Discrete perturbation theory for Mie potentials

The discrete perturbation approach in its version for soft-core continuous potentials is applied to a family of Mie (α, γ) potentials. Within this approach, once a discrete version of the potential is given, only the knowledge of the square-well Helmholtz free-energy perturbation terms are required to obtain the Helmholtz free-energy for the discrete version of the original potential. The free-energy so obtained is analytical and expressed as a function of density, temperature and the intermolecular parameters, and from it all thermodynamic properties can be obtained in a straightforward way. By varying the exponents α and γ some illustrative cases of Mie fluids are considered. Single state pressures and the vapor-liquid phase diagram are obtained and compared with simulation data. The best performance of this equation of state is achieved at supercritical states and when the vapor-liquid phase diagram appears at not so low temperatures. Within this approach the corresponding states principle is analyzed. The methodology presented can be useful to study other families of potentials models for simple and complex fluids.