# Triangular well model

(Redirected from Equations of state for the triangular well model)

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

where is the intermolecular pair potential, is the distance , is the hard diameter, is the well depth and λ > 1.

## Contents

## 2 dimensions[edit]

^{[3]}

## Equation of state[edit]

^{[4]}
^{[5]}
^{[6]}
^{[7]}
^{[8]}

## Virial coefficients[edit]

, ^{[9]}
^{[10]}
and ^{[11]}

## Critical point[edit]

## Solid phase[edit]

^{[12]}

## References[edit]

- ↑ Takeo Nagayima "Statistical Mechanics of One-dimensional Substances I", Proceedings of the Physico-Mathematical Society of Japan
**22**pp. 705-720 (1940) - ↑ Takeo Nagayima "Statistical Mechanics of One-dimensional Substances. II", Proceedings of the Physico-Mathematical Society of Japan
**22**pp. 1034-1047 (1940) - ↑ 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) - ↑ 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) - ↑ 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) - ↑ Hervé Guérin "Improved analytical thermodynamic properties of the triangular-well fluid from perturbation theory", Journal of Molecular Liquids
**170**pp. 37-40 (2012) - ↑ 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) - ↑ 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) - 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) - M. Bárcenas, G. Odriozola and P. Orea "Coexistence and interfacial properties of triangle-well fluids", Molecular Physics
**112**pp. 2114-2121 (2014)