Monte Carlo Equation of State of Molecules Interacting with the Lennard‐Jones Potential. I. A Supercritical Isotherm at about Twice the Critical Temperature

1957 ◽  
Vol 27 (3) ◽  
pp. 720-733 ◽  
Author(s):  
W. W. Wood ◽  
F. R. Parker
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Equation Of State ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones

scholarly journals VI. The equation of state

1949 ◽  
Vol 196 (1044) ◽  
pp. 73-92 ◽  
Keyword(s):  
Equation Of State ◽  
Numerical Evaluation ◽  
Approximate Equation ◽  
Transcendental Equation ◽  
Lennard Jones Potential ◽  
Unstable Region ◽  
Jones Potential ◽  
Real Roots ◽  
Lennard Jones ◽  
The Difference

The present paper is concerned with the study of an approximate equation of state, first derived by Green, which covers both phases, liquid and gas, and can be used for numerical evaluation. It contains explicitly the roots of a certain transcendental equation. The difference between the liquid and the gas corresponds to the existence or non-existence of real roots of this equation. The solution of the transcendental equation has been reduced, by using a suitable expansion, to the solution of an algebraic equation. In this way explicit expressions for the equation of state are obtained which, however, are too involved to be generally discussed. The theory can be applied to argon using the Lennard-Jones potential for the interaction between argon atoms, and the results are shown in diagrams. The character of the singularity separating liquid and gas can be seen from these diagrams to lie at the lowest point of the isotherm in the unstable region. An estimate of the position of the critical point is made and found in fair agreement with the experiental data.

Pressure in Ultra Thin Perfluoropolyether Film

2005 ◽  
Author(s):  
N. Kubota ◽  
A. Kobayashi ◽  
M. S. Mayeed ◽  
T. Kato
Keyword(s):  
Thin Film ◽  
Monte Carlo ◽  
Free Surface ◽  
Substrate Surface ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones ◽  
Flat Substrate ◽  
Pressure Distributions ◽  
Head Surface

The density and pressure variations in the ultra thin liquid perfluoropolyether (PFPE) film (2nm) are carried out by Monte Carlo simulations of Lennard-Jones systems. First of all, the variations of density and pressure of ultra thin PFPE film that has a free surface on the flat substrate are carried out. The substrate is assumed to be continuous without atomic structure and exerting Lennard-Jones potential on liquid molecules in the ultra thin film. Next, the variations of density and pressure in the ultra thin PFPE liquid film between the two solids are examined. This is assumed to be due to the contact between the flying head and the PFPE film. From results of the 2500 steps calculation, it is clarified that the density distribution between two solids becomes symmetrical in shape and the pressure distributions concentrate on the substrate surface and the flying head surface do not occur in the liquid between the two surfaces.

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