A new perturbation expansion for fluids of nonspherical molecules

Abstract

The free energy of a fluid composed of nonspherical molecules is expanded about that for a reference fluid of rigid, nonspherical molecules. The expansion procedure involved separating the intermolecular pair potential into repulsive and attractive regions for each set of relative orientations, and is similar to that used by Weeks, Chandler, and Andersen for monatomic fluids. The properties of the reference system are evaluated using the expansion of Bellemans. Calculated thermodynamic properties are compared with Monte Carlo results for fluids with a potential u_LJ + u_a, where u_LJ is the Lennard‐Jones model and u_a is either the point dipole, point quadrupole, or an anisotropic overlap potential. For dipoles, agreement is satisfactory for values of the reduced dipole moment μ/(εσ³)^1/2 up to about 1, while for quadrupoles good agreement is found for Q/(εσ⁵)^1/2 up to about 0.8. For larger multipole moments the Bellemans expansion fails. For anisotropic overlap potentials the method seemed satisfactory for all values of anisotropic strength tested. A simplified form of the perturbation expansion is also obtained by introducing a generalized van der Waals model. The resulting equation of state is tested against data for CO₂ in the dense gas and liquid regions, including the vapor–liquid equilibrium region. The functional form of this equation gives an accurate representation of the data for all temperatures and densities except those in the critical region, and also for the low temperature dilute gas.