The narrow-pulse criterion for pulsed-gradient NMR spin-echo function of gradient separation can yield the diffusion coefdiffusion in the presence of impenetrable barriers is examined from ficient. an expression by Stepisnik [Physica B 183, 343 (1993)] for the Most of the diffusion experiments in the past three decades attenuation caused by diffusion in any magnetic-field gradient for have been about bulk diffusion in homogeneous liquids various parameters. These parameters are d, D, a, D, and g, where where the diffusing species do not encounter any barriers d and D are the duration and the interval between bipolar magduring the measurement. Now, diffusion in restricted spaces, netic-field-gradient pulses, respectively, a is the separation of the considered early on by Woessner (11), Stejskal and Tanner impenetrable barriers, D is the diffusion coefficient, and g is the (4-6), and Cotts and co-workers (12-14), among others, gradient strength. The pulsed-gradient spin-echo (PGSE) experi-
is gaining interest because, in conjunction with NMR imment is a subclass of this set. The attenuation, with the assumption that the diffusive motion of the spins leads to Gaussian distribution aging, it has led to the possibility of determining anisotropic of spin phases, goes to known expressions in the free-diffusion microstructures of heterogeneous systems. Such microstruc-(DD/a 2 ΣΆ 1), restricted-diffusion ( dD/a 2 ΣΆ 1 ΣΆ DD/a 2 ), and tures studied by NMR diffusion measurements can have dirapid-diffusion (1 ΣΆ dD/a 2 ) limits. This general expression is mensions much smaller than the resolution of NMR images found to be valid for all combinations of D and d provided that (8). The microstructure boundaries will affect diffusion gdga/2p Γ
qa ΣΆ 1. A criterion for the applicability of the commeasurements if the time to traverse the microstructure is monly used narrow-pulse expressions for the signal attenuation is comparable to or shorter than some experimental times. For calculated from the fraction F of total attenuation that takes place example, the mean diffusive displacement of water in 1 ms only during the gradient. An independent check was performed at room temperature is about 1 mm, so the wall effects on from the shifts of the diffraction minima as a function of increasing pulse widths obtained from the simulation by Blees [J. Magn. water diffusing in the presence of a magnetic-field-gradient Reson. A 109, 203 (1994)].
If the narrow-pulse criterion is valid pulse in a 1 mm pore cannot be ignored when the pulse is for F ΣΆ 0.1 or for less than a 5% shift in the second minimum of longer than 1 ms.
the diffraction pattern, a sufficient condition for its applicability Such microstructures can be studied by one of two related is dD/a 2 ΣΆ 0.02, a much more stringent condition than is usually NMR methods. One is to study the magnitude of the echo supposed.