Thermodynamics of fluids obtained by mapping the collision properties

A method for deriving theoretical relations for thermodynamic properties of simple model fluids is developed. The method uses mean collision properties to write the thermodynamics of a system in terms of the equation of state of an equivalent system used as reference. The equivalent fluid is formed by particles interacting with a square-well (SW) potential whose properties are known accurately. The equivalence to the SW fluid is made by means of mapping equations for the SW potential parameters. Solution of the mapping equations at a few state points plus the use of simple parametric equations for the SW potential parameters allows us to write the equation of state (EOS) of the fluid. The EOS derived by this method illuminates the relation between thermodynamic properties of the fluid and relevant features of the intermolecular potential, and gives reliable predictions of the thermodynamics including the liquid-vapor equilibrium. This is tested by obtaining the EOS of the Lennard-Jones fluid and comparing it with very accurate empirical EOS available for this system. The EOS for fluids with a commonly used interaction potential (EXP6) are derived and used to discuss the liquid-vapor equilibria of these systems, with the particular attention to deviations from corresponding-state behavior.