An empirical equation of state correlation is proposed for the Lennard-Jones model fluid. The equation in terms of the Helmholtz energy is based on a large molecular simulation data set and thermal virial coefficients. The underlying data set consists of directly simulated residual Helmholtz energy derivatives with respect to temperature and density in the canonical ensemble. Using these data introduces a new methodology for developing equations of state from molecular simulation. The correlation is valid for temperatures 0.5 < T/Tc < 7 and pressures up to p/pc = 500. Extensive comparisons to simulation data from the literature are made. The accuracy and extrapolation behavior are better than for existing equations of state.

Literature data on thermophysical properties of the Lennard-Jones fluid, which were sampled with Molecular Dynamics and Monte Carlo simulations, were reviewed and assessed. The literature data was complemented by simulation data from the present work that was taken in regions in which previously only sparse data was available. Data on homogeneous state points (for given temperature T and density ρ: pressure p, thermal expansion coefficient α, isothermal compressibility β, thermal pressure coefficient γ, internal energy u, isochoric heat capacity c v , isobaric heat capacity c p , Grüneisen coefficient Γ, Joule-Thomson coefficient µ JT , speed of sound w, Helmholtz energy a, chemical potential µ, surface tension γ) was considered as well as data on the vapor-liquid equilibrium (for given T : vapor pressure p s , saturated liquid and vapor densities ρ and ρ , enthalpy of vaporization ∆h v). The entire set of available data, which contains about 35,000 data points, was digitalized and included in a database, which is made available in the electronic supplementary material of this paper. Different consistency tests were applied to assess the accuracy and precision of the data. The data on homogeneous states were evaluated point-wise using data from their respective 1 vicinity and equations of state. Approximately 5% of all homogeneous bulk data were discarded as outliers. The vapor-liquid equilibrium data were assessed by tests based on the compressibility factor, the Clausius-Clapeyron equation, and by an outlier test. Seven particularly reliable vapor-liquid equilibrium data sets were identified. The mutual agreement of these data sets is approximately ±1% for the vapor pressure, ±0.2% for the saturated liquid density, ±1% for the saturated vapor density, and ±0.75% for the enthalpy of vaporizationexcluding the region close to the critical point.

Rosenfeld proposed two different scaling approaches to model the transport properties of fluids, separated by 22 years, one valid in the dilute gas, and another in the liquid phase. In this work, we demonstrate that these two limiting cases can be connected through the use of a novel approach to scaling transport properties and a bridging function. This approach, which is empirical and not derived from theory, is used to generate reference correlations for the transport properties of the Lennard-Jones 12-6 fluid of viscosity, thermal conductivity, and self-diffusion. This approach, with a very simple functional form, allows for the reproduction of the most accurate simulation data to within nearly their statistical uncertainty. The correlations are used to confirm that for the Lennard-Jones fluid the appropriately scaled transport properties are nearly monovariate functions of the excess entropy from low-density gases into the supercooled phase and up to extreme temperatures. This study represents the most comprehensive metastudy of the transport properties of the Lennard-Jones fluid to date.

An equation of state is developed for the Lennard-Jones model fluid, truncated and shifted at r c = 2.5σ . The underlying dataset contains thermodynamic properties at 706 state points including pressure, residual internal energy, first volume derivative of the residual internal energy, and residual isochoric heat capacity as a function of temperature and density. The equation of state is explicit in terms of the Helmholtz energy, allowing the determination of any thermodynamic property by differentiation. It is valid for temperatures 0.6 < T /T c < 10 and pressures p/ p c < 70. High accuracy and good extrapolation behavior of the equation of state are established.

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