Nirbhay N. Yadav

Numerical analysis of NMR diffusion measurements in the short gradient pulse limit

Pulsed gradient spin-echo (PGSE) NMR diffusion measurements provide a powerful technique for probing porous media. The derivation of analytical mathematical models for analysing such experiments is only straightforward for ideal restricting geometries and rapidly becomes intractable as the geometrical complexity increases. Consequently, in general, numerical methods must be employed. Here, a highly flexible method for calculating the results of PGSE NMR experiments in porous systems in the short gradient pulse limit based on the finite element method is presented. The efficiency and accuracy of the method is verified by comparison with the known solutions to simple pore geometries (parallel planes, a cylindrical pore, and a spherical pore) and also to Monte Carlo simulations. The approach is then applied to modelling the more complicated cases of parallel semipermeable planes and a pore hopping model. Finally, the results of a PGSE measurement on a toroidal pore, a geometry for which there is presently no current analytical solution, are presented. This study shows that this approach has great potential for modelling the results of PGSE experiments on real (3D) porous systems. Importantly, the FEM approach provides far greater accuracy in simulating PGSE diffraction data.

NMR q-space imaging of macroscopic pores using singlet spin states

NMR q-space imaging is a powerful non-invasive technique used to determine structural characteristics of pores in applications ranging from medical to material science. To date, the application of q-space imaging has primarily been limited to microscopic pores in part because of limitations of the effective observation time due to relaxation. Here we report on the use of singlet spin states for NMR q-space imaging, which allow significantly greater observation times. This opens the way for studying larger pores in materials such as biological tissue, emulsions, and rocks.

An improved approach to calibrating high magnetic field gradients for pulsed field gradient experiments.

Probes capable of generating short high intensity pulsed magnetic field gradients are commonly used in diffusion studies of systems with very short T(2). Traditional methods of calibrating magnetic field gradients present unique challenges at ultrahigh field strengths and are often inapplicable. Currently the most accurate method of determining magnetic gradient strength is to use the known diffusion coefficient of a standard sample and determine gradient strength from the echo attenuation plot of a diffusion experiment, however, there are problems with finding suitable standards for high intensity gradients. Here, we show that molecules containing at least two receptive nuclei (i.e. one with high and one with low gyromagnetic ratios) are excellent systems for calibrating high intensity gradients.

Impediments to the accurate structural characterisation of a highly concentrated emulsion studied using NMR diffusion diffraction.

Pulsed gradient spin-echo (PGSE) NMR diffusion studies with subsequent analysis using the Gaussian phase distribution (GPD) approach have long been used to determine the structure of emulsions. With the increasing availability of spectrometers equipped with higher gradient strength generation capabilities it is possible to extend PGSE measurements to where diffusive diffraction effects become evident. However the GPD approach cannot predict these diffraction-like coherence features which can be a rich source of information. With appropriate modelling based on the short gradient pulse approximation (SGP) such coherence features can provide morphological characteristics such as pore size, tortuosity, and connectivity. Further, the deviation of coherence features from ideal cases can be used to elucidate additional features such as the polydispersity of emulsion droplets which is a fundamental and crucial physical characteristic that influences the emulsion stability, rheology, and functionality. In this study analysis of PGSE NMR diffusion diffraction coherence features using the multiple propagator matrix formalism extension of the SGP approach is used to study structural characteristics of a highly concentrated emulsion.

Restricted diffusion in annular geometrical pores

Nuclear magnetic resonance (NMR) diffusion (including diffusion MRI) experiments are only as powerful as the models used to analyse the NMR diffusion data. A major problem, especially with measurements on biological systems, is that the existing models are only very poor approximations of cellular shape. Here, diffusion propagators and pulsed gradient spin-echo attenuation equations are derived in the short gradient pulse limit for diffusion within the annular region of a concentric cylinder of finite length and, similarly, within the annular region of a concentric sphere. The models include the possibility of relaxation at the boundaries and, in the case of the concentric cylinder, having the cylinder arbitrarily oriented with respect to the direction of the applied field gradient. The two models are also of interest due to their direct analogy to optical double slit diffraction. Also expressions for the mean square displacements, which are very useful information for determining the diffusion coefficient within these complex geometries, are obtained as well as for the limiting cases of diffusion on cylindrical and spherical shells and in a ring.