The NMR line shape of a gas of hydrogen molecules in nanopores

Abstract

We consider a closed nanopore filled with hydrogen gas in an external magnetic field. Only hydrogen molecules with spin I = 1 contribute to nuclear magnetic resonance (NMR) spin dynamics. Rapid molecular diffusion leads to partial averaging of dipole-dipole interactions (DDI) of spins I = 1 of different molecules. A method for the calculation of the NMR line shape of a hydrogen gas in nanopores is developed. Significant technical difficulties in calculations of the NMR line shape of the system of spins I = 1 coupled by DDI can be overcome with the introduction of a self-interaction with an averaged DDI coupling constant. The accuracy of this procedure is proportional to \( 1/\sqrt N \), where N is the number of hydrogen molecules in the nanocavity. In this approximation the NMR line is Gaussian. The second and fourth moments of the NMR line shape are calculated both from the known line shape and with the Van Vleck theory. They coincide up to the terms of the order of 1/N. The obtained results are in good agreement with experimental data for thin films with ellipsoidal nanopores. The developed theory allows one to extract information about sizes, shapes and orientations of nanopores in solids.