Abstract
We consider a system of rodlike molecules interacting with a model pair potential , where is the center-of-mass distance and is an angle-dependent range parameter. It is shown that if the pair correlation function scales as , then the orientational degrees of freedom decouple from the translational ones to all orders in the density . To lowest order in , 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 modulated by an angle-dependent excluded-volume term. The order parameter is predicted to have a discontinuity at the transition point, which is independent of but which slowly increases with the axial ratio 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 , which decreases with . For , 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 . 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 . For this leads to good agreement with experiment and shows that most of the features of the transition can be explained with purely repulsive interactions.
- Received 12 May 1978
DOI:https://doi.org/10.1103/PhysRevA.19.1225
©1979 American Physical Society