Analytical equations of state for triangle-well and triangle-shoulder potentials

In this work we apply the Discrete Perturbation Theory (Benavides and Gil-Villegas, 1999) to obtain an equation of state for the cases of attractive and repulsive triangle potentials of variable range. This technique provides an analytical expression for the Helmholtz free-energy explicit in density, temperature and in the parameters that characterize the intermolecular interaction. We present single state thermodynamic properties for both potentials and vapor-liquid diagrams (attractive case) for different potential ranges and compare with available and new simulation data. For the triangle-well potential, this equation is accurate in a wider range interval (ranges >1.2) than previous theoretical results and to our knowledge it is the first analytical equation of state for the triangle-shoulder potential.