# Difference between revisions of "Kirkwood superposition approximation"

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− | [[John G. Kirkwood]] (Eq. 40 Ref. 1, Eq. 5.6 Ref. 2) | + | The '''Kirkwood superposition approximation''' takes its name from [[John G. Kirkwood]] (see Eq. 40 Ref. 1, Eq. 5.6 Ref. 2) |

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It appears that this was used as a basis of a closure for the | It appears that this was used as a basis of a closure for the | ||

− | Kirkwood integral equation (Ref. 1) and the Yvon, and Born-Green | + | Kirkwood [[integral equations |integral equation]] (Ref. 1) and the Yvon, and Born-Green |

(Ref. 2) until the work of Morita and Hiroike (Ref. 3). | (Ref. 2) until the work of Morita and Hiroike (Ref. 3). | ||

It was pointed out in Ref.s 4 and 5, that there is an inconsistency between | It was pointed out in Ref.s 4 and 5, that there is an inconsistency between | ||

− | the pressure and the compressibility equation if this superposition approximation is used to generate <math>g(r)</math>. | + | the [[Pressure equation |pressure]] and the [[compressibility equation]] if this superposition approximation is used to generate <math>g(r)</math>. |

This approximation is rigorously correct for one-dimensional systems, and is only true in three-dimensions in the limit of zero density. | This approximation is rigorously correct for one-dimensional systems, and is only true in three-dimensions in the limit of zero density. | ||

+ | It has recently been shown that the Kirkwood superposition approximation precludes the existence of a critical point (Ref. 6). | ||

==References== | ==References== | ||

#[http://dx.doi.org/10.1063/1.1749657 John G. Kirkwood, "Statistical Mechanics of Fluid Mixtures", Journal of Chemical Physics '''3''' pp. 300-313 (1935)] | #[http://dx.doi.org/10.1063/1.1749657 John G. Kirkwood, "Statistical Mechanics of Fluid Mixtures", Journal of Chemical Physics '''3''' pp. 300-313 (1935)] | ||

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#[http://dx.doi.org/10.1103/PhysRev.85.777 B. R. A. Nijboer and L. Van Hove "Radial Distribution Function of a Gas of Hard Spheres and the Superposition Approximation", Physical Review '''85''' pp. 777 - 783 (1952)] | #[http://dx.doi.org/10.1103/PhysRev.85.777 B. R. A. Nijboer and L. Van Hove "Radial Distribution Function of a Gas of Hard Spheres and the Superposition Approximation", Physical Review '''85''' pp. 777 - 783 (1952)] | ||

#[http://links.jstor.org/sici?sici=0080-4630%2819530122%29216%3A1125%3C203%3AOTTOF%3E2.0.CO%3B2-5 G. S. Rushbrooke and H. I. Scoins "On the Theory of Fluids", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, '''216''' pp. 203-218 (1953)] | #[http://links.jstor.org/sici?sici=0080-4630%2819530122%29216%3A1125%3C203%3AOTTOF%3E2.0.CO%3B2-5 G. S. Rushbrooke and H. I. Scoins "On the Theory of Fluids", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, '''216''' pp. 203-218 (1953)] | ||

− | #[http://dx.doi.org/10.1143/PTP.21.421 Ryuzo Abe "On the Kirkwood Superposition Approximation", Progress of Theoretical Physics '''21''' pp. 421-430 (1959)] | + | #[http://dx.doi.org/10.1063/1.4824388 Jarosław Piasecki , Piotr Szymczak and John J. Kozak "Communication: Nonexistence of a critical point within the Kirkwood superposition approximation", Journal of Chemical Physics '''139''' 141101 (2013)] |

− | + | ;Related reading | |

+ | *[http://dx.doi.org/10.1143/PTP.21.421 Ryuzo Abe "On the Kirkwood Superposition Approximation", Progress of Theoretical Physics '''21''' pp. 421-430 (1959)] | ||

+ | *[http://dx.doi.org/10.1063/1.1725757 Russell V. Cochran and L. H. Lund "On the Kirkwood Superposition Approximation", Journal of Chemical Physics '''41''' pp. 3499-3504 (1964)] | ||

+ | *[http://dx.doi.org/10.1088/0034-4885/31/2/301 G. H. A. Cole "Classical fluids and the superposition approximation", Reports on Progress in Physics '''31''' pp. 419-470 (1968)] | ||

[[Category: Statistical mechanics]] | [[Category: Statistical mechanics]] |

## Latest revision as of 18:27, 6 November 2013

The **Kirkwood superposition approximation** takes its name from John G. Kirkwood (see Eq. 40 Ref. 1, Eq. 5.6 Ref. 2)

It appears that this was used as a basis of a closure for the
Kirkwood integral equation (Ref. 1) and the Yvon, and Born-Green
(Ref. 2) until the work of Morita and Hiroike (Ref. 3).
It was pointed out in Ref.s 4 and 5, that there is an inconsistency between
the pressure and the compressibility equation if this superposition approximation is used to generate .
This approximation is rigorously correct for one-dimensional systems, and is only true in three-dimensions in the limit of zero density.
It has recently been shown that the Kirkwood superposition approximation precludes the existence of a critical point (Ref. 6).

## References[edit]

- John G. Kirkwood, "Statistical Mechanics of Fluid Mixtures", Journal of Chemical Physics
**3**pp. 300-313 (1935) - M. Born and H. S. Green "A General Kinetic Theory of Liquids. I. The Molecular Distribution Functions" Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
**188**pp. 10-18 (1946) - Tohru Morita and Kazuo Hiroike "A New Approach to the Theory of Classical Fluids. I" Progress of Theoretical Physics
**23**pp. 1003-1027 (1960) - B. R. A. Nijboer and L. Van Hove "Radial Distribution Function of a Gas of Hard Spheres and the Superposition Approximation", Physical Review
**85**pp. 777 - 783 (1952) - G. S. Rushbrooke and H. I. Scoins "On the Theory of Fluids", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences,
**216**pp. 203-218 (1953) - Jarosław Piasecki , Piotr Szymczak and John J. Kozak "Communication: Nonexistence of a critical point within the Kirkwood superposition approximation", Journal of Chemical Physics
**139**141101 (2013)

- Related reading

- Ryuzo Abe "On the Kirkwood Superposition Approximation", Progress of Theoretical Physics
**21**pp. 421-430 (1959) - Russell V. Cochran and L. H. Lund "On the Kirkwood Superposition Approximation", Journal of Chemical Physics
**41**pp. 3499-3504 (1964) - G. H. A. Cole "Classical fluids and the superposition approximation", Reports on Progress in Physics
**31**pp. 419-470 (1968)