Theory for the reorientational dynamics in glass-forming liquids

The mode-coupling theory for ideal liquid-glass transitions is extended so that the structural relaxation for the reorientational degrees of freedom of a linear molecule, which is immersed in a system of spherical particles, can be described. Closed equations of motion for the correlation functions formed with tensor density fluctuations are derived, which deal with the molecule's translational and reorientational motion. From these equations the nonergodicity parameters of a hard dumbbell molecule are calculated, which quantify its arrest in a hard-sphere glass. For top-down symmetric molecules it is shown that the odd-angular-momentum variables can exhibit an ergodic-to-nonergodic transition, characterized by a continuous increase of the Edwards-Anderson parameters near the critical points.