Modified Lennard-Jones Potentials with a Reduced Temperature-Correction Parameter for Calculating Thermodynamic and Transport Properties: Noble Gases and Their Mixtures (He, Ne, Ar, Kr, and Xe)

The three-parameter Lennard-Jones (12-6) potential function is proposed to calculate thermodynamic property (second virial coefficient) and transport properties (viscosity, thermal conductivity, and diffusion coefficient) of noble gases (He, Ne, Ar, Kr, and Xe) and their mixtures at low density. Empirical modification is made by introducing a reduced temperature-correction parameter τ to the Lennard-Jones potential function for this purpose. Potential parameters (σ, ε, and τ) are determined individually for each species when the second virial coefficient and viscosity data are fitted together within the experimental uncertainties. Calculated thermodynamic and transport properties are compared with experimental data by using a single set of parameters. The present study yields parameter sets that have more physical significance than those of second virial coefficient methods and is more discriminative than the existing transport property methods in most cases of pure gases and of gas mixtures. In particular, the proposed model is proved with better results than those of the two-parameter Lennard-Jones (12-6) potential, Kihara Potential with group contribution concepts, and other existing methods.

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Theoretical Assessment of Compressibility Factor of Gases by Using Second Virial Coefficient

Zeitschrift für Naturforschung A ◽

10.1515/zna-2017-0225 ◽

2018 ◽

Vol 73 (2) ◽

pp. 121-125

Author(s):

Bahtiyar A. Mamedov ◽

Elif Somuncu ◽

Iskender M. Askerov

Keyword(s):

Virial Coefficient ◽

Second Virial Coefficient ◽

Compressibility Factor ◽

Analytical Approximation ◽

Accurate Evaluation ◽

Numerical Examples ◽

Lennard Jones ◽

Theoretical Assessment ◽

Good Agreement

AbstractWe present a new analytical approximation for determining the compressibility factor of real gases at various temperature values. This algorithm is suitable for the accurate evaluation of the compressibility factor using the second virial coefficient with a Lennard–Jones (12-6) potential. Numerical examples are presented for the gases H2, N2, He, CO2, CH4 and air, and the results are compared with other studies in the literature. Our results showed good agreement with the data in the literature. The consistency of the results demonstrates the effectiveness of our analytical approximation for real gases.

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Quantum Mechanical Second Virial Coefficient of a Lennard‐Jones Gas. Helium

The Journal of Chemical Physics ◽

10.1063/1.1671663 ◽

1969 ◽

Vol 50 (9) ◽

pp. 4034-4055 ◽

Cited By ~ 78

Author(s):

M. E. Boyd ◽

S. Y. Larsen ◽

J. E. Kilpatrick

Keyword(s):

Virial Coefficient ◽

Second Virial Coefficient ◽

Quantum Mechanical ◽

Lennard Jones

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Evaluation of Quantum Corrections to Second Virial Coefficient with Lennard-Jones (12-6) Potential

Journal of Physics Conference Series ◽

10.1088/1742-6596/766/1/012010 ◽

2016 ◽

Vol 766 ◽

pp. 012010 ◽

Cited By ~ 1

Author(s):

B. A. Mamedov ◽

E. Somuncu

Keyword(s):

Virial Coefficient ◽

Second Virial Coefficient ◽

Quantum Corrections ◽

Lennard Jones

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Quantum second virial coefficient of a one-dimensional Lennard-Jones gas

Molecular Physics ◽

10.1080/00268976500100101 ◽

1965 ◽

Vol 9 (1) ◽

pp. 77-85 ◽

Cited By ~ 2

Author(s):

John R. Sams

Keyword(s):

Virial Coefficient ◽

Second Virial Coefficient ◽

One Dimensional ◽

Lennard Jones

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An Estimation of Thermodynamic and Transport Properties of Cryogenic Hydrogen Using Classical Molecular Simulation

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 2, Fora ◽

10.1115/ajk2011-36005 ◽

2011 ◽

Author(s):

Hiroki Nagashima ◽

Takashi Tokumasu ◽

Shin-ichi Tsuda ◽

Nobuyuki Tsuboi ◽

Mitsuo Koshi ◽

...

Keyword(s):

Ab Initio ◽

Transport Properties ◽

Molecular Simulation ◽

Potential Model ◽

Classical Method ◽

Quantum Effect ◽

Corresponding States ◽

Density Region ◽

Lennard Jones ◽

Thermodynamic And Transport Properties

In this paper, we estimated the thermodynamic and transport properties of cryogenic hydrogen using classical molecular simulation to clarify the limit of classical method on the estimation of those properties of cryogenic hydrogen. Three empirical potentials, the Lennard-Jones (LJ) potential, two-center Lennard-Jones (2CLJ) potential, and modified Buckingham (exp-6) potential, and an ab initio potential model derived by the molecular orbital (MO) calculation were applied. Molecular dynamics (MD) simulations were performed across a wide density-temperature range. Using these data, the equation of state (EOS) was obtained by Kataoka’s method, and these were compared with NIST (National Institute of Standards and Technology) data according to the principle of corresponding states. Moreover, we investigated transport coefficients (viscosity coefficient, diffusion coefficient and thermal conductivity) using time correlation function. As a result, it was confirmed that the potential model has a large effect on the estimated thermodynamic and transport properties of cryogenic hydrogen. On the other hand, from the viewpoint of the principle of corresponding states, we obtained the same results from the empirical potential models as from the ab initio potential, showing that the potential model has only a small effect on the reduced EOS: the classical MD results could not reproduce the NIST data in the high-density region. This difference is thought to arise from the quantum effect in actual liquid hydrogen.

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The analytical evaluation of the first-order density cluster integral in the radial distribution function

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1970.0212 ◽

1970 ◽

Vol 320 (1542) ◽

pp. 323-348 ◽

Cited By ~ 2

Keyword(s):

Hard Sphere ◽

Virial Coefficient ◽

Second Virial Coefficient ◽

Scattering Data ◽

X Ray ◽

Lennard Jones ◽

X Ray Scattering ◽

Cluster Integrals ◽

Square Well ◽

Three Body

It is shown how to evaluate the two-body, and three-body cluster integrals, ɳ 3 , ɳ * 3 , β 3 , β * 3 (equations (1.1) to (1.4)) for the hard-sphere, square-well and Lennard-Jones ( v :½ v ) potentials; the three-body potential used is the dipole-dipole-dipole potential of Axilrod & Teller. Explicit expressions are presented for the integrals ɳ * 3 , β * 3 using the above potentials; in the case of the first integral, its values for both small and large values of the separation distance are also given, for the Lennard-Jones ( v :½ v ) potential. Similar considerations have been carried out for ɳ 3 and β 3 , except that explicit expressions for the hard-sphere, and square-well potentials are not given, since these had been done before by other authors. The intermediate expressions for the four cluster integrals, are in terms of single integrals, and such expressions are valid for any continuous potential. Numerical results based on some of the expressions in this paper are compared with the results of numerical evaluation of the above integrals by other authors, and the agreement is seen to be good. Making use of the Mikolaj-Pings relation, the above results are used to obtain relationships between the second virial coefficient, and X-ray scattering data, as well as a means of deducing the pair potential at large separations, directly from a knowledge of X-ray scattering data, and the second virial coefficient.

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Takahasi Nearest-Neighbour Gas Revisited III; Lennard-Jones Gases

Zeitschrift für Naturforschung A ◽

10.5560/zna.2013-0062 ◽

2013 ◽

Vol 68 (12) ◽

pp. 773-776

Author(s):

Akira Matsumoto

Keyword(s):

Virial Coefficient ◽

Analytical Formula ◽

Second Virial Coefficient ◽

Thermodynamic Quantities ◽

Inflexion Point ◽

Lennard Jones ◽

First Order Phase Transition ◽

Higher Temperature ◽

Lower Temperature ◽

First Order Phase

Some thermodynamic quantities for the Lennard-Jones (12,6) potential are expressed as analytical formula at an isobaric process. The parameters of Lennard-Jones gases for 18 substances are obtained by the second virial coefficient data. Also some thermodynamic quantities for benzene are calculated numerically and drawn graphically. The inflexion point of the length L which depends on temperature T and pressure P corresponds physically to a boiling point. L indicates the liquid phase from lower temperature to the inflexion point and the gaseous phase from the inflexion point to higher temperature. The boiling temperatures indicate reasonable values comparing with experimental data. The behaviour of L suggests a chance of a first-order phase transition in one dimension.

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A POTENTIAL FUNCTION FOR LIQUID HELIUM AT 0°K.

Canadian Journal of Physics ◽

10.1139/p54-083 ◽

1954 ◽

Vol 32 (12) ◽

pp. 759-763 ◽

Cited By ~ 1

Author(s):

C. F. A. Beaumont

Keyword(s):

Liquid Helium ◽

Potential Function ◽

High Temperatures ◽

Radial Distribution ◽

Isothermal Compressibility ◽

Virial Coefficient ◽

Distribution Curve ◽

Second Virial Coefficient ◽

Fair Agreement ◽

Radial Distribution Curve

A new potential function for liquid helium is obtained by modifying the Margenau potential function and summing over a suggested structure for the liquid. The new potential function leads to fair agreement with the first peak of the radial distribution curve for liquid helium, with the isothermal compressibility, and with second virial coefficient data at high temperatures.

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