Theory for spin-lattice relaxation in nematic liquid crystals

A theory is developed for spin-lattice relaxation in the nematic phase which includes both local and collective motion. It is found that the frequency dependence of the relaxation rate $T_1^{-1\mathrm{}}$ depends on the correlation time for the motion at the local molecular level, ${\tau }_c$. When $\omega {\tau }_c\ll 1$, where $\omega$ is the Larmor frequency, the theory gives the ${\omega }^{\frac{1}{2}}$ law characteristic of $p-\mathrm{azoxyanisole}$ (PAA). When $\omega {\tau }_c\lesssim 1$, the theory gives the more complex frequency dependence observed in the more viscous compound $4-n-\mathrm{methoxybenzylidene}-4^{\prime }n-\mathrm{butylanaline}$ (MBBA). A correlation is drawn between ${\tau }_c$ and the retarded relaxation time observed in electric dipole studies which corresponds to reorientation of the long molecular axis. The dependence of $T_1^{-1\mathrm{}}$ on the orientation of the director in the magnetic field is included in the calculation. A model is presented to include intermolecular effects on $T_1$.