Triangular well model

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The triangular well model, proposed by Takeo Nagayima in one dimension [1][2], is given by


\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 \Phi_{12}(r) is the intermolecular pair potential, r is the distance r := |\mathbf{r}_1 - \mathbf{r}_2|, \sigma is the hard diameter, \epsilon is the well depth and λ > 1.

2 dimensions[edit]

[3]

Equation of state[edit]

[4] [5] [6] [7] [8]

Virial coefficients[edit]

B_2, B_3 [9] [10] and B_4 [11]

Critical point[edit]

Solid phase[edit]

[12]

References[edit]

  1. Takeo Nagayima "Statistical Mechanics of One-dimensional Substances I", Proceedings of the Physico-Mathematical Society of Japan 22 pp. 705-720 (1940)
  2. Takeo Nagayima "Statistical Mechanics of One-dimensional Substances. II", Proceedings of the Physico-Mathematical Society of Japan 22 pp. 1034-1047 (1940)
  3. Yuri Reyes, Mariana Bárcenas, Gerardo Odriozola and Pedro Orea "Thermodynamic properties of triangle-well fluids in two dimensions: MC and MD simulations", Journal of Chemical Physics 145 174505 (2016)
  4. J. Largo and J. R. Solana "A simplified perturbation theory for equilibrium properties of triangular-well fluids", Physica A 284 pp. 68-78 (2000)
  5. Mustafa Koyuncu "Equation of state of a long-range triangular-well fluid", Molecular Physics 109 pp. 565-573 (2011)
  6. 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)
  7. Hervé Guérin "Improved analytical thermodynamic properties of the triangular-well fluid from perturbation theory", Journal of Molecular Liquids 170 pp. 37-40 (2012)
  8. L.D. Rivera, M. Robles and M. López de Haro "Equation of state and liquid–vapour equilibrium in a triangle-well fluid", Molecular Physics 110 pp. 1317-1323 (2012)
  9. 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)
  10. 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)
  11. 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)
  12. 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)
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