Equation-Of-Motion For 2 Coupled Spin-1 Nuclei Under A Coherent And Random Hamiltonian

The time dependence of the density operator for two coupled spin-1 nuclei, such as dideuterium D2 and dinitrogen N-14(2), under the second rank intramolecular dipolar and the first rank spin-rotation Hamiltonians has been derived. It is shown that the relaxation rates for the ortho and para species are not identical. We report the five independent rates for the para and the 21 independent rates for the ortho species. Due to cross relaxation between spin orders which precess at a common frequency, the relaxation for the ortho configuration is not always single exponential. There are 15 cross-relaxation terms between certain spin orders for the ortho species in the slow-motion regime. The complexity of our coupled spin system is discussed for the solid and the Jeener-Broekaert echo sequences. The Zeeman spin-lattice relaxation rates R10 for ortho- and para-dideuterium have been measured experimentally in partially oriented nematic solvents at 304 K using H-2 NMR. The solvents used are PCH-7, 1132, and a 55 wt% 1132/EBBA mixture. These oriented solvents make it possible to separate the resonances of the ortho and para configurations thereby facilitating the R10 determination directly without multiexponential analysis. The R10 of para-dideuterium is about twice that of ortho-dideuterium in all experiments. Using our calculated expressions for R10 based on quadrupolar, dipolar, and spin-rotation interactions, and performing the proper averaging over the rotational states, we obtain excellent agreement with our experimental results. Good agreement has been obtained with published low-temperature studies as well.