Proton NMR relaxation of the bipolar quasi-invariants of nematic methyl deuterated PAAD within the high temperature Redfield relaxation theory

SEGNORILE, BARBERIS, GONZÁLEZ, ZAMAR

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

aps

Año: 2006 vol. 74 p. 1702 - 1702

1063-651X

The high-temperature Redfield spin-lattice relaxation theory is used for calculating the relaxation times ofthe different dipolar quasi-invariants in an eight-spin system which represents methyl deuterated para-azoxyanisole ͑PAAd6͒ in the nematic phase. According to previous experiments, this system can be consideredas composed of weakly coupled pairs of strongly interacting spins, the ortho protons of the aromatic rings,thus, it possesses four quasi-invariants of the motion: Zeeman, dipolar intrapair and interpair, and singletorders. We write the set of coupled differential equations which describe the relaxation of the generalizedinverse spin temperatures of the four quasi-invariants. The relaxation constants are then calculated in terms ofexperimental two-spin spectral densities of the lattice motions. The relation between the multispin and thetwo-spin spectral densities is also deduced. Calculation shows that the Zeeman and singlet quasi-invariants areuncoupled from the dipolar ones, and that the relaxation time of the singlet order is much longer than those ofthe Zeeman and dipolar orders. The calculated cross relaxation rate between the dipolar orders through thelattice is small enough to be observable in the experiment. We also show that the nonsecular term associatedwith the collective motions dominates relaxation of the intrapair and interpair energies in PAAd6, while thelocal motions do not play a significant role, in qualitative agreement with the reported experimental behavior.The dipolar relaxation times predicted by the theory are significantly larger than the experimental ones, thedifference being even more pronounced for the interpair quasi-invariant. We show that the discrepancy cannotbe overcome neither by resorting to a realistic model for the spin system nor considering the various possiblecross-relaxation pathways among the quasi-invariants. This feature points out the high- temperature approxi-mation as a source of the discrepancy. We discuss the effect that slow and ultraslow molecular modes couldhave on the relaxation of the dipolar order.