-diffusion coupled with simple random walk simulations and obstruction models can be used to find a ‘diffusion-averaged’ characteristic dimension ratio to better represents diffusive properties in macroscopically aligned samples. Random walk simulations and experimental diffusion ellipsoids were used with structural obstruction models to determine ‘diffusion-averaged’ characteristic dimension ratios for aligned LLC hexagonal phases of non-ionic surfactants using different probe molecules and these were compared to SAXS obtained values presented elsewhere.