Nuclear magnetic resonance relaxometry of water in two and quasi-two dimensions

Abstract

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.

Model for the interpretation of nuclear magnetic resonance relaxometry of hydrated porous silicate materials

“…The Y are the spherical harmonic functions of order two and the presence of the asterisk superscript on the Y indicates the complex conjugate. The powder average has been taken resulting in the factor 1 5 [22].…”

Explicit calculation of nuclear-magnetic-resonance relaxation rates in small pores to elucidate molecular-scale fluid dynamics

“…This model therefore simplifies the complex intra-pore dynamics of real fluids to three characteristic time constants,τ b , τ and τ d . Aspects of this general model, henceforth referred to as the 3τ model, are widely used throughout literature [1][2][3][4][5][6][7][8].Nuclear magnetic resonance (NMR) relaxation analysis is a uniquely powerful tool to access molecular correlation times of fluids in porous media [1][2][3][4][5][6][7][8][9]. It is rivalled only by small-angle scattering techniques, especially with neutrons, but has the advantage of being widely available using laboratory-scale equipment.…”

“…Nuclear magnetic resonance (NMR) relaxation analysis is a uniquely powerful tool to access molecular correlation times of fluids in porous media [1][2][3][4][5][6][7][8][9]. It is rivalled only by small-angle scattering techniques, especially with neutrons, but has the advantage of being widely available using laboratory-scale equipment.…”

“…Several models have been proposed (for example, [1,2,6,7,10]) but that which builds most successfully on the general dynamics of the model illustrated in Fig. 1 in terms of fitting experimental data is due to Korb and co-workers [3][4][5][6]10].…”

“…The powder average has been taken reflecting the (assumed) uniform random orientation of pores in experimental samples [7,12]. Substitution of Eqs.…”