Pulse gradient spin-echo based (PGSE) NMR diffusion experiments [1] can be very useful in probing the structure of microscopic pores. This NMR method application is possible since the diffusion of chemical entities in restricted environments such as in microscopic pores is generally slower than that in free solution environments so that information about the size, shape, and uniformity of the pore can be possibly deduced. In some cases, such as in red blood cells [2] and polystyrene beads [3] in various solvents, the NMR diffusion decay signals result in useful diffusion-diffraction like patterns which directly reflect the pore dimension and shape.
In many porous systems, however, the existing models used in analysing NMR restricted diffusion data are often inadequate. This is especially true in biological systems wherein the models used are usually poor approximations of cellular shape. In this study, the diffusion propagators and pulsed gradient spin-echo attenuation equations are derived for various idealised restricted geometries such as rectangular pores and the annular regions of concentric cylinders and spheres [4]. The obtained theoretical results are compared with the experimental NMR diffusion-diffraction profiles taking to account surface wall relaxations, orientation of magnetic field gradients and other factors.