Nuclear Spin-Lattice Relaxation in Liquid Crystals by Fluctuations in the Nematic Director

We show that a finite cutoff of the hydrodynamic modes (order fluctuations) in the nematic liquid-crystalline phase explains the measured spin-lattice relaxation in this phase. A calculation of $T_1$ based upon such a cutoff and a fit to the data of MBBA (4-$n$-methoxybenzylidene-4′ -$n$-butylaniline) show this cutoff to be 1 molecular length. At $T_{1\rho }$ frequencies, far from the cutoff, order fluctuations are shown to be the dominant relaxation mechanism. This is done by comparing the predicted angular dependence of $T_{1\rho }$ for these modes with that measured in MBBA.