NEMATIC ORDERING IN A SYSTEM OF RODS

We consider a system of rodlike molecules interacting with a model pair potential φ(rσ), where r is the center-of-mass distance and σ is an angle-dependent range parameter. It is shown that if the pair correlation function g scales as g(rσ), then the orientational degrees of freedom decouple from the translational ones to all orders in the density n. To lowest order in n, our free energy reduces to Onsager's virial-expansion result. The approximation transforms the system into a fluid of spheres interacting with a central potential φ(y) modulated by an angle-dependent excluded-volume term. The order parameter Q is predicted to have a discontinuity Qc at the transition point, which is independent of φ(y) but which slowly increases with the axial ratio k of the molecules. Calculations are done for the hard-rod fluid using the equation of state for the transformed hard-sphere fluid. A transition to an orientationally ordered state occurs at a critical value of the packing fraction ηc, which decreases with k. For k3.5, ηc is so high that the system tends to crystallize before the ordered liquid state is reached. Using perturbation theory, calculations are done for a soft-rod fluid, where the transformed system of spheres interacts with a potential φ(y)=εym. The transition temperature as a function of density and molecular shape is obtained, and it is shown that the order parameter obeys the scaling law Q=Q(η(εkt)m3). For m=12 this leads to good agreement with experiment and shows that most of the features of the transition can be explained with purely repulsive interactions. © 1979 The American Physical Society.