Orientational pair correlations in dilute solutions of rodlike molecules

The orientational correlation times for the first and second rank spherical harmonics of single particle and collective orientational variables are calculated assuming that the rotorlike molecules undergo correlated rotational and translational motion. Rotation–translation coupling arises through the Oseen tensor operating between the rotors and introduces a concentration dependence in the single particle and collective times. A linear concentration dependence stems from the averaged Liouville operator, as found previously, and through the memory function, whose direct calculation has been hitherto ignored. Even in the presence of the memory function, the Keyes–Kivelson ratio of the collective and single particle correlation times is unaffected to linear order in the concentration of the tagged molecules. However, the memory function and the associated torque correlation function incorporate a linearly increasing concentration dependence in the single particle times.