Difference between revisions of "Duh Haymet"

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:<math>B(\gamma^{*})= - \frac{1}{2} \gamma^{*2} \left[ \frac{1}{ \left[ 1+ \left( \frac{5\gamma^{*} +11}{7\gamma^{*} +9} \right) \gamma^{*}  \right]} \right]</math>
 
:<math>B(\gamma^{*})= - \frac{1}{2} \gamma^{*2} \left[ \frac{1}{ \left[ 1+ \left( \frac{5\gamma^{*} +11}{7\gamma^{*} +9} \right) \gamma^{*}  \right]} \right]</math>
  
where (Eq. 10) <math>\gamma^{*}(r) = \gamma (r)  - \beta \Phi_p(r)</math> where <math>\Phi_p (r)</math>  is the perturbative part of the pair potential
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where (Eq. 10) <math>\gamma^{*}(r) = \gamma (r)  - \beta \Phi_p(r)</math> where <math>\Phi_p (r)</math>  is the perturbative (attractive) part of the pair potential.
(Note: in the [[WCA separation]] for the [[Lennard Jones]] system, the `perturbative part' is the attractive part).
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==References==
 
==References==
 
#[http://dx.doi.org/10.1063/1.470724    Der-Ming Duh and A. D. J. Haymet "Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function", Journal of Chemical Physics '''103''' pp. 2625-2633 (1995)]
 
#[http://dx.doi.org/10.1063/1.470724    Der-Ming Duh and A. D. J. Haymet "Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function", Journal of Chemical Physics '''103''' pp. 2625-2633 (1995)]

Revision as of 15:43, 26 February 2007

The Duh-Haymet (Ref. 1) (1995) Padé (3/2) approximation for the Bridge function for the Lennard Jones system is (Eq. 13)


B(\gamma^{*})= - \frac{1}{2} \gamma^{*2} \left[ \frac{1}{ \left[ 1+ \left( \frac{5\gamma^{*} +11}{7\gamma^{*} +9} \right) \gamma^{*}  \right]} \right]

where (Eq. 10) \gamma^{*}(r) = \gamma (r)  - \beta \Phi_p(r) where \Phi_p (r) is the perturbative (attractive) part of the pair potential.


References

  1. Der-Ming Duh and A. D. J. Haymet "Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function", Journal of Chemical Physics 103 pp. 2625-2633 (1995)