Some notes on the dynamics of nematic liquid crystals

Abstract

The hydrodynamic equations for a nematic liquid crystal involve not only the densities of the conserved variables but also director fluctuations. Mori's generalized Langevin equation is used to obtain expressions for the correlation functions of the hydrodynamic variables and we give the Green—Kubo relations for the transport coefficients. The approach is very similar to that used previously by Förster, but there are some differences and these are discussed. Careful consideration is given to what the correct microscopic expression for director fluctuations might be, and to a potential plateau problem that might arise when attempting to calculate transport coefficients associated with director fluctuations from computer simulation. Both these topics may be of interest to computer simulators. Finally, a brief account is given of mode-coupling effects in the nematic phase and the possible effects of these on the long time behaviour of several time correlation functions.