Diffusion NMR for Determining the Homogeneous Length-Scale in Lamellar Phases

Abstract

The size of the anisotropic domains in a lyotropic liquid crystal is estimated using a new protocol for diffusion NMR. Echo attenuation decays are recorded for different durations of the displacement-encoding gradient pulses, while keeping the effective diffusion time and the range of the wave vectors constant. Deviations between the sets of data appear if there are non-Gaussian diffusion processes occurring on the time-scale defined by the gradient pulse duration and the length-scale defined by the wave vector. The homogeneous length-scale is defined as the minimum length-scale for which the diffusion appears to be Gaussian. Simulations are performed to show that spatial variation of the director orientation in an otherwise homogeneous system is sufficient to induce non-Gaussian diffusion. The method is demonstrated by numerical solutions of the Bloch-Torrey equation and experiments on a range of lamellar liquid crystals with different domain sizes.

Microanisotropy imaging: quantification of microscopic diffusion anisotropy and orientational order parameter by diffusion MRI with magic-angle spinning of the q-vector

“…If during the diffusion encoding, molecules would have enough time to migrate between anisotropic domains with different orientations, this would affect the diffusion variance in both isotropic and directional DW. In the limit of long diffusion times, the variance observed in a directional DW vanishes [38], while in isotropic DW the variance is expected to increase due to incoherent averaging across microdomains. The dependence of the q-MAS DW on diffusion time can be viewed in analogy to the effects of the MAS in solid-state NMR spectroscopy.…”

“…Here we implement a numerically optimized version of the q-MAS pulse sequence [37] on a high-performance microimaging system, limited to specimens with maximum 10 mm diameter, and on a standard whole-body clinical scanner. The efficiency of the q-MAS sequence is demonstrated using two materials with pronounced water diffusion anisotropy: lyotropic liquid crystals [24,25,27,34,[38][39][40] and pureed asparagus [41][42][43][44]. For contrast, a yeast cells suspension is used, exhibiting two isotropic diffusion components [34,[45][46][47].…”

NMR diffusion-encoding with axial symmetry and variable anisotropy: Distinguishing between prolate and oblate microscopic diffusion tensors with unknown orientation distribution

“…1,2 From a diffusion NMR perspective, it is fruitful to consider porous materials such as lyotropic liquid crystals, 3,4 paper, 5 and brain tissue, 6 as collections of microscopic "domains," in which the water self-diffusion is approximately Gaussian and quantified by a diffusion tensor. 7 Unfortunately, characterization of the material is hampered by the fact that the effects of diffusion tensor trace, anisotropy, and orientation are entangled when using conventional diffusion-encoding with the StejskalTanner sequence, 8 which is ubiquitous in both porous media research and clinical magnetic resonance imaging (MRI).…”

Investigations of vesicle gels by pulsed and modulated gradient NMR diffusion techniques

“…24 The magnetic field gradient strength g and the pulse duration d were varied. These two parameters determine the sensitivity to diffusion and define the wave number q as…”

“…24 Because of the concentration and attenuation differences, the different species were assigned different threshold values to define a deviation (10% for the water peak and 2% for the TMA-peak). The l hom is only well defined for long-range diffusion and thus the data at the longest t d is used to determine it.…”