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

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.

Unified Description of Proton NMR Relaxation in Water, Acetonitrile, and Methane from Molecular Dynamics Simulations in the Liquid, Supercritical, and Gas Phases

A comprehensive calculation of proton NMR relaxation in water, acetonitrile, and methane across a wide range of the phase diagram is provided via ab initio and force-field-based molecular dynamics simulations. The formalism used for the spin-rotation (SR) contribution to relaxation is developed for use with any molecular symmetry and utilizes the full molecular SR tensors, which are calculated from first-principles via Kohn-Sham (KS) DFT. In combination with calculations of the dipolar contribution, near-quantitative agreement with total measured relaxation rates is achieved.

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.

Hydrated Collagen: Where Physical Chemistry, Medical Imaging, and Bioengineering Meet

It is well-known that collagen is the most abundant protein in the human body; however, what is not often appreciated is its fascinating physical chemistry and molecular physics. In this Perspective, we aim to expose some of the physicochemical phenomena associated with the hydration of collagen and to examine the role collagen's hydration water plays in determining its biological function as well as applications ranging from radiology to bioengineering. The main focus is on the Magic-Angle Effect, a phenomenon observed in Nuclear Magnetic Resonance (NMR) spectroscopy and Magnetic Resonance Imaging (MRI) of anisotropic collagenous tissues such as articular cartilage and tendon. While the effect has been known in NMR and MRI for decades, its exact molecular mechanism remains a topic of debate and continuing research in scientific literature. We survey some of the latest research aiming to develop a comprehensive molecular-level model of the Magic-Angle Effect. We also touch on other fields where understanding of collagen hydration is important, particularly nanomechanics and mechanobiology, biomaterials, and piezoelectric sensors.

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.