scholarly journals Characteristic Curves of the Lennard-Jones Fluid

2021 ◽  
Author(s):  
Simon Stephan ◽  
Ulrich K. Deiters
Keyword(s):  
Virial Coefficient ◽  
Equations Of State ◽  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Intermolecular Potentials ◽  
Characteristic Curves ◽  
The Past ◽  
Lennard Jones ◽  
Physically Based ◽  
Third Virial Coefficient

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.

Intermolecular forces and properties of fluid. I. The automatic calculation of higher virial coefficients and some values of the fourth coefficient for the Lennard-Jones potential

1960 ◽  
Vol 254 (1279) ◽  
pp. 487-498 ◽  
Keyword(s):  
Virial Coefficient ◽  
Mathematical Problem ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Lennard Jones ◽  
Experimental Values ◽  
First Time

The prediction of the virial coefficients for particular intermolecular potentials is generally regarded as a difficult mathematical problem. Methods have only been available for the second and third coefficient and in fact only few calculations have been made for the latter. Here a new method of successive approximation is introduced which has enabled the fourth virial coefficient to be evaluated for the first time for the Lennard-Jones potential. It is particularly suitable for automatic computation and the values reported here have been obtained by the use of the EDSAC I. The method is applicable to other potentials and some values for these will be reported subsequently. The values obtained cannot yet be compared with any experimental results since these have not been measured, but they can be used in the meantime to obtain more accurate experimental values of the lower coefficients.

INVESTIGATION OF THE PERTURBED VIRIAL EQUATIONS WITH ARBITRARY TEMPERATURE-DEPENDENT SECOND AND THIRD VIRIAL COEFFICIENTS

2011 ◽  
Vol 25 (19) ◽  
pp. 2593-2600 ◽  
Author(s):  
JIANXIANG TIAN
Keyword(s):  
Virial Coefficient ◽  
Equations Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Compressibility Factor ◽  
Critical Properties ◽  
Temperature Dependent ◽  
Packing Factor ◽  
Third Virial Coefficient ◽  
Real Fluids

In this paper, the perturbed virial equations of state with temperature-dependent virial coefficients are constructed using the Carnahan–Starling (CS) hard sphere equation as reference. Considering the second virial coefficient, some critical properties are interaction-independent and the critical packing factor is in the range of that of real fluids. But the critical compressibility factor and the liquid–vapor equilibrium properties disagree with experiments. When both the second and the third virial coefficient are considered, the critical properties are interaction-dependent but are out of the range of experimental results of real fluids. As a conclusion, the fourth virial coefficients are required for further consideration.

COMPRESSIBILITY OF GASES AT HIGH TEMPERATURES: IX. SECOND VIRIAL COEFFICIENTS AND THE INTERMOLECULAR POTENTIAL OF NEON

1955 ◽  
Vol 33 (4) ◽  
pp. 589-596 ◽  
Author(s):  
G. A. Nicholson ◽  
W. G. Schneider
Keyword(s):  
Low Temperature ◽  
High Temperatures ◽  
Pressure Range ◽  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Second Virial Coefficients ◽  
Lennard Jones

The second virial coefficients of neon have been determined in the temperature range 0° to 700 °C. and the pressure range 10 to 80 atmospheres. These data were combined with published low temperature (−150° to 0 °C.) second virial data, to investigate the intermolecular potentials of neon using both a Lennard-Jones potential, with a 9th and 12th power repulsion term, and also a modified Buckingham exponential–six potential. The agreement between observed and calculated values of B(T) was excellent for both the exponential–six and the Lennard-Jones 12:6 potentials and slightly less satisfactory for the Lennard-Jones 9:6 potential.

The statistical mechanics of assemblies of axially symmetric molecules - II. Second virial coefficients

1954 ◽  
Vol 221 (1147) ◽  
pp. 508-516 ◽  
Keyword(s):  
Carbon Dioxide ◽  
General Theory ◽  
Force Field ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Crystal Data ◽  
Axially Symmetric ◽  
Second Virial Coefficients

A general theory of the second virial coefficient of axially symmetric molecules is developed, the directional part of the intermolecular field being treated as a perturbationon the central-force part. The method is applicable to any type of intermolecular potential, particular models of directional interaction being obtained by suitable choices of parameters. Simple expressions are given for the second virial coefficient due to several types of directional force. The theory is illustrated by some calculations on the force field of carbon dioxide and its relation to the second virial coefficient and crystal data. These indicate that there is strong quadrupole interaction between carbon dioxide molecules.

scholarly journals The Third Virial Coefficient of a Lennard‐Jones Gas by Kihara's Method with Tables for the 6—9 Potential

1954 ◽  
Vol 22 (3) ◽  
pp. 464-468 ◽  
Author(s):  
Leo F. Epstein ◽  
Celesta J. Hibbert ◽  
Marion D. Powers ◽  
Glenn M. Roe
Keyword(s):  
Virial Coefficient ◽  
The Third ◽  
Lennard Jones ◽  
Third Virial Coefficient
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