Triangular well model

The triangular well model 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. This model was first proposed by T. Nagayima in 1940 (Refs. 1-3) in one dimension.

Equation of state

Main article: Equations of state for the triangular well model

Virial coefficients

$B_{2}$ and $B_{3}$:

• 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)

$B_{4}$:

• 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)

Solid phase

1. 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)

References

(Note: the following three Nagayima references have not yet been checked. Numbers 1 and 3 were found in the Feinberg and De Rocco paper, and Ref 2 in the Shiqi Zhou paper).

1. T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan 22 pp. 705- (1940)
2. T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan 22 pp. 855- (1940)
3. T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan 22 pp. 1034- (1940)
4. 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)
5. 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)
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)
7. 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)
8. 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)
9. Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics 130 014502 (2009)