Review and Comparison of Equations of State for the Lennard-Jones Fluid

The Lennard-Jones (LJ) potential is widely used for describing simple fluids; it is also a point of departure for developing models of complex fluids. Thermodynamic properties of the LJ fluid have been studied by molecular simulations by many authors and a critical review of the available data, which comprises about 35,000 data points, has been published recently [J. Chem. Inf. Mod. 59 (2019) 4248–4265]. The importance of the LJ fluid has also triggered the development of a large number of equations of state (EOS). In the present work, 20 LJ EOS were critically assessed by comparing their results with consolidated data from computer experiments. A large variety of thermophysical properties was considered: vapor pressure; saturated densities; enthalpy of vaporization; critical properties; thermal, caloric, and entropic properties at homogeneous state points; and second and third virial coefficients. It was found that none of the available LJ EOS meets the following two criteria: (1) it does not yield unphysical artifacts when used for extrapolations, and (2) it describes data from computer experiments within their statistical uncertainty in most fluid regions. Furthermore, a re-parameterization of the monomer term of the PC-SAFT EOS was carried out by fitting it to data of the LJ fluid. The new LJ EOS yields good results for the LJ fluid, but does not outperform the best existing LJ EOS.

Characteristic Curves of the Lennard-Jones Fluid

Equations of state based on intermolecular potentials are often developed about the Lennard-Jones (LJ) potential. Many of such EOS have been proposed in the past. In this work, 20 LJ EOS were examined regarding their performance on Brown’s characteristic curves and characteristic state points. Brown’s characteristic curves are directly related to the virial coefficients at specific state points, which can be computed exactly from the intermolecular potential. Therefore, also the second and third virial coefficient of the LJ fluid were investigated. This approach allows a comparison of available LJ EOS at extreme conditions. Physically based, empirical, and semi-theoretical LJ EOS were examined. Most investigated LJ EOS exhibit some unphysical artifacts.

Method for constructing the fundamental equation of state that takes into account the peculiarities of the substance behaviour in a wide vicinity of the critical point

On the basis of the phenomenological theory of the critical point and the Benedek hypothesis, an expression for the Helmholtz free energy F with scale functions in the density-temperature variables has been developed. The proposed free energy equation has been tested on the example of constructing the fundamental equation of state of 2,3,3,3-tetrafluoropropene (R1234yf). By comparison with the known experimental data on the equilibrium properties of R1234yf – density and pressure on the phase equilibrium line, p-ρ-T-data in the single-phase region, the second and third virial coefficients, isochoric heat capacity, isobaric heat capacity and the sound velocity – the operating range of the equation of state of R1234yf has been established according to temperature from 220 K to 420 K and pressure up to 20 MPa.