On the applicability of the Redfield high-temperature theory for proton dipolar order relaxation in liquid crystals

Abstract

Nuclear magnetic resonance experiments on the Larmor frequency dependence of the intrapair dipolar order relaxation time T1D showed the existence of discrepancies between the usual two-spin theory and the experimental data. Field-cycling experiments of T1D in methyl deuterated para azoxyanisole (PAA-d6) in the nematic phase [J. Chem. Phys. 110, 8155 (1999)] showed that the difference cannot be assigned to the common assumption of isolated spin pairs or to the neglecting of the alkyl chain protons in the theoretical interpretation. Though the applicability of the spin temperature and short correlation time assumptions have not been justified for nematic liquid crystals, they have been used in all the available theoretical approaches for dipolar order relaxation. In this work, we calculate T1D of PAA-d6 within the Redfield high-temperature theory of spin–lattice relaxation but avoid the usual assumptions of short correlation times and random phase. First, we find that this fact does not alter the expression for T1D in the simple case of an ensemble of isolated spin pairs. Then we take the four benzene protons as the spin system and find that this refinement gives no relevant contribution able to explain the discrepancies between theory and experiments. Also, we find that the random phase assumption becomes redundant in the calculation of T1D, whenever the relevant spin Hamiltonian is nondegenerate. Thus, in these cases the spin temperature hypothesis is justified in liquid crystals, where the spin system contains few spins. We conclude that the Redfield high-temperature relaxation theory fails to describe T1D in thermotropic liquid crystals, since it underestimates the prominent role of the slow cooperative motions.