Director orientations in lyotropic liquid crystals: diffusion MRI mapping of the Saupe order tensor

Abstract

The macroscopic physical properties of a liquid crystalline material depend on both the properties of the individual crystallites and the details of their spatial arrangement. We propose a diffusion MRI method to estimate the director orientations of a lyotropic liquid crystal as a spatially resolved field of Saupe order tensors. The method relies on varying the shape of the diffusion-encoding tensor to disentangle the effects of voxel-scale director orientational order and the local diffusion anisotropy of the solvent. Proof-of-concept experiments are performed on water in lamellar and reverse hexagonal liquid crystalline systems with intricate patterns of director orientations.