Equation of State for the Lennard-Jones Fluid

Abstract

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.

Probing the link between residual entropy and viscosity of molecular fluids and model potentials

“…S19). The value of ε/k B was set equal to the critical temperature of the molecular fluid divided by 1.32 (T * c = 1.32 for the Lennard-Jones equation of state [61]; the repulsive WCA potential is fully repulsive and therefore does not have a critical point) and σ was left as an adjustable parameter. In this way, corresponding states between the Lennard-Jones analog (the repulsive WCA potential) and the molecular fluid are enforced.…”

Theoretical Prediction of Thermal Polarization

“…So far, we have treated f LJ as an input parameter and determined it numerically to match a density gradient. However, we may be able to predict the force acting on the LJ site from the equation of state (EOS), for which accurate fits exist [15,16]. Starting from the Gibbs-Duhem relation, we find an explicit expression for the external force in terms of the chemical potential µ (SI Sec.…”

Simulation‐based equations of state for the Lennard‐Jones fluid: Apparent success and hidden failure

“…Its functional form has extensively been adopted by other researchers 5,18,20,28,29 to reproduce extended molecular simulation data. The success of earlier models has motivated others to introduce more accurate MPS‐LJ EOSs with different functional forms 5,20‐23 …”

“…In the literature, developers have utilized common methods for evaluating and testing their MPS‐LJ EOSs. The most obvious initial evaluation was to reproduce the molecular simulation data of the LJ fluid with high accuracy 17,18,21‐23,29 . Another widely used method was to study the physical behaviors of various thermodynamic properties over a broad range of temperatures, pressures, and densities.…”

“…Another widely used method was to study the physical behaviors of various thermodynamic properties over a broad range of temperatures, pressures, and densities. The extrapolation behavior of these properties was also used as a criterion for evaluation 21 . Other authors 21 imposed constraints using uncommon quantities such as Gruneisen parameter 39,40 and phase identification parameter, 41 which are determined by some partial derivatives from the equation of state.…”