Diffusion in porous systems and the influence of pore morphology in pulsed gradient spin-echo nuclear magnetic resonance studies

Abstract

We report a combined experimental, theoretical, and simulation study of pulsed gradient spin-echo (PGSE) nuclear magnetic resonance (NMR) for fluid saturated porous media. A simple pore hopping theory is developed on the basis of the assumption that diffusion within pores is very much faster than diffusion between pores. For suitable periodic media, the theoretical results are found to be in good agreement with random-walk simulations. The theory for glasslike media is then used to analyze experimental PGSE NMR data for a water-saturated random loose pack of nearly monodisperse polystyrene spheres. The structural parameters extracted by this method are consistent with the known geometry of such packings. An important observation from the simulations is that the long-time effective diffusion constant is already accessed at times so short that a single spin will only have diffused across one pore width.

Predictions for pulsed-field–gradient NMR experiments of diffusion in fractal spaces

“…Analogies with PFG NMR and scattering or diffraction have previously been observed (Callaghan et al 1992), and it is possible to provide an alternative derivation of the power law in (21) using these ideas. For the PFG experiment,…”

“…Such dynamical behaviour may be caused by normal Brownian motion confined to a fractal space of dimension d f , and it is this type of system, where d w ≥ 2, in which our interest here lies. It is our desire in this paper to make some predictions in the context of pulsed-field-gradient (PFG) NMR for the q-space behaviour (Callaghan et al 1992) of diffusion in fractal spaces. The motivation for this stems from the recognition 1 that several structures which are frequently investigated using NMR techniques, such as porous media, lung tissue and smectic liquid crystals, have been found to possess fractal characteristics.…”

Mapping of 3He apparent diffusion coefficient anisotropy at sub‐millisecond diffusion times in an elastase‐instilled rat model of emphysema

“…Anisotropic ADCs depend on diffusion time due to the relationship between diffusion distance and medium size (22,23). In particular, changes in 3 He anisotropy, particularly D T , resulting from emphysema (e.g., alveoli changes) are expected to be more significant at sub-millisecond diffusion times (24).…”

A new view of the spin echo diffusive diffraction in porous structures

“…It aims to clear up details like the diffraction dependences on time, the dependence on the width of gradient pulse and on the type of applied gradient sequences as obtained by experiments and computer simulations [18,19,20], but remains unanswered in the frame of propagator theory. The method might elucidate the dependence of diffraction on the mechanism of scattering at interfaces as well.…”