Nuclear-magnetic-resonance relaxation due to the translational diffusion of fluid confined to quasi-two-dimensional pores

Nuclear magnetic resonance (NMR) relaxation experimentation is an e ective technique for non-destructively probing the dynamics of proton-bearing uids in porous media. The frequencydependent relaxation rate T−1 1 can yield a wealth of information on the uid dynamics within the pore provided data can be t to a suitable spin di usion model. A spin di usion model yields the dipolar correlation function G(t) describing the relative translational motion of pairs of 1H spins which then can be Fourier transformed to yield T−1 1 . G(t) for spins con ned to a quasi-two-dimensional (Q2D) pore of thickness h is determined using theoretical and Monte Carlo techniques. G(t) shows a transition from three- to two-dimensional (2D) motion with the transition time proportional to h2. T−1 1 is found to be independent of frequency over the range 0.01{100 MHz provided h ? 5 nm and increases with decreasing frequency and decreasing h for pores of thickness h < 3 nm. T−1 1 increases linearly with the bulk water di usion correlation time b allowing a simple and direct estimate of the bulk water di usion coe cient from the high-frequency limit of T−1 1 dispersion measurements in systems where the in uence of paramagnetic impurities is negligible. Monte Carlo simulations of hydrated Q2D pores are executed for a range of surfaceto- bulk desorption rates for a thin pore. G(t) is found to decorrelate when spins move from the surface to the bulk, display three-dimensional properties at intermediate times and nally show a bulk-mediated surface di usion (L evy) mechanism at longer times. The results may be used to interpret NMR relaxation rates in hydrated porous systems in which the paramagnetic impurity density is negligible