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

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. We recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker-Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole-dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé-Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory.

Nuclear spin relaxation in aqueous paramagnetic ion solutions

A Brownian shell model describing the random rotational motion of a spherical shell of uniform particle density is presented and validated by molecular dynamics simulations. The model is applied to proton spin rotation in aqueous paramagnetic ion complexes to yield an expression for the Larmor-frequency-dependent nuclear magnetic resonance spin-lattice relaxation rate T_{1}^{-1}(ω) describing the dipolar coupling of the nuclear spin of the proton with the electronic spin of the ion. The Brownian shell model provides a significant enhancement to existing particle-particle dipolar models without added complexity, allowing fits to experimental T_{1}^{-1}(ω) dispersion curves without arbitrary scaling parameters. The model is successfully applied to measurements of T_{1}^{-1}(ω) from aqueous manganese(II), iron(III), and copper(II) systems where the scalar coupling contribution is known to be small. Appropriate combinations of Brownian shell and translational diffusion models, representing the inner and outer sphere relaxation contributions, respectively, are shown to provide excellent fits. Quantitative fits are obtained to the full dispersion curve of each aquoion with just five fit parameters, with the distance and time parameters each taking a physically justifiable numerical value.

Predicting 1H NMR relaxation in Gd3+-aqua using molecular dynamics simulations

Atomistic molecular dynamics simulations are used to predict ¹H NMR T₁ relaxation of water from paramagnetic Gd³⁺ ions in solution at 25 °C. Simulations of the T₁ relaxivity dispersion function r₁ computed from the Gd³⁺-¹H dipole-dipole autocorrelation function agree within ≃8% of measurements in the range f₀ ≃ 5 ↔ 500 MHz, without any adjustable parameters in the interpretation of the simulations, and without any relaxation models. The simulation results are discussed in the context of the Solomon-Bloembergen-Morgan inner-sphere relaxation model, and the Hwang-Freed outer-sphere relaxation model. Below f₀ ≲ 5 MHz, the simulation overestimates r₁ compared to measurements, which is used to estimate the zero-field electron-spin relaxation time. The simulations show potential for predicting r₁ at high frequencies in chelated Gd³⁺ contrast-agents used for clinical MRI.

Advances in the Interpretation of Frequency-Dependent Nuclear Magnetic Resonance Measurements from Porous Material

Fast-field-cycling nuclear magnetic resonance (FFC-NMR) is a powerful technique for non-destructively probing the properties of fluids contained within the pores of porous materials. FFC-NMR measures the spin-lattice relaxation rate R 1 ( f ) as a function of NMR frequency f over the kHz to MHz range. The shape and magnitude of the R 1 ( f ) dispersion curve is exquisitely sensitive to the relative motion of pairs of spins over time scales of picoseconds to microseconds. To extract information on the nano-scale dynamics of spins, it is necessary to identify a model that describes the relative motion of pairs of spins, to translate the model dynamics to a prediction of R 1 ( f ) and then to fit to the experimental dispersion. The principles underpinning one such model, the 3 τ model, are described here. We present a new fitting package using the 3 τ model, called 3TM, that allows users to achieve excellent fits to experimental relaxation rates over the full frequency range to yield five material properties and much additional derived information. 3TM is demonstrated on historic data for mortar and plaster paste samples.

Density Functional Theory Study of Water Molecule Adsorption on the α-Quartz (001) Surface with and without the Presence of Na+, Mg2+, and Ca2

Adsorption of the single water molecule on the α-quartz (001) surface with and without the presence of Na⁺, Mg²⁺ and Ca²⁺ was analyzed utilizing the density functional theory method. Our results demonstrate that the optimal adsorption configuration of the single water molecule on the α-quartz (001) surface lies in the bridge being configured with two formed hydrogen bonds. These were Os-Hw and Hs-Ow (s and w represent, respectively, surface and water molecules), while the main hydrogen bond is Hw-Os. Furthermore, the corresponding adsorption energy was ∼-72.60 kJ/mol. In this study, the presence of metal ions helped to deflect the spatial position of the water molecule, and the distance between Ow and Hs was altered significantly. Furthermore, the charge transfer between the interacting atoms increased in the presence of metal ions, wherein the effects of Ca²⁺ and Na⁺ proved to be significant compared to Mg²⁺. Finally, it emerged that metal ions interacted with the water molecule and were subsequently adsorbed on the α-quartz (001) surface. This occurred due to the electrostatic attraction, consequently impacting the hydration characteristics of the quartz surface.

Enhanced NMR relaxation of fluids confined to porous media: A proposed theory and experimental tests

We propose a theory to account for the NMR relaxation of water protons in situations in which the fluid is confined to porous structures exhibiting a scarce distribution of paramagnetic centers on their surface. Though much of what is stated and assumed concerns the response of water, the model has sufficiently general features to be able to explain proton relaxation of other polar fluids under similar conditions. One of the main results of the paper is to show that the local anisotropy introduced by the dominant dipolar coupling in the relaxation rates of active surface elements induces a measurable dependence on sample orientation in the overall relaxation rates of the saturating fluid provided its confining structure is not statistically isotropic. Measurements of T_{1} proton relaxation on water saturating microcapillary tubes are performed to reveal the effect.

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

Nuclear-magnetic-resonance (NMR) spin-lattice (T_{1}^{-1}) and spin-spin (T_{2}^{-1}) relaxation rate measurements can act as effective nondestructive probes of the nanoscale dynamics of ^{1}H spins in porous media. In particular, fast-field-cycling T_{1}^{-1} dispersion measurements contain information on the dynamics of diffusing spins over time scales spanning many orders of magnitude. Previously published experimental T_{1}^{-1} dispersions from a plaster paste, synthetic saponite, mortar, and oil-bearing shale are reanalyzed using a model and associated theory which describe the relaxation rate contributions due to the interaction between spin ensembles in quasi-two-dimensional pores. Application of the model yields physically meaningful diffusion correlation times for all systems. In particular, the surface diffusion correlation time and the surface desorption time take similar values for each system, suggesting that surface mobility and desorption are linked processes. The bulk fluid diffusion correlation time is found to be two to five times the value for the pure liquid at room temperature for each system. Reanalysis of the oil-bearing shale yields diffusion time constants for both the oil and water constituents. The shale is found to be oil wetting and the water T_{1}^{-1} dispersion is found to be associated with aqueous Mn^{2+} paramagnetic impurities in the bulk water. These results escalate the NMR T_{1}^{-1} dispersion measurement technique as the primary probe of molecular-scale dynamics in porous media yielding diffusion parameters and a wealth of information on pore morphology.

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 effective technique for nondestructively probing the dynamics of proton-bearing fluids in porous media. The frequency-dependent relaxation rate T_{1}^{-1} can yield a wealth of information on the fluid dynamics within the pore provided data can be fit to a suitable spin diffusion model. A spin diffusion model yields the dipolar correlation function G(t) describing the relative translational motion of pairs of ^{1}H spins which then can be Fourier transformed to yield T_{1}^{-1}. G(t) for spins confined 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 motion with the transition time proportional to h^{2}. 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 diffusion correlation time τ_{b} allowing a simple and direct estimate of the bulk water diffusion coefficient from the high-frequency limit of T_{1}^{-1} dispersion measurements in systems where the influence of paramagnetic impurities is negligible. Monte Carlo simulations of hydrated Q2D pores are executed for a range of surface-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.