Nuclei with non-zero spin, such as the hydrogen nuclei, act like tiny “magnets” that can be excited by suitably applied external magnetic fields. The phenomena by which the “magnets” return to equilibrium is termed Nuclear Magnetic Resonance (NMR) relaxation, a process characterized by two time constants T1 and T2, corresponding to relaxation in the longitudinal and transverse directions, respectively. T1 and T2 are dependent on the equilibrium structure and dynamics of the system. This feature provides an avenue to probe matter non-destructively, with applications ranging from medical imaging to well logging.

The traditional interpretation of T1 and T2 in liquids has long relied on rather severe assumptions about the fluid structure and dynamics, such as treating molecules as hard spheres and the magnetic dipoles as freely rotating. In this work, we remove these approximations by leveraging atomistic simulations that can accurately predict the structure and dynamics of fluids. By relating the auto-correlation of magnetic dipole-dipole interactions to NMR relaxation, we revisit the interpretation of NMR relaxation in bulk and confined fluids.

In the fast-motion regime, where fluid viscosity is low and traditional theories would be expected to hold, we instead find that the relaxation is sensitively dependent on the shape and internal motions of the molecule. To explore the slow-motion regime where fluid viscosity is high, we studied heptane confined in a polymer matrix and the glass-former glycerol across a range of temperatures. For heptane in a polymer matrix, the simulated relaxation times show excellent agreement with measurements; importantly, we find that confinement greatly enhances the NMR relaxation, and there is no need to invoke the physics of paramagnetism, as is often done. For glycerol, simulations once again capture measurements, and in the high viscosity regime, in contrast with polymers, the relaxation rate decreases due to the hydrogen bonding network. In the presence of a genuine paramagnetic ion, Gadolinium (III), a well-known contrast agent used in Magnetic Resonance Imaging (MRI), simulations can capture the NMR relaxivity at MRI frequencies, with expected discrepancies at low frequencies attributable to electron spin relaxation effects.

Overall, this work exposes the limitations of traditional theories but also shows that by using theory and simulations, one can enhance the interpretation of available experiments, opening new avenues to probe matter using relaxation methods.