Characteristic Curves of the Lennard-Jones Fluid
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Characteristic Curves of the Lennard‑Jones Fluid Simon Stephan1 · Ulrich K. Deiters2 Received: 21 May 2020 / Accepted: 25 July 2020 / Published online: 20 August 2020 © The Author(s) 2020
Abstract 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. Keywords Lennard-Jones fluid · Equation of state · Characteristic curves · Virial coefficients
1 Introduction The Lennard-Jones (12,6) potential [1, 2] has been extensively used since the early days of computer simulation [3–6] for the modeling of repulsive and dispersive interactions of simple fluids. It is probably the most frequently investigated monomer model fluid in molecular simulation [7]. The Lennard-Jones (LJ) potential can be favorably used for testing new theories and simulation methods, e.g., for mixtures, phase changes, non-equilibrium phenomena, and interfaces between phases
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s1076 5-020-02721-9) contains supplementary material, which is available to authorized users. * Simon Stephan [email protected]‑kl.de 1
Laboratory of Engineering Thermodynamics (LTD), TU Kaiserslautern, Erwin‑Schrödinger‑Straße 44, 67663 Kaiserslautern, Germany
2
Institute of Physical Chemistry, University of Cologne, Greinstraße 4‑6, 50939 Cologne, Germany
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International Journal of Thermophysics (2020) 41:147
[8–19]. Also, the Lennard-Jones potential is often used as a starting point for the development of many state-of-the-art force fields for complex molecules [20–22]. The Lennard-Jones potential is defined as [( ) ( )6 ] 𝜎 𝜎 12 − uLJ (r) = 4𝜀 , (1) r r where 𝜀 and 𝜎 are the energy and size parameter, respectively. The distance between two particles is denoted by r. Different versions of the LJ potential are used in the literature depending on the treatment of the long–range interactions, which has an important influence on the thermodynamic properties [23–32]. The present work is limited to the ’full’ Lennard-Jones potential, i.e., including long-range correction schemes [33]. Analytical model functions of the LJ fluid for the description of the thermodynamic properties, i.e., equations of state (EOS), are crucial for many applications, e.g., the development of theories for more complex fluids like polymers, electrolyte solution
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