title: Proton NMR relaxation of the dipolar quasi-invariants of nematic methyl deuterated para-azoxyanisole within the high-temperature Redfield relaxation theory.
abstract: The high-temperature Redfield spin-lattice relaxation theory is used for calculating the relaxation times of the different dipolar quasi-invariants in an eight-spin system which represents methyl deuterated para-azoxyanisole (PAAd6) in the nematic phase. According to previous experiments, this system can be considered as 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 singlet orders. We write the set of coupled differential equations which describe the relaxation of the generalized inverse spin temperatures of the four quasi-invariants. The relaxation constants are then calculated in terms of experimental two-spin spectral densities of the lattice motions. The relation between the multispin and the two-spin spectral densities is also deduced. Calculation shows that the Zeeman and singlet quasi-invariants are uncoupled from the dipolar ones, and that the relaxation time of the singlet order is much longer than those of the Zeeman and dipolar orders. The calculated cross relaxation rate between the dipolar orders through the lattice is small enough to be observable in the experiment. We also show that the nonsecular term associated with the collective motions dominates relaxation of the intrapair and interpair energies in PAAd6, while the local 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, the difference being even more pronounced for the interpair quasi-invariant. We show that the discrepancy cannot be overcome neither by resorting to a realistic model for the spin system nor considering the various possible cross-relaxation pathways among the quasi-invariants. This feature points out the high- temperature approximation as a source of the discrepancy. We discuss the effect that slow and ultraslow molecular modes could have on the relaxation of the dipolar order.
authors.affiliation: Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba M. Allende y H. de la Torre-Ciudad Universitaria, X5016LAE Córdoba, Argentina.
authors.forename: H H
authors.initials: HH
authors.lastname: Segnorile
authors.forename: L
authors.initials: L
authors.lastname: Barberis
authors.forename: C E
authors.initials: CE
authors.lastname: González
authors.forename: R C
authors.initials: RC
authors.lastname: Zamar