Percus–Yevick equation of state for the two‐dimensional Lennard‐Jones fluid

1977 ◽  
Vol 66 (10) ◽  
pp. 4503-4508 ◽  
Author(s):  
Eduardo D. Glandt ◽  
Donald D. Fitts
Keyword(s):  
Equation Of State ◽  
Two Dimensional ◽  
Lennard Jones

scholarly journals The interaction of atoms and molecules with solid surfaces XII—Critical phenomena in a two-dimensional gas

1937 ◽  
Vol 163 (912) ◽  
pp. 132-138 ◽  
Keyword(s):  
Critical Temperature ◽  
Equation Of State ◽  
Critical Phenomena ◽  
Three Dimensional ◽  
Inert Gases ◽  
Two Dimensional ◽  
Lennard Jones ◽  
Low Concentrations ◽  
High Concentrations ◽  
The Right

In a paper recently published by Professor Lennard-Jones and the author (Lennard-Jones and Devonshire 1937) the equation of state of a gas at high concentrations has been calculated in terms of the interatomic fields. The equation found had the right kind of properties and, in particular, using the interatomic fields previously determined from the observed equation of state at low concentrations (Lennard-Jones 1931), the critical temperature was given correctly to within a few degrees for the inert gases. In this paper we shall apply the same method to determine the equation of state of a two-dimensional gas. Although such a gas cannot strictly be obtained in practice, an inert gas adsorbed on a surface (or in fact any gas held by van der Waals’ forces only) would probably behave very much like one, the fluctuations of the potential field over the surface not being of much importance. In confirmation of this it may be noted that the specific heat of argon adsorbed on charcoal was found by Simon (Simon 1935) to be equal to that of a perfect two-dimensional gas down to 60° K. A gas adsorbed on a liquid would be an even better representation of a two-dimensional one. Some measurements on the adsorption of krypton and xenon on liquid mercury have been made by Cassel and Neugebauer (Cassel and Neugebauer 1936), and they found no trace of any critical phenomena though they worked at temperatures considerably below the critical temperature of xenon. Our results are in agreement with this, for they show that the critical temperature of a two-dimensional gas should be about half that of the corresponding three-dimensional one.

The equation of state of the two-dimensional Lennard–Jones fluid

1986 ◽  
Vol 64 (6) ◽  
pp. 677-684 ◽  
Author(s):  
M. Rami Reddy ◽  
Seamus F. O'Shea
Keyword(s):  
Equation Of State ◽  
Virial Coefficients ◽  
Nonlinear Least Squares ◽  
Virial Equation ◽  
Two Dimensional ◽  
Marquardt Method ◽  
Lennard Jones ◽  
Virial Equation Of State ◽  
First Time ◽  
Critical Constants

By combining pressure and energy data from the virial equation of state, through fifth virial coefficients, with the second and third virial coefficients themselves and the results of computer-simulation calculations, we have constructed an equation of state for the two-dimensional Lennard–Jones fluid for 0.45 ≤ T* ≤ 5 and 0.01 ≤ ρ* ≤ 0.8. The fitted data include some in the metastable region, and, therefore, the equation of state also describes "van der Waals loops" including unstable regions. The form used is a modified Benedict–Webb–Rubin equation having 33 parameters including one nonlinear one. The fitting was done using a nonlinear least squares algorithm based on a Levenberg–Marquardt method. A total of 211 simulation points, 97 reported here for the first time, were used in the fitting, and the overall standard deviation is less than 2% for both energy and pressure. Second and third virial coefficients derived from the fit in the supercritical region are in excellent agreement with exact values. The critical constants derived from the fit are in reasonable agreement with published estimates.

Molecular dynamics study of the two‐dimensional Lennard‐Jones equation of state

1984 ◽  
Vol 80 (11) ◽  
pp. 5859-5860 ◽  
Author(s):  
C. Bruin ◽  
A. F. Bakker ◽  
Marvin Bishop
Keyword(s):  
Molecular Dynamics ◽  
Equation Of State ◽  
Two Dimensional ◽  
Lennard Jones

High-density equation of state for a two-dimensional Lennard-Jones solid

2018 ◽  
Vol 148 (17) ◽  
pp. 174505 ◽  
Author(s):  
Kaihang Shi ◽  
Kai Gu ◽  
Yifan Shen ◽  
Deepti Srivastava ◽  
Erik E. Santiso ◽  
...  
Keyword(s):  
Equation Of State ◽  
High Density ◽  
Two Dimensional ◽  
Lennard Jones ◽  
Density Equation

Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

2018 ◽  
Vol 13 (3) ◽  
pp. 59-63 ◽  
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Gas Dynamics ◽  
Hydrodynamic Type ◽  
System Of Equations ◽  
Two Dimensional ◽  
Equations Of Gas Dynamics ◽  
Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

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.

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