A. Coy

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

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.

Pulsed gradient spin echo nuclear magnetic resonance for molecules diffusing between partially reflecting rectangular barriers

The application of pulsed gradient spin echo nuclear magnetic resonance (NMR) to the case of molecules trapped between two plane parallel boundaries, has been examined theoretically, with computer simulation and by experiment. A new closed‐form analytic expression is obtained for the averaged propagator and the echo attenuation when the walls have finite relaxivity and this expression is verified by computer simulations. It is shown that ‘‘diffraction’’ effects are still strongly apparent when wall relaxation is taken into account and that deviations in the barrier spacing parameter obtained from the position of the echo minimum, are weak. In particular we show that for the pulsed gradient spin echo (PGSE) pulse separation time on the order of a2/2D, the deviation is less than 10% provided that the relaxation is not so severe as to reduce the zero gradient signal amplitude below 10% of its unrelaxed value. We further examine the influence of finite gradient pulse and find, as with wall relaxation, that di...

Microstructure of porous media probed by NMR techniques in sub-micrometer length scales

It is shown that field-cycling NMR relaxation spectroscopy in combination with pulsed-gradient spin-echo diffusion studies especially in the supercon fringe field version are suitable techniques for the investigation of length scales of porous media in the range 10 A to 10 microns. Data for water adsorbed in fine particle agglomerates, porous glass and ceramics are reported. An orientational structure factor is introduced permitting the characterization of hydrated surfaces on the basis of reorientations mediated by translational displacements of the adsorbed molecules. Known lengths such as the mean pore or particle size have been reproduced in this way. In length scales beyond these structural elements, the geometry of the internal surfaces can be discussed in terms of wavenumber-space fractals.

Diffusion of fluids in porous solids probed by pulsed field gradient spin echo NMR

Abstract The response to the pulsed field gradient spin echo (PGSE) NMR experiment is described for fluid diffusing in pore networks. The behaviour is discussed in terms of the field gradient wavevector, q (=γδg/2π) and the diffusion time Δ. An analytical theory is outlined and compared with computer simulations for a regular lattice of pores. Theoretical results are also presented for a pore glass. In both cases effects of the confining structure are predicted to become of increasing importance as qb increases, where b is the pore separation. When qb is an integer, maxima occur in the spin echo amplitude as a function of q, analogous with diffraction from the pore network structure. For a regular lattice structure it is shown that when qb is an integer the PGSE response as a function of Δ has the appearance of completely bounded diffusion. The conditions on q and Δ required to measure the structure averaged diffusion coefficient, Deff, are deduced. Experimental results are shown for the diffusion of water contained in the spaces between loosely packed polystyrene spheres. These show the characteristics predicted by the pore glass theory.

Some biophysical applications of motional contrast in n.m.r. microscopy

The principal advantage of the n.m.r. imaging method lies in the specific contrasts which are available. In this work we describe the use of velocity and diffusion contrast methods in biophysical applications and at microscopic spatial resolution. In the first example, involving water-protein interactions, the relationship between water self-diffusion and water concentration, as measured using pulsed gradient spin echo n.m.r., is shown. It is demonstrated that this relationship can be used to provide a water concentration image. The result is compared with the conventional proton density and transverse relaxation maps. The next example concerns the use of dynamic n.m.r. microscopy to obtain water diffusion and velocity maps for wheat grain in vivo. Finally we suggest how the method may be used in the study of polymer-water interactions in an unusual adjunct to conventional polymer self-diffusion studies.

Chapter 13 Scattering wavevector analysis of pulsed gradient spin echo data

Publisher Summary The scattering analogy provides a useful description of the Pulsed Gradient Spin Echo (PGSE) method. It lends itself naturally to the use of Fourier analysis and the mathematics of diffraction when designing PGSE experiments and in treating the resulting echo signals. Care is needed in allowing for finite time, finite pulse width and relaxation effects. This chapter examines the use of conventional least squares approaches to multi-parameter fitting that can result in valuable structural and dynamical insight. When used as a contrast in imaging, the PGSE method allows the motion to be spatially localized. The use of Fourier analysis provides access to the local propagator and permits the use of fitting procedures, which reveal motional features of specific interest. The use of sophisticated localized propagator analysis offers promising avenues of investigation in the development of more powerful nuclear magnetic resonance (NMR) imaging methodologies.