Equation of motion for two coupled spin-1 nuclei under a coherent and random Hamiltonian

Journal Article · Sat Oct 01 04:00:00 EDT 1994 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.50.9245· OSTI ID:7052093

ter Beek, L C; Burnell, E E ^[1]

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1. Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, British Columbia, V6T1Z1 (Canada)

The time dependence of the density operator for two coupled spin-1 nuclei, such as dideuterium D[sub 2] and dinitrogen [sup 14]N[sub 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 [ital ortho] and [ital para] species are not identical. We report the five independent rates for the [ital para] and the 21 independent rates for the [ital ortho] species. Due to cross-relaxation between spin orders which precess at a common frequency, the relaxation for the [ital ortho] configuration is not always single exponential. There are 15 cross-relaxation terms between certain spin orders for the [ital 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 [ital R][sub 10] for [ital ortho]- and [ital para]-dideuterium have been measured experimentally in patially oriented nematic solvents at 304 K using [sup 2]H-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 [ital ortho] and [ital para] configurations thereby facilitating the [ital R][sub 10] determination directly without multiexponential analysis. The [ital R][sub 10] of [ital para]-dideuterium is about twice that of [ital ortho]-dideuterium in all experiments. Using our calculated expressions for [ital R][sub 10] 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.

• OSTI ID: 7052093
• Journal Information: Physical Review, B: Condensed Matter; (United States), Journal Name: Physical Review, B: Condensed Matter; (United States) Vol. 50:13; ISSN PRBMDO; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

08 HYDROGEN
080800* -- Hydrogen-- Properties & Composition
CORRELATION FUNCTIONS
CRYSTALS
DEUTERIUM COMPOUNDS
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FLUIDS
FUNCTIONS
HYDROGEN COMPOUNDS
ISOTOPES
LIGHT NUCLEI
LIQUID CRYSTALS
LIQUIDS
MAGNETIC RESONANCE
MOLECULES
NITROGEN 14
NITROGEN COMPOUNDS
NITROGEN ISOTOPES
NUCLEAR MAGNETIC RESONANCE
NUCLEI
ODD-ODD NUCLEI
PARTIAL DIFFERENTIAL EQUATIONS
RELAXATION
RESONANCE
SOLVENT PROPERTIES
SPECTRAL DENSITY
SPECTRAL FUNCTIONS
SPIN-LATTICE RELAXATION
STABLE ISOTOPES
TEMPERATURE DEPENDENCE
TEMPERATURE RANGE
TEMPERATURE RANGE 0273-0400 K