Probing short length scales with restricted diffusion in a static gradient using the CPMG sequence.

We experimentally verify a new method of extracting the surface-to-volume ratio (S/V) of porous media with diffusion NMR. In contrast to the widely used pulsed field gradient (PFG) technique, which employs the stimulated echo coherence pathway, we use here the direct Carr-Purcell-Meiboom-Gill (CPMG) path. Even for high echoes, which exhibit ample attenuation due to diffusion in the field gradient, the relevant ruler length for the direct pathway is fixed by the diffusion length during a single inter-pulse spacing.

Short-time restricted diffusion in a static gradient and the attenuation of individual coherence pathways.

We experimentally explore some of the implications of a recent theoretical study [J. Magn. Reson.

Effect of internal gradients in the nuclear magnetic resonance measurement of the surface-to-volume ratio.

We consider a system of spins diffusing in a static inhomogeneous (nonuniform-gradient) magnetic field B in a restricted geometry and in the presence of surface relaxation. We show that the short-time diffusional decay of nuclear magnetization is controlled by the field scattering kernel F(t) identical with [B(t)-B(0)](2), which is a measure of the average field inhomogeneity sampled by the spins in time t and does not depend on the particular sequence of radio-frequency pulses used. Magnetization in arbitrary sequences can be straightforwardly computed by evaluating elementary integrals of F(t).

Effects of finite-width pulses in the pulsed-field gradient measurement of the diffusion coefficient in connected porous media.

We analytically compute the apparent diffusion coefficient D(app) for an open restricted geometry, such as an extended porous medium, for the case of a pulsed-field gradient (PFG) experiment with finite-width pulses. In the short- and long-time limits, we give explicit, model-independent expressions that correct for the finite duration of the pulses and can be used to extract the pore surface-to-volume (S/V) ratio as well as the tortuosity. For all times, we compute D(app) using a well-established model form of the actual time-dependent diffusion coefficient D(t) that can be obtained from an ideal narrow-pulse PFG.

Restricted diffusion in grossly inhomogeneous fields.

We analyze the effects of geometrical restriction on the nuclear magnetization of spins diffusing in grossly inhomogeneous fields where radio-frequency (RF) pulses are weak relative to the total field inhomogeneity, making the rotation angle space-dependent and thus exciting multiple coherence pathways. We show how to separate the effects of restricted diffusion from the effects of the pulses in the case when the change in the field experienced by a diffusing spin in the course of the experiment is small compared to the RF magnitude. We then derive explicit formulas for the contribution of individual coherence pathways to the total magnetization in arbitrary pulse sequences.