An equation of state for Stockmayer fluids based on a perturbation theory for dipolar hard spheres

We develop a perturbation theory for the difference between the Helmholtz energy of a Stockmayer fluid, i.e., a fluid interacting by a Lennard-Jones plus point-dipole potential, and a Lennard-Jones fluid. We show that the difference can be approximated by the perturbational Helmholtz energy contribution of a dipolar hard-sphere fluid with a suitably chosen effective hard-sphere diameter, relative to a hard-sphere fluid with the same effective diameter. We analyze both a third and fourth order perturbation theory, both written as Padé approximations. Several recipes for calculating the hard-sphere diameter are investigated; we find that the Weeks-Chandler-Andersen diameter is most suitable. Results of the perturbation theory are shown to be in good agreement with reference data for the Helmholtz energy, internal energy, and isochoric heat capacity as obtained from molecular simulations performed in this work and to vapor-liquid equilibrium data from the literature. Theoretical predictions of the proposed model are compared to results from the perturbation theory of Gubbins and Twu [Chem. Eng. Sci. 33, 863 (1978)], which is a theory based on a Lennard-Jones reference fluid. We find the theories are in good agreement. Our approach can easily be applied to van der Waals potentials, other than Lennard-Jones potentials. If a dipolar Mie fluid is considered, the approach merely requires calculation of the effective hard-sphere diameter for a Mie potential. We further note that the approach has a reduction in the variable space of the underlying correlation integrals, i.e., the correlation functions of a hard-sphere fluid depend on density only, whereas the Lennard-Jones reference correlation functions depend on density and temperature.