Theory for spin-lattice relaxation in nematic liquid crystals

Abstract

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 ${T}_{1}^{\ensuremath{-}1}$ depends on the correlation time for the motion at the local molecular level, ${\ensuremath{\tau}}_{c}$. When $\ensuremath{\omega}{\ensuremath{\tau}}_{c}\ensuremath{\ll}1$, where $\ensuremath{\omega}$ is the Larmor frequency, the theory gives the ${\ensuremath{\omega}}^{\frac{1}{2}}$ law characteristic of $p\ensuremath{-}\mathrm{azoxyanisole}$ (PAA). When $\ensuremath{\omega}{\ensuremath{\tau}}_{c}\ensuremath{\lesssim}1$, the theory gives the more complex frequency dependence observed in the more viscous compound $4\ensuremath{-}n\ensuremath{-}\mathrm{methoxybenzylidene}\ensuremath{-}{4}^{\ensuremath{'}}n\ensuremath{-}\mathrm{butylanaline}$ (MBBA). A correlation is drawn between ${\ensuremath{\tau}}_{c}$ and the retarded relaxation time observed in electric dipole studies which corresponds to reorientation of the long molecular axis. The dependence of ${T}_{1}^{\ensuremath{-}1}$ on the orientation of the director in the magnetic field is included in the calculation. A model is presented to include intermolecular effects on ${T}_{1}$.