Equations of state from generalized perturbation theory. Part 1. The hard-core Lennard-Jones fluid

1991 ◽  
Vol 63 (1-2) ◽  
pp. 1-25 ◽  
Author(s):  
Gary M. Sowers ◽  
Stanley I. Sandler
Keyword(s):  
Perturbation Theory ◽  
Equations Of State ◽  
Hard Core ◽  
Lennard Jones ◽  
Generalized Perturbation Theory

scholarly journals Equation of State for the Lennard-Jones Truncated and Shifted Fluid with a Cut-off Radius of 2.5 σ based on Perturbation Theory and its Applications to Interfacial Thermodynamics

2021 ◽  
Author(s):  
Michaela Heier ◽  
Simon Stephan ◽  
Jinlu Liu ◽  
Walter G. Chapman ◽  
Hans Hasse ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Equation Of State ◽  
Density Functional ◽  
Equations Of State ◽  
Bulk Liquid ◽  
Gradient Theory ◽  
Functional Theory ◽  
Lennard Jones ◽  
Interesting Candidate ◽  
Influence Parameter

An equation of state is presented for describing thermodynamic properties of the Lennard-Jones truncated and shifted (LJTS) potential with a cut-off radius of 2.5 σ. It is developed using perturbation theory with a hard-sphere reference term and labelled with the acronym PeTS (perturbed truncated and shifted). The PeTS equation of state describes the properties of the bulk liquid and vapour and the corresponding equilibrium of the LJTS fluid well. Furthermore, it is developed so that it can be used safely in the entiremetastable and unstable region, which is an advantage compared to existing LJTS equations of state. This makes the PeTS equation of state an interesting candidate for studies of interfacial properties. The PeTS equation of state is applied here in two theories of interfaces, namely density gradient theory (DGT) and density functional theory (DFT). The influence parameter of DGT as well as the interaction averaging diameter of DFT are fitted to data of the surface tension of the LJTS fluid obtained from molecular simulation. The results from both theories agree very well with those from the molecular simulations.

A Two-Potential Model for the Equations of State of Gases at Moderate and High Densities

1971 ◽  
Vol 38 (4) ◽  
pp. 813-819
Author(s):  
J. S. Yu
Keyword(s):  
Potential Model ◽  
Equations Of State ◽  
Second Virial Coefficient ◽  
Pair Potential ◽  
Hard Core ◽  
Core Model ◽  
Molecular Motions ◽  
Lennard Jones ◽  
Dilute Gases ◽  
Hard Core Model

The isothermal compression, up to nearly half the liquid densities, of argon, nitrogen, and methane at three different temperatures ranging from 0–150 deg C are investigated by using the cell method originally developed by Lennard-Jones and Devonshire. A two-potential model is adopted in the evaluation of the classical partition function to partially take into account the contributions arising from the correlations of molecular motions. The Lennard-Jones 6–12 potential and the Kihara hard core model are used, respectively, for the calculation of the energy of the geometrically symmetric lattice and the energy of augmentation arising from molecular motions. The potential parameters used in the calculations are those derived from fitting the second virial coefficient of dilute gases. The resulting calculated isotherms are compared with experimental measurements; agreement obtained is good for the range of density considered. The Kihara hard-core model with parameters determined for dilute gases is found to be ineffective at very high densities. This agrees with the conclusion derived from the Monte Carlo and molecular dynamics calculations that the Lennard-Jones 12–6 potential is tolerably good in representing the effective pair potential at liquid densities.

A generalized perturbation theory program for CANDU core analysis

2001 ◽  
Vol 28 (2) ◽  
pp. 169-189 ◽  
Author(s):  
Do Heon Kim ◽  
Jong Kyung Kim ◽  
Hangbok Choi
Keyword(s):  
Perturbation Theory ◽  
Core Analysis ◽  
Generalized Perturbation Theory

A general iterative time-independent perturbation theory

1985 ◽  
Vol 63 (9) ◽  
pp. 1157-1161 ◽  
Author(s):  
F. Castaño ◽  
L. Laín ◽  
M. N. Sanchez ◽  
A. Torre
Keyword(s):  
Perturbation Theory ◽  
Power Series ◽  
Iterative Method ◽  
Perturbation Methods ◽  
Lennard Jones ◽  
Insight Into ◽  
Considerable Insight

An iterative method for time-independent perturbation theory is presented. Lennard-Jones–Brillouin–Wigner (LBW) and Rayleigh–Schrödinger (RS) power series are shown to be particular cases of the iteration and the combined expansion–iteration. Improvements in convergence of the power series are suggested and analyzed.The iterative method gives considerable insight into the nature and relative convergence of the currently used time-independent perturbation methods.

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