The Narrow Pulse Approximation and Long Length Scale Determination in Xenon Gas Diffusion NMR Studies of Model Porous Media

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D( t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D( t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D( t) is observed in the same samples. The use of gas also allows us to probe D( t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (∼1–1.5 bead diameters). The Padé approximation can be used as a reference for expected xenon D( t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Padé interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Padé length), which is found to be ∼0.13 b for all bead packs, where b is the bead diameter.