Self-diffusion in the nematic and smectic a phases of an aligned fluid of hard spherocylinders

The short to moderate time behaviour of the velocity-time correlation function (TCF) has been examined by molecular dynamics and by kinetic theory for a nematic and a smectic A liquid crystalline phase of perfectly aligned spherocylinders in three dimensions. The kinetic theory is a generalized Langevin formulation in which the uncorrelated collisions are accommodated by means of an Enskog friction and the correlated caging recollisions via the memory function. In the nematic phase, the TCFs both parallel and perpendicular to the director are well described by the Enskog theory alone. In the smectic A phase, a second order parameter arises and the dynamics along the director are strongly caged (i.e., indicating the importance of correlated backscattering), whereas the perpendicular motions still adhere to an uncorrelated collision scenario. The interesting questions of the existence and the nature of long-time tails in the TCFs are left for a future study.