Model for spin relaxation by correlated internal motions in liquid crystals

The effects of correlated internal rotations in an alkyl chain on the spectral densities of motion in liquid crystals are examined using the master-equation method. It is assumed that the overall reorientation of molecules is decoupled from the internal motions in their alkyl end chains. The pentyl chain that is attached to a cylindrical biphenyl core in 4-n-pentyl-4'-cyanobiphenyl (5CB) is studied as a specific example. The reorientation of a symmetric top in an anisotropic potential is described by the small-step rotational diffusion model. The equilibrium probability of each conformer, which is required to construct the transition-rate matrix for the master equation, is obtained using the Emsley-Luckhurst theory. The effects of the nematic mean field on the chain dynamics are discussed. Both J₁({ω}) and J₂(2{ω}) in 5CB are found to be frequency dependent, with J₂(2{ω}) being weaker.