NMR Spin-Rotation Relaxation and Diffusion of Methane

TL;DR

This study uses molecular dynamics simulations to investigate NMR relaxation and diffusion of methane across different phases, developing new methods to analyze spin-rotation interactions and their relation to molecular diffusion.

Contribution

The paper introduces a minimization technique for computing angular velocity in non-rigid molecules and compares kinetic and diffusion models for NMR relaxation times in methane.

Findings

Simulated diffusion coefficients agree with experimental data.

Deviations from Langevin theory are quantified and linked to phase and density.

A new relation between relaxation time and diffusion coefficient is proposed.

Abstract

The translational-diffusion coefficient $D_T$ and the spin-rotation contribution to the $^1$H NMR relaxation time $T_{1J}$ for methane (CH$_4$) are investigated using MD (molecular dynamics) simulations, over a wide range of densities $\rho$ and temperatures $T$, spanning the liquid, supercritical, and gas phases. The simulated $D_T$ agree well with measurements, without any adjustable parameters in the interpretation of the simulations. A minimization technique is developed to compute the angular-velocity for non-rigid spherical molecules, which is used to simulate the autocorrelation function $G_{\!J}(t)$ for spin-rotation interactions. With increasing $D_T$ (i.e. decreasing $\rho$), $G_{\!J}(t)$ shows increasing deviations from the single-exponential decay predicted by the Langevin theory for hard spheres, and the deviations are quantified using inverse Laplace transforms of $G_{\!J}(t)$. $T_{1J}$ is derived from $G_{\!J}(t)$ using the kinetic model "km" for gases ($T_{1J}^{km}$), and the diffusion model "dm" for liquids ($T_{1J}^{dm}$). $T_{1J}^{km}$ shows better agreement with $T_1$ measurements at higher $D_T$, while $T_{1J}^{dm}$ shows better agreement with $T_1$ measurements at lower $D_T$. $T_{1J}^{km}$ is shown to dominate over the MD simulated $^1$H-$^1$H dipole-dipole relaxation $T_{1RT}$ at high $D_T$, while the opposite is found at low $D_T$. At high $D_T$, the simulated spin-rotation correlation-time $\tau_J$ agrees with the kinetic collision time $\tau_K$ for gases, from which a new relation $1/T_{1J}^{km} \propto D_T$ is inferred, without any adjustable parameters.