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

Abstract

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. We compare D app and D( t) and find that, regardless of pulse widths and geometry-dependent parameters, the two quantities deviate by less than 20%. These results are in sharp contrast with the studies on closed geometries [J. Magn. Reson. A 117 (1995) 209], where the effects of finite gradient-pulse widths are large. The analytical results presented here can be easily adapted for different pulse protocols and time sequences.