Theory of molecular motions in flexible nematogens

Liquid crystal phases are typically formed by molecules having several degrees of internal freedom. These systems exhibit, therefore, complex dynamics, with internal motions superimposed on the rotational diffusion of the whole molecule. The problem of the internal transitions has been treated in terms of a master equation for jumps between configurational sites, derived by projecting the multidimensional diffusion equation for the torsional variables on a suitable set of site functions. The coupling with the overall diffusion has been taken into account explicitly, by considering the conformational dependence of both the mean field torque and the molecular diffusion tensor. A Marcelja-like potential acting on the various molecular moieties has been used, and the frictional effects have been calculated for the different chain conformations. In this way, the rates for the internal transitions are orientation dependent, and the solution of the diffusional problem requires a matrix representation in the full space of angular and site functions. The nematogen 4-n-pentyl-4′-cyanobiphenyl, for which a large amount of experimental data is available from detailed NMR relaxation measurements, is taken as a reference system. The spectral densities of the relevant correlation functions for the deuterons in the various positions of the molecule have been calculated, for different degrees of ordering and different choices of the energetic and hydrodynamic parameters.