Molecular dynamics (MD) and Monte Carlo (MC) methods are used to determine the spin-pair correlation function, G * (t), for the diffusion of bulk water in three-dimensions (3D) and pore water in two-dimensions (2D) and quasi-two-dimensions (Q2D). The correlation function is required for the determination of the nuclear magnetic resonance (NMR) spin-lattice and spin-spin relaxation times T 1 and T 2 . It is shown that the analytic form of the powder-average correlation function, introduced by Sholl [C. A. Sholl, J. Phys. C: Solid State Phys. 7, 3378 (1974)] for the diffusion of spins on a 3D lattice, is of general validity. An analytic expression for G * (t) for a uniform spin fluid is derived in 2D. An analytic expression for the long-time behaviour of G * (t) is derived for spins diffusing on 3D, 2D and Q2D lattices. An analytic correction term, which accounts for spin-pairs outside the scope of the numerical simulations, is derived for 3D and 2D and shown to improve the accuracy of the simulations. The contributions to T 1 due to translational and rotational motion obtained from the MD simulation of bulk water at 300 K are 7.4 s and 10±1 s respectively, at 150MHz leading to an overall time of 4.3 ± 0.4 s compared the experimental value of 3.8 s. In Q2D systems, in which water is confined by alpha-quartz surfaces to thicknesses of 1-5 nm, T 1 for both translational and rotational relaxation is reduced due to the orientation and adsorption of spins at the surfaces. A novel method of parameterising the MC lattice-diffusion simulations in 3D, 2D and Q2D systems is presented. MC results for G * (t) for 3D and 2D systems are found to be consistent with an analytic uniform fluid model for t 40 ps. The value of T 1 for translational diffusion obtained from the MC simulation of bulk water is found to be 4.8 s at 15 MHz. G * (t) obtained from MC simulations of Q2D systems, where water is confined by hard walls, is found to execute a distinct transition from 3D to 2D behaviour. The T 1 is found to be similar to the 3D bulk water result at all pore thicknesses.

Nuclear magnetic resonance (NMR) relaxation experimentation is an effective technique for non-destructively probing the dynamics of proton-bearing fluids in porous media. The frequencydependent relaxation rate T to-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 finally show a bulk-mediated surface diffusion (Lévy) 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.

Nuclear magnetic resonance (NMR) relaxation experimentation is an effective technique for probing the dynamics of proton spins in porous media but interpretation requires the application of appropriate spin diffusion models. Molecular dynamics (MD) simulations of porous silicate-based systems containing a quasi-two-dimensional water-filled pore are presented. The MD simulations suggest that the residency time of the water on the pore surface is in the range 0.03-12 ns, typically 2-5 orders of magnitude less than values determined from fits to experimental NMR measurements using the established surface-layer (SL) diffusion models of Korb and co-workers [Phys. Rev. E 56, 1934Rev. E 56, , (1997]. Instead, MD identifies four distinct water layers in a tobermorite-based pore containing surface Ca 2+ ions. Three highly-structured water layers exist within 1 nm of the surface and the central region of the pore contains a homogeneous region of bulk-like water. These regions are referred to as layer 1 and 2 (L1, L2), transition layer (TL) and bulk (B), respectively. Guided by the MD simulations, a two-layer (2L) spin-diffusion NMR relaxation model is proposed comprising two two-dimensional layers of slow-and fast-moving water associated with L2 and layers TL+B respectively. The 2L model provides an improved fit to NMR relaxation times obtained from cementitious material compared to the SL model, yields diffusion correlation times in the range 18-75 ns and 28-40 ps in good agreement with MD, and resolves the surface residency time discrepancy. The 2L model, coupled with NMR relaxation experimentation, provides a simple yet powerful method of characterising the dynamical properties of proton-bearing porous silicate-based systems such as porous glasses, cementitious materials and oil-bearing rocks.

Nuclear magnetic resonance (NMR) relaxometry is a powerful technique to characterise diffusive motion of fluids in nanoporous to microporous media. Molecular simulations can be used to predict NMR relaxation parameters using a dipolar spin-spin correlation function. In this Paper, molecular dynamics simulations of water diffusion in anomalous 11Å tobermorite, consisting of three slit pores and one gel pore of width ∼ 1.0 nm, have been performed. The spin-spin correlation function components corresponding to both 2D and quasi-2D translation and rotation of water are presented. It was found that motion in the slit pores is highly correlated, leading to a significantly shorter relaxation time compared to bulk water. The correlation between the slit pores and the gel pore was found to be negligible compared to that within either the gel pore or the slit pore exclusively. Nevertheless, this correlation function can be useful in quantifying water diffusion within the slit pores, which occurs primarily through stochastic site jumping. It was found that stronger surface interaction leads to lower relaxation times, while the hydroxyls on the surface help further lower the water relaxation times.

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