Editing Triangular well model
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 1: | Line 1: | ||
The '''triangular well model''' | {{stub-general}} | ||
The '''triangular well model''' is given by | |||
:<math> | :<math> | ||
Line 11: | Line 12: | ||
where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth | where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r</math> is the distance <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, <math>\sigma</math> is the hard diameter, <math>\epsilon</math> is the well depth | ||
and λ > 1. | and λ > 1. | ||
This model was firts proposed by T. Nagayima in 1940 (Refs. 1-3). | |||
==Equation of state== | ==Equation of state== | ||
:''Main article: [[Equations of state for the triangular well model]]'' | |||
==Virial coefficients== | ==Virial coefficients== | ||
<math>B_2</math> | <math>B_2</math> and <math>B_3</math>: | ||
*[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)] | |||
*[http://dx.doi.org/10.1063/1.1696837 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)] | |||
<math>B_4</math>: | |||
*[http://dx.doi.org/10.1063/1.1675133 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)] | |||
==Critical point== | ==Critical point== | ||
==Solid phase== | ==Solid phase== | ||
#[http://dx.doi.org/10.1080/00268970110120300 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== | ==References== | ||
(Note: the following three Nagayima references have not yet been checked. Numbers 1 and 3 were found in the [http://dx.doi.org/10.1063/1.1725746 Feinberg and De Rocco] paper, and Ref 2 in the [http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou] paper). | |||
#T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 705- (1940) | |||
#T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 855- (1940) | |||
#T. Nagayima "", Proceedings of the Physico-Mathematical Society of Japan '''22''' pp. 1034- (1940) | |||
#[http://dx.doi.org/10.1139/p72-195 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)] | |||
#[http://dx.doi.org/10.1139/p74-010 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)] | |||
#[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)] | |||
#[http://dx.doi.org/10.1080/00268970701725013 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)] | |||
#[http://dx.doi.org/10.1080/00268970701832397 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)] | |||
#[http://dx.doi.org/10.1063/1.3049399 Shiqi Zhou "Thermodynamics and phase behavior of a triangle-well model and density-dependent variety", Journal of Chemical Physics '''130''' 014502 (2009)] | |||
[[category: models]] | [[category: models]] |