Pulsed-field-gradient (PFG) NMR observations of spatial where E(q, D) is the echo amplitude relative to the amplitude at q Γ
0 as a function of the magnitude of the wave restrictions to diffusion have great potential for aiding spatial structure determination in a wide variety of porous media. vector for motion encoding q and the diffusion time D, the J n are the standard (cylindrical) Bessel functions, the b nk Some practical examples of current interest include the noninvasive determination of nerve fiber orientation and size, are given by characterization of pore sizes and permeability in oil-bearing rock formations, and structure and transport property deter-
] mination in packed beds and other porous media of use in chemical reaction engineering and separation processes.
a is the cylinder radius, D is the diffusion coefficient of the Toward these ends, several important advances in the theobserved species, and M is the surface relaxivity of the cylinory of PFG NMR measurements on systems exhibiting reder walls. stricted diffusion have been published in the past few years
We report below a favorable comparison of Eq. [1] and (1-8). Recently, Callaghan (1) has published exact, analytiexperimental data obtained from PFG NMR measurements cal expressions for the echo attenuation in planar, cylindrical, on a water-filled 100 mm i.d. capillary tube. and spherical pores valid for conditions of short gradient Measurements were performed with a Bruker Avance pulses and possible wall or surface-induced relaxation. The DMX spectrometer operating at 600 MHz for protons and present note describes a comparison of experimental PFG coupled with a 14 T, 89-mm-bore Bruker/Magnex magnet. NMR data for a water-filled cylinder and the analytical treat-This system is equipped with an actively shielded gradient ment (1).
set capable of 0.96 T/m at 40 A. For restricted geometries and long diffusion times, PFG Precision-bore glass capillaries (i.d. 100 mm) were ob-NMR data exhibit diffusive diffraction; destructive intertained from Wilmad Glass. A single capillary was filled with ference of magnetization contributing to the echo occurs deionized water, inserted into a 5 ml micropipette, sealed at at particular values of the product qa , where q Γ
gg d / 2p, the ends with wax, and inserted into a 2.5 mm i.d., 6-turn, g is the magnetogyric ratio of the observed nucleus, d is the transverse solenoid for NMR measurements. duration of the magnetic-field-gradient pulses for motion Pulsed-field-gradient NMR measurements were perencoding, g is the applied pulsed gradient, and a is a charformed using the ''13-interval, condition I'' alternating-diacteristic dimension of the restricted geometry. This berection (9), pulsed-gradient, stimulated-echo (10, 11) sehavior may prove useful for the characterization of the quence combined with gradient prepulses and longitudinal length scales and geometries of restrictions to diffusion in storage before readout (12, 13) in order to avoid eddy-curporous media.
rent-induced artifacts. A schematic of the pulse sequence is For the specific case of restricted diffusion in a cylindrical shown in Fig. 1. Spoiling gradient pulses orthogonal to the geometry with the pulsed field gradients oriented orthogonal motion-encoding gradient pulses were applied during the two longitudinal storage periods. A 256-transient-phase cy-to the axis of the cylinder, Callaghan found that (1) E(q, D) Γ
β k