Hypernetted‐chain equation of state for the two‐dimensional Lennard‐Jones fluid

1978 ◽  
Vol 68 (10) ◽  
pp. 4546-4550 ◽  
Author(s):  
Eduardo D. Glandt ◽  
Donald D. Fitts
Keyword(s):  
Equation Of State ◽  
Two Dimensional ◽  
Lennard Jones ◽  
Chain Equation ◽  
Hypernetted Chain

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.

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 A fast method of solving the hypernetted-chain equation for molecular Lennard-Jones fluids

1995 ◽  
Vol 84 (4) ◽  
pp. 743-755 ◽  
Author(s):  
J.A. Anta ◽  
E. Lomba ◽  
C. Martín ◽  
M. Lombardero ◽  
F. Lado
Keyword(s):  
Fast Method ◽  
Lennard Jones ◽  
Chain Equation ◽  
Hypernetted Chain

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.

A perturbed Lennard–Jones chain equation of state for polymer liquids

2000 ◽  
Vol 168 (1) ◽  
pp. 19-29 ◽  
Author(s):  
Y.C Chiew ◽  
S.K.H Ting ◽  
K.K Leong
Keyword(s):  
Equation Of State ◽  
Lennard Jones ◽  
Polymer Liquids ◽  
Chain Equation
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