NMR spin-rotation relaxation and diffusion of methane

Abstract

The translational diffusion-coefficient and the spin-rotation contribution to the H NMR relaxation rate for methane (CH) are investigated using MD (molecular dynamics) simulations, over a wide range of densities and temperatures, spanning the liquid, supercritical, and gas phases. The simulated diffusion-coefficients 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 for spin-rotation interactions. With increasing diffusivity, the autocorrelation function shows increasing deviations from the single-exponential decay predicted by the Langevin theory for rigid spheres, and the deviations are quantified using inverse Laplace transforms. The H spin-rotation relaxation rate derived from the autocorrelation function using the "kinetic model" agrees well with measurements in the supercritical/gas phase, while the relaxation rate derived using the "diffusion model" agrees well with measurements in the liquid phase.H spin-rotation relaxation is shown to dominate over the MD-simulated H-H dipole-dipole relaxation at high diffusivity, while the opposite is found at low diffusivity. At high diffusivity, the simulated spin-rotation correlation time agrees with the kinetic collision time for gases, which is used to derive a new expression for H spin-rotation relaxation, without any adjustable parameters.

Spin Excitations of a Proximate Kitaev Quantum Spin Liquid Realized in Cu2IrO3

“…Distribution function Pð1=T 1 Þ of 1=T 1 at representative temperatures directly computed from the recovery data MðtÞ based on the inverse Laplace transform[41]. For clarity, the origin is shifted vertically except for 4.2 K. Pð1=T 1 Þ is centered around a single value of 1=T 1 above 60 K; the peak location at 77 and 200 K agrees very well with 1=T 1 estimated from the singlecomponent fit with Eq.…”

“…A more precise, model-independent way to investigate the spin dynamics with 1=T 1 under the presence of distributions in the relaxation mechanisms is to take the inverse Laplace transform of MðtÞ and directly deduce the distribution function Pð1=T 1 Þ of 1=T 1 [40,41]:…”

“…We numerically inverted MðtÞ [41] utilizing Tikhonov regularization (i.e., a smoothing factor) [44,45], and deduced the distribution function Pð1=T 1 Þ as summarized in Fig. 8 at representative temperatures.…”

“…7(a) does not depend on the details of how we estimate 1=T 1 from the nuclear spin recovery curve MðtÞ. The proof comes from the distribution function Pð1=T 1 Þ of 1=T 1 directly calculated from the inverse Laplace transform of the nuclear magnetization MðtÞ [40,41], as explained in Sec. III C.…”

Molecular dynamics simulations of $^1$H NMR relaxation in Gd$^{3+}$--aqua

“…MD simulation were previously used for like-spins, e.g. 1 H-1 H dipole-dipole pairs, such as liquid-state alkanes, aromatics, and water [47][48][49][50], as well as methane over a large range of densities [51]. In all these cases, good agreement was found between simulated and measured 1 H NMR relaxation and diffusion, without any adjustable parameters in the interpretation of the simulations.…”