AN ACCURATE INTEGRAL-EQUATION FOR MOLECULAR FLUIDS .5. HARD PROLATE ELLIPOSIDS OF REVOLUTION

Percus Yevick (PY), hypernetted chain (HNC) and modified Verlet (VM) i ntegral equation theories are used to study the structure and thermody namic properties of hard prolate ellipsoids of revolution in the isotr opic fluid region. Results for the spherical harmonic coefficients of the pair distribution function and for the compressibility factors are compared with new Monte Carlo results reported in this work for lengt h-to-breadth ratios a/b = 2, 3, and 5. For a/b = 2 and 3, the VM harmo nic coefficients are in good agreement with the simulation results and arc better than those of PY and HNC theories. For a/b = 5, HNC theory gives numerically precise harmonic coefficients, the VM results being only slightly inferior, a behaviour consistent with that found previo usly for very long spherocylinders. VM theory gives equation of state results in excellent agreement with the simulation data at all values of a/b and densities, whereas the PY and HNC results are generally poo r. The thermodynamic consistency of each of the PY, HNC and VM theorie s is tested by comparing the compressibility factors calculated from t he pressure and compressibility equations. A recently derived formula for the chemical potential is used as another consistency test of the theories. At all state points considered, the consistency of VM theory is excellent and much better than that of PY and HNC theories. The or ientational spinodal density eta(s) of the isotropic fluid phase was e stimated by extrapolating the inverse Kerr constant to zero. We find t hat VM theory gives values of eta(s) that are higher than the HNC valu es and lower than the PY values. The correct values of eta(s) likely l ie between the HNC and VM results.