scholarly journals Review and Comparison of Equations of State for the Lennard-Jones Fluid

2021 ◽  
Author(s):  
Simon Stephan ◽  
Jens Staubach ◽  
Hans Hasse
Keyword(s):  
Equations Of State ◽  
Virial Coefficients ◽  
Computer Experiments ◽  
Enthalpy Of Vaporization ◽  
Homogeneous State ◽  
Critical Properties ◽  
Simple Fluids ◽  
Lennard Jones ◽  
Data Points ◽  
Point Of Departure

The Lennard-Jones (LJ) potential is widely used for describing simple fluids; it is also a point of departure for developing models of complex fluids. Thermodynamic properties of the LJ fluid have been studied by molecular simulations by many authors and a critical review of the available data, which comprises about 35,000 data points, has been published recently [J. Chem. Inf. Mod. 59 (2019) 4248–4265]. The importance of the LJ fluid has also triggered the development of a large number of equations of state (EOS). In the present work, 20 LJ EOS were critically assessed by comparing their results with consolidated data from computer experiments. A large variety of thermophysical properties was considered: vapor pressure; saturated densities; enthalpy of vaporization; critical properties; thermal, caloric, and entropic properties at homogeneous state points; and second and third virial coefficients. It was found that none of the available LJ EOS meets the following two criteria: (1) it does not yield unphysical artifacts when used for extrapolations, and (2) it describes data from computer experiments within their statistical uncertainty in most fluid regions. Furthermore, a re-parameterization of the monomer term of the PC-SAFT EOS was carried out by fitting it to data of the LJ fluid. The new LJ EOS yields good results for the LJ fluid, but does not outperform the best existing LJ EOS.

scholarly journals Critical phenomena in gases - I

1937 ◽  
Vol 163 (912) ◽  
pp. 53-70 ◽  
Keyword(s):  
Critical Temperature ◽  
Critical Phenomena ◽  
Equations Of State ◽  
Van Der Waals ◽  
Usual Method ◽  
Critical Properties ◽  
Lennard Jones ◽  
Finite Power ◽  
Empirical Equations Of State

The exact measurements of the isotherms of gases have proved extremely valuable in the determination of interatomic forces. For this purpose it has been found necessary to express the pv values of a gas as a finite power series in the density or in the pressure, and the coefficients so obtained have been compared with theoretical expressions in terms of interatomic fields. Many accounts of the method have been given and it is not necessary to give further details here (cf. Lennard-Jones 1931). While these methods are valid for gases at low densities where binary encounters are predominant, they fail for gases at high densities such as obtain in the neighbourhood of the critical point. Michels and his collaborators (Michels and others 1937) have recently studied the isotherms of gases at pressures as high as 3000 atm., and they find that the usual method of representing isotherms as simple functions of density or pressure ceases to be useful. The equation of state of van der Waals was astonishingly successful in accounting for the critical phenomena of gases and the form of the isotherms for temperatures below the critical temperature. Other empirical equations of state, for example that of Dieterici, were even more successful in reproducing the observed relations between the critical pressure, volume and temperature, and their very success has often obscured the fact that they were not logical theories of critical phenomena in gases, based as they were on arguments which were valid only for gases of low concentration. Thus the van der Waals equation, valuable as it has been and useful as it still is, implies that the internal energy of a vapour and its liquid phase is proportional only to the first power of the density, and this cannot be true for gases or vapours at densities comparable with those of liquids. The problem still remains of explaining why gases exhibit critical properties and of correlating the observed values of the critical temperature with the forces which atoms or molecules exert on each other.

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.

scholarly journals Third virial coefficients and critical properties of quadrupolar two center Lennard-Jones models

2003 ◽  
Vol 5 (13) ◽  
pp. 2851-2857 ◽  
Author(s):  
L. G. MacDowell ◽  
C. Menduiña ◽  
C. Vega ◽  
E. de Miguel
Keyword(s):  
Virial Coefficients ◽  
Critical Properties ◽  
Lennard Jones

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.

Equation of state of a Lennard-Jones 12-6 pairwise additive fluid

1980 ◽  
Vol 45 (4) ◽  
pp. 977-983 ◽  
Author(s):  
Jan Sýs ◽  
Anatol Malijevský
Keyword(s):  
Equation Of State ◽  
Empirical Equation ◽  
The State ◽  
Critical Properties ◽  
Lennard Jones ◽  
State Behaviour ◽  
Compressibility Factors

An empirical equation of state was proposed, which is based on pseudoexperimental data on the state behaviour. The equation can be used at reduced temperatures from the range 0.7-100.0 and reduced densities up to 2. Calculated compressibility factors and critical properties agree well with available literature data.

Effects of the repulsive and attractive forces on phase equilibrium and critical properties of two-dimensional non-conformal simple fluids

2021 ◽  
pp. 115234
Author(s):  
B. Ibarra-Tandi ◽  
J.A. Moreno-Razo ◽  
J. Munguía-Valadez ◽  
J. López-Lemus ◽  
M.A. Chávez-Rojo
Keyword(s):  
Phase Equilibrium ◽  
Two Dimensional ◽  
Critical Properties ◽  
Simple Fluids
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