Triangular well model: Difference between revisions
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and λ > 1. | and λ > 1. | ||
==Equation of state== | ==Equation of state== | ||
:'' | <ref>[http://dx.doi.org/10.1016/S0378-4371(00)00232-6 J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A '''284''' pp. 68-78 (2000)]</ref> | ||
<ref>[http://dx.doi.org/10.1080/00268976.2010.538738 Mustafa Koyuncu "Equation of state of a long-range triangular-well fluid", Molecular Physics '''109''' pp. 565-573 (2011)]</ref> | |||
==Virial coefficients== | ==Virial coefficients== | ||
<math>B_2</math>, <math>B_3</math> <ref>[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]</ref> | <math>B_2</math>, <math>B_3</math> <ref>[http://dx.doi.org/10.1063/1.1725746 M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics '''41''' pp. 3439-3450 (1964)]</ref> | ||
Revision as of 16:05, 19 February 2011
The triangular well model, proposed by T. Nagayimain one dimension [1][2], is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}\left( r \right) = \left\{ \begin{array}{ccc} \infty & ; & r \leq \sigma \\ \frac{\epsilon (r/\sigma - \lambda)}{(\lambda -1)} & ; &\sigma < r \leq \lambda \sigma \\ 0 & ; & r > \lambda \sigma \end{array} \right. }
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r)} is the intermolecular pair potential, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} is the distance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r := |\mathbf{r}_1 - \mathbf{r}_2|} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} is the hard diameter, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon} is the well depth and λ > 1.
Equation of state
Virial coefficients
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B_2} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B_3} [5] [6] and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B_4} [7]
Critical point
Solid phase
References
- ↑ T. Nagayima "Statistical Mechanics of One-dimensional Substances I", Proceedings of the Physico-Mathematical Society of Japan 22 pp. 705-720 (1940)
- ↑ T. Nagayima "Statistical Mechanics of One-dimensional Substances. II", Proceedings of the Physico-Mathematical Society of Japan 22 pp. 1034-1047 (1940)
- ↑ J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A 284 pp. 68-78 (2000)
- ↑ Mustafa Koyuncu "Equation of state of a long-range triangular-well fluid", Molecular Physics 109 pp. 565-573 (2011)
- ↑ M. J. Feinberg and Andrew G. De Rocco "Intermolecular Forces: The Triangle Well and Some Comparisons with the Square Well and Lennard-Jones", Journal of Chemical Physics 41 pp. 3439-3450 (1964)
- ↑ R. H. Fowler, H. W. Graben, Andrew G. De Rocco and M. J. Feinberg "Some Additional Results for the Triangle-Well Potential Model", Journal of Chemical Physics 43 pp. 1083-1084 (1965)
- ↑ W. C. Farrar and Andrew G. De Rocco "Perturbation Theory for a High-Temperature Triangle-Well Fluid", Journal of Chemical Physics 54 pp. 2024-2025 (1971)
- ↑ Jhumpa Adhikari and David A. Kofke "Monte Carlo and cell model calculations for the solid-fluid phase behaviour of the triangle-well model", Molecular Physics 100 pp. 1543-1550 (2002)
- Related reading
- Damon N. Card and John Walkley "Perturbation Calculations for a Triangular Well Potential at Low Densities", Canadian Journal of Physics 50 pp. 1419–1426 (1972)
- Damon N. Card and John Walkley "Monte Carlo and Perturbation Calculations for a Triangular Well Fluid", Canadian Journal of Physics 52 pp. 80-88 (1974)
- J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A 284 pp. 68-78 (2000)
- F. F. Betancourt-Cárdenas, L. A. Galicia-Luna and S. I. Sandler "Thermodynamic properties for the triangular-well fluid", Molecular Physics 105 pp. 2987-2998 (2007)
- F. F. Betancourt-Cárdenas, L. A. Galicia-Luna, A. L. Benavides, J. A. Ramírez and E. Schöll-Paschinger "Thermodynamics of a long-range triangle-well fluid", Molecular Physics 106 pp. 113-126 (2008)
- Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics 130 014502 (2009)