Nuclear magnetic spin-lattice relaxation and molecular motion in solid white phosphorus and in liquid phosphorus

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Abstract
The 31P spin-lattice relaxation rates have been measured in solid white phosphorus and in liquid phosphorus over the temperature range 110 K to 400 K and at Larmor frequencies of 10 MHz and 30 MHz. The contributions to the measured relaxation rate from the different interactions have been separated. In the low-temperature, crystalline phase there are important contributions to the relaxation rate from the anisotropic chemical shielding and the intramolecular dipole-dipole interactions which are modulated by the reorientational motion of the molecule. Interference effects between these two interactions, which are important in liquids, are demonstrated to be quenched by the strong dipolar interactions in the solid. The reorientational correlation time is given by and the chemical shielding anisotropy by In the high-temperature, plastic-crystalline phase the reorientational correlation time is as obtained from the anisotropic chemical shielding relaxation rate which is separated from the other contributions by its quadratic dependence on the Larmor frequency. Using this τ R the intramolecular dipole-dipole relaxation rate is calculated. The contribution from the translational diffusion modulated intermolecular dipole-dipole interaction is calculated from the self-diffusion coefficient. When these contributions are subtracted from the observed relaxation rate, there remains a frequency-independent relaxation rate, proportional to 1/δ R , which is attributed to the spin-rotational interaction. The latter is shown to be quantitatively consistent with large-angle reorientational jumps of the P4 molecules by 120° about their C 3v axes. The relaxation in the liquid phase is dominated by the spin-rotational interaction and the expression representing the spin-rotational relaxation rate is the same as the one derived in the plastic-crystalline phase. The mechanism of molecular reorientation in the liquid is therefore the same as in the plastic-crystalline phase.

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