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

Molecular Modes Elucidate the Nuclear Magnetic Resonance Relaxation of Viscous Fluids

The Bloembergen, Purcell, and Pound (BPP) theory of nuclear magnetic resonance (NMR) relaxation in fluids dating back to 1948 continues to be the linchpin in interpreting NMR relaxation data in applications ranging from characterizing fluids in porous media to medical imaging (MRI). The BPP theory is founded on assuming molecules are hard spheres with 1H-1H dipole pairs reorienting randomly; assumptions that are severe in light of modern understanding of liquids. Nevertheless, it is intriguing to this day that the BPP theory was consistent with the original experimental data for glycerol, a hydrogen-bonding molecular fluid for which the hard-sphere-rigid-dipole assumption is inapplicable. To better understand this incongruity, atomistic molecular simulations are used to compute 1H NMR T1 relaxation dispersion (i.e., frequency dependence) in two contrasting cases: glycerol, and a (non hydrogen-bonding) viscosity standard. At high viscosities, simulations predict distinct functional forms of T1 for glycerol compared to the viscosity standard, in agreement with modern measurements, yet both in contrast to BPP theory. The cause of these departures from BPP theory is elucidated, without assuming any relaxation models and without any free parameters, by decomposing the simulated T1 response into dynamic molecular modes for both intramolecular and intermolecular interactions. The decomposition into dynamic molecular modes provides an alternative framework to understand the physics of NMR relaxation for viscous fluids.

NMR Investigation of Water in Salt Crusts: Insights from Experiments and Molecular Simulations

The evaporation of water from bare soil is often accompanied by the formation of a layer of crystallized salt, a process that must be understood in order to address the issue of soil salinization. Here, we use nuclear magnetic relaxation dispersion measurements to better understand the dynamic properties of water within two types of salt crusts: sodium chloride (NaCl) and sodium sulfate (Na₂SO₄). Our experimental results display a stronger dispersion of the relaxation time T₁ with frequency for the case of sodium sulfate as compared to sodium chloride salt crusts. To gain insight into these results, we perform molecular dynamics simulations of salt solutions confined within slit nanopores made of either NaCl or Na₂SO₄. We find a strong dependence of the value of the relaxation time T₁ on pore size and salt concentration. Our simulations reveal the complex interplay between the adsorption of ions at the solid surface, the structure of water near the interface, and the dispersion of T₁ at low frequency, which we attribute to adsorption-desorption events.

Spin-lattice relaxation time in water/graphene-oxide dispersion

We present the results of the calculations of the spin-lattice relaxation time of water in contact with graphene oxide by means of all-atom molecular dynamics simulations. We fully characterized the water-graphene oxide interaction through the calculation of the relaxation properties of bulk water and of the contact angle as a function of graphene oxide oxidation state and comparing them with the available experimental data. We then extended the calculation to investigate how graphene oxide alters the dynamical and relaxation properties of water in different conditions and concentrations. We show that, despite the diamagnetic nature of the graphene oxide, the confining effects of the bilayers strongly affect the longitudinal relaxation properties of interfacial water, which presents a reduced dynamics due to hydrogen bonds with oxygen groups on graphene oxide. This property makes graphene oxide an interesting platform to investigate water dynamics in confined geometries and an alternative contrast-agent for magnetic resonance imaging applications, especially in view of the possibility to functionalize graphene oxide from theranostic perspectives.

Effect of Nanoconfinement on NMR Relaxation of Heptane in Kerogen from Molecular Simulations and Measurements

Kerogen-rich shale reservoirs will play a key role during the energy transition, yet the effects of nanoconfinement on the NMR relaxation of hydrocarbons in kerogen are poorly understood. We use atomistic MD simulations to investigate the effects of nanoconfinement on the ¹H NMR relaxation times T₁ and T₂ of heptane in kerogen. In the case of T₁, we discover the important role of confinement in reducing T₁ by ∼3 orders of magnitude from that of bulk heptane, in agreement with measurements of heptane dissolved in kerogen from the Kimmeridge Shale, without any models or free parameters. In the case of T₂, we discover that confinement breaks spatial isotropy and gives rise to residual dipolar coupling which reduces T₂ by ∼5 orders of magnitude from the value for bulk heptane. We use the simulated T₂ to calibrate the surface relaxivity and thence predict the pore-size distribution of the organic nanopores in kerogen, without additional experimental data.

Nuclear Magnetic Resonance Dipolar Cross-Relaxation Interaction between Nanoconfined Fluids and Matrix Solids

Many different methods have been developed to investigate fluid-solid interactions in nanoporous systems. These methods either only work in the liquid phase or provide an indirect measurement by probing the fluid-solid interaction based on a measured property change of the fluid or solid under different sample conditions. Here, we report a direct measurement technique using NMR dipolar cross-relaxation between the nanoconfined fluids and the matrix solids. The method was tested using a methyl-functionalized mesostructured silica saturated with methanol as a model sample. A formal theory was established to describe the enhanced dipolar cross-relaxation interaction between the nanoconfined fluids and the matrix solids. Both the experiment and theory showed that nanoconfinement of the fluids enhances the dipolar cross-relaxation interaction between the fluid and the matrix solids, which can be applied to investigate the fluid-solid interaction for various materials of a similar nanostructure.

NMR Intermolecular Dipolar Cross-Relaxation in Nanoconfined Fluids

Spin relaxation, a defining mechanism of nuclear magnetic resonance (NMR), has been a prime method for determining three-dimensional molecular structures and their dynamics in solution. It also plays key roles for contrast enhancement in magnetic resonance imaging (MRI). In bulk solutions, rapid Brownian molecular diffusion modulates dipolar interactions between a spin pair from different molecules, resulting in very weak intermolecular relaxations. We show that in fluids confined in nanospace or nanopores (nanoconfined fluids) the correlation of dipolar coupling between spin pairs of different molecules is greatly enhanced by the nanopore constraint boundaries on the molecular diffusion, giving rise to an enhanced correlation for the spin pair. As a result, the intermolecular dipolar interaction behaves cooperatively, which leads to a large intermolecular dipolar relaxation rate and opposite in sign to the bulk solution. We found that the classical NMR relaxation theory fails to capture these observations in a nanoconfined fluid environment. Hence, we developed a formal theory and experimentally confirmed that enhanced correlation and cooperated relaxation are ubiquitous in nanoconfined fluids. The newly discovered phenomenon and the developed NMR method reveal new applications in a broad range of synthesized and naturally occurring materials in the field of nanofluidics to study molecular dynamics and structure as well as for MRI image enhancement.

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.

Direct Correlation between Adsorption Energetics and Nuclear Spin Relaxation in a Liquid-saturated Catalyst Material

The ratio of NMR relaxation time constants <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>T</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:mo>/</mml:mo> <mml:msub><mml:mi>T</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> </mml:math> provides a non-destructive indication of the relative surface affinities exhibited by adsorbates within liquid-saturated mesoporous catalysts. In the present work we provide supporting evidence for the existence of a quantitative relationship between such measurements and adsorption energetics. As a prototypical example with relevance to green chemical processes we examine and contrast the relaxation characteristics of primary alcohols and cyclohexane within an industrial silica catalyst support. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>T</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:mo>/</mml:mo> <mml:msub><mml:mi>T</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> </mml:math> values obtained at intermediate magnetic field strength are in good agreement with DFT adsorption energy calculations performed on single molecules interacting with an idealised silica surface. Our results demonstrate the remarkable ability of this metric to quantify surface affinities within systems of relevance to liquid-phase heterogeneous catalysis, and highlight NMR relaxation as a powerful method for the determination of adsorption phenomena within mesoporous solids.

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.

Molecular dynamics simulations of NMR relaxation and diffusion of bulk hydrocarbons and water

Molecular dynamics (MD) simulations are used to investigate ¹H nuclear magnetic resonance (NMR) relaxation and diffusion of bulk n-C₅H₁₂ to n-C₁₇H₃₆ hydrocarbons and bulk water. The MD simulations of the ¹H NMR relaxation times T_1,2 in the fast motion regime where T₁=T₂ agree with measured (de-oxygenated) T₂ data at ambient conditions, without any adjustable parameters in the interpretation of the simulation data. Likewise, the translational diffusion D_T coefficients calculated using simulation configurations agree with measured diffusion data at ambient conditions. The agreement between the predicted and experimentally measured NMR relaxation times and diffusion coefficient also validate the forcefields used in the simulation. The molecular simulations naturally separate intramolecular from intermolecular dipole-dipole interactions helping bring new insight into the two NMR relaxation mechanisms as a function of molecular chain-length (i.e. carbon number). Comparison of the MD simulation results of the two relaxation mechanisms with traditional hard-sphere models used in interpreting NMR data reveals important limitations in the latter. With increasing chain length, there is substantial deviation in the molecular size inferred on the basis of the radius of gyration from simulation and the fitted hard-sphere radii required to rationalize the relaxation times. This deviation is characteristic of the local nature of the NMR measurement, one that is well-captured by molecular simulations.

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

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, 1934 (1997)]. Instead, MD identifies four distinct water layers in a tobermorite-based pore containing surface Ca2+ 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 bulklike 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 characterizing the dynamical properties of proton-bearing porous silicate-based systems such as porous glasses, cementitious materials, and oil-bearing rocks.

Superstatistics model for T₂ distribution in NMR experiments on porous media

We propose analytical functions for T2 distribution to describe transverse relaxation in high- and low-fields NMR experiments on porous media. The method is based on a superstatistics theory, and allows to find the mean and standard deviation of T2, directly from measurements. It is an alternative to multiexponential models for data decay inversion in NMR experiments. We exemplify the method with q-exponential functions and χ(2)-distributions to describe, respectively, data decay and T2 distribution on high-field experiments of fully water saturated glass microspheres bed packs, sedimentary rocks from outcrop and noisy low-field experiment on rocks. The method is general and can also be applied to biological systems.