Thermodynamic properties of the 3D Lennard-Jones/spline model

Bjørn Hafskjold,Karl Patrick Travis,Amanda Bailey Hass,Morten Hammer,Ailo Aasen,Øivind Wilhelmsen

doi:10.1080/00268976.2019.1664780

Abstract

The Lennard-Jones (LJ) spline potential is a truncated LJ potential so that both the pair potential and the force continuously approach zero at . We present a systematic map of the thermodynamic properties of the LJ spline model from molecular dynamics and Gibbs ensemble Monte Carlo simulations. Results are presented for gas/liquid, liquid/solid and gas/solid coexistence curves, the Joule-Thomson inversion curve, and several other thermodynamic properties. The critical point for the model is estimated to be and , respectively. The triple point is estimated to and . The coexistence densities, saturation pressure, and supercritical isotherms of the LJ spline model were fairly well represented by the Peng-Robison equation of state. We find that Barker-Henderson perturbation theory works less good for the LJ spline than for the LJ model. The first-order perturbation theory overestimates the critical temperature and pressure by about 10% and 90%, respectively. A second-order perturbation theory is not much better. Our assessment is that the mean compressibility approximation gives a poor representation of the second-order perturbation term. Our main conclusion is that we at the moment do not have a theory or model that adequately represents the thermodynamic properties of the LJ spline system.

Highlights

The Lennard-Jones (LJ) potential is a simple model capable of describing many real systems, in particular the noble gases
We have presented a comprehensive map of the thermodynamic properties of the Lennard-Jones spline (LJ/s) model obtained with molecular dynamics (MD) and Gibbs ensemble Monte Carlo (GEMC) simulations
We have estimated the critical point for the LJ/s model to be Tc∗ = 0.885 ± 0.002, Pc∗ = 0.075 ± 0.001, and n∗c = 0.332 ± 0.001, respectively

Summary

Introduction

The Lennard-Jones (LJ) potential is a simple model capable of describing many real systems, in particular the noble gases. When used in computer simulations, the intermolecular potential is truncated, typically at a distance of 2.5 − 5 molecular diameters. This truncation has little effect on the system’s structure, but in order to fully represent the LJ system’s thermodynamic properties, the contributions from the long-range. The LJ/s potential is a LJ potential truncated in a unique way. As such, it avoids the need for further specification and risk of ambiguity in how the potential is used in a simulation. The pair potential of the LJ/s model is σ r

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Results

Conclusion