Critical Role of Confinement in the NMR Surface Relaxation and Diffusion of n-Heptane in a Polymer Matrix Revealed by MD Simulations

NMR Relaxation of Gas Adsorbed in Microporous Material

NMR relaxometry has been widely applied to characterize fluid confined in porous media because of its versatility, chemical selectivity, and noninvasive nature. Here we extend its usage to gas adsorbed in microporous materials by establishing a new quantitative model based on the molecular level NMR relaxation mechanism revealed by the molecular simulation of a prototypical adsorption system, CH4 adsorbed in ZIF-8. The model enables new NMR relaxometry-based characterization methods for thermodynamic, dynamic, and structural properties of adsorption systems, as demonstrated and validated by the experiments where the adsorption capacity and self-diffusivity of H2, CH4, and small alcohols adsorbed in ZIF-8 are deduced from the NMR relaxation data. The findings can serve for a better understanding of the composition-structure-properties relationships of a wide range of adsorption systems which is essential for the development and application of new functional microporous 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.

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.

Quantifying the Effect of Spatial Confinement on the Diffusion and Nuclear Magnetic Resonance Relaxation of Water/Hydrocarbon Mixtures: A Molecular Dynamics Simulation Study

We implement molecular dynamics (MD) simulations to explore the relaxation mechanisms involved in the description of translational diffusion and rotational dynamics in water/hydrocarbon interfaces. The analysis of density profiles, self-diffusion coefficients, and nuclear magnetic resonance (NMR) relaxation properties as a function of the confinement layer width and type of hydrocarbons improves the understanding of confined water properties at water/oil interfaces. Density profile fluctuations reveal the presence of water-oil interactions close to the interface. MD results show that self-diffusion coefficients and NMR relaxation times of planar and cylindrical water/oil interfaces are strongly influenced by layer thickness and geometry. Shorter (between 20 and 60%) self-diffusion coefficients and ¹H NMR relaxation times were obtained for water/n-pentane, water/n-decane, and water/n-hexadecane systems than bulk diffusion coefficients. An increase in Larmor frequency from 2.3 MHz to 400 MHz shows that longitudinal relaxation time (T₁) of confined oil has slightly larger differences at higher frequencies than the transverse relaxation time (T₂). At 400 MHz, n-alkanes (n-pentane, n-decane, and n-hexadecane) exhibit longer relaxation times than at smaller frequency values (2.3 and 22 MHz). Analysis of spin-spin and spin-lattice times provides relevant information about inter- and intramolecular relaxation mechanisms of water and oil as a function of geometry and width of the interface layer. These MD results suggest that the strength of confinement and geometry play a vital role in the diffusion and NMR relaxation properties of water/oil interfaces.

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.

NMR 1H-1H Dipole Relaxation in Fluids: Relaxation of Individual 1H-1H Pairs versus Relaxation of Molecular Modes

The intramolecular ¹H NMR dipole-dipole relaxation of molecular fluids has traditionally been interpreted within the Bloembergen-Purcell-Pound (BPP) theory of NMR intramolecular relaxation. The BPP theory draws upon Debye's theory for describing the rotational diffusion of the ¹H-¹H pair and predicts a monoexponential decay of the ¹H-¹H dipole-dipole autocorrelation function between distinct spin pairs. Using molecular dynamics (MD) simulations, we show that for both n-heptane and water this is not the case. In particular, the autocorrelation function of individual ¹H-¹H intramolecular pairs itself evinces a rich stretched-exponential behavior, implying a distribution in rotational correlation times. However, for the high-symmetry molecule neopentane, the individual ¹H-¹H intramolecular pairs do conform to the BPP description, suggesting an important role of molecular symmetry in aiding agreement with the BPP model. The intermolecular autocorrelation functions for n-heptane, water, and neopentane also do not admit a monoexponential behavior of individual ¹H-¹H intermolecular pairs at distinct initial separations. We suggest expanding the autocorrelation function in terms of modes, provisionally termed molecular modes, that do have an exponential relaxation behavior. With care, the resulting Fredholm integral equation of the first kind can be inverted to recover the probability distribution of the molecular modes. The advantages and limitations of this approach are noted.

Elucidating the 1H NMR Relaxation Mechanism in Polydisperse Polymers and Bitumen Using Measurements, MD Simulations, and Models

The mechanism behind the ¹H nuclear magnetic resonance (NMR) frequency dependence of T₁ and the viscosity dependence of T₂ for polydisperse polymers and bitumen remains elusive. We elucidate the matter through NMR relaxation measurements of polydisperse polymers over an extended range of frequencies (f₀ = 0.01-400 MHz) and viscosities (η = 385-102 000 cP) using T₁ and T₂ in static fields, T₁ field-cycling relaxometry, and T_1ρ in the rotating frame. We account for the anomalous behavior of the log-mean relaxation times T_1LM ∝ f₀ and T_2LM ∝ (η/T)^-1/2 with a phenomenological model of ¹H-¹H dipole-dipole relaxation, which includes a distribution in molecular correlation times and internal motions of the nonrigid polymer branches. We show that the model also accounts for the anomalous T_1LM and T_2LM in previously reported bitumen measurements. We find that molecular dynamics (MD) simulations of the T₁ ∝ f₀ dispersion and T₂ of similar polymers simulated over a range of viscosities (η = 1-1000 cP) are in good agreement with measurements and the model. The T₁ ∝ f₀ dispersion at high viscosities agrees with previously reported MD simulations of heptane confined in a polymer matrix, which suggests a common NMR relaxation mechanism between viscous polydisperse fluids and fluids under nanoconfinement, without the need to invoke paramagnetism.