Martynov Sarkisov: Difference between revisions

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the expansion of the bridge function in powers of the [[thermal potential]].
the expansion of the bridge function in powers of the [[thermal potential]].


(1983 Eq.16  Ref. 1) closure in terms of the bridge function,  for [[hard sphere model | hard sphere]]s, is
The closure in terms of the bridge function (Eq. 16 of <ref>[http://dx.doi.org/10.1080/00268978300102111 G. A. Martynov; G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics '''49''' 1495-1504 (1983)]</ref>),  for [[hard sphere model | hard sphere]]s, is


:<math>B[\omega(r)]= - A_2 \omega(r_{12})^2 = \sqrt{(1+2\gamma(r))}-\gamma(r)  -1</math>  
:<math>B[\omega(r)]= - A_2 \omega(r_{12})^2 = \sqrt{(1+2\gamma(r))}-\gamma(r)  -1</math>  
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where <math>\omega(r)</math> is the thermal potential and <math>A_2=1/2</math>. (This closure formed the basis for the
where <math>\omega(r)</math> is the thermal potential and <math>A_2=1/2</math>. (This closure formed the basis for the
[[Ballone-Pastore-Galli-Gazzillo]] closure for hard sphere mixtures).
[[Ballone-Pastore-Galli-Gazzillo]] closure for hard sphere mixtures).
Charpentier and Jaske (Ref. 2) have
Charpentier and Jaske <ref>[http://dx.doi.org/10.1063/1.1332808 I. Charpentier and N. Jakse "Exact numerical derivatives of the pair-correlation function of simple liquids using the tangent linear method", Journal of Chemical Physics '''114''' pp. 2284-2292 (2001)]</ref> have
observed that the value of <math>A_2</math> differs drastically from 0.5 for temperatures
observed that the value of <math>A_2</math> differs drastically from 0.5 for temperatures
greater than <math>T^*\approx 2.74</math>, thus the Martynov-Sarkisov closure is deficient in the supercritical domain.
greater than <math>T^*\approx 2.74</math>, thus the Martynov-Sarkisov closure is deficient in the supercritical domain.


==References==
==References==
#[http://dx.doi.org/10.1080/00268978300102111 G. A. Martynov; G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics '''49''' 1495-1504 (1983)]
<references/>
#[http://dx.doi.org/10.1063/1.1332808 I. Charpentier and N. Jakse "Exact numerical derivatives of the pair-correlation function of simple liquids using the tangent linear method", Journal of Chemical Physics '''114''' pp. 2284-2292 (2001)]
'''Related reading'''
#[http://dx.doi.org/10.1063/1.466138      G. Sarkisov and D. Tikhonov "Martynov–Sarkisov integral equation for the simple fluids"  Journal of Chemical Physics '''99''' pp. 3926-3932  (1993)]
*[http://dx.doi.org/10.1063/1.466138      G. Sarkisov and D. Tikhonov "Martynov–Sarkisov integral equation for the simple fluids"  Journal of Chemical Physics '''99''' pp. 3926-3932  (1993)]
#[http://dx.doi.org/10.1063/1.478276  G. A. Martynov, G. N. Sarkisov and A. G. Vompe "New closure for the Ornstein–Zernike equation" Journal of Chemical Physics '''110''' pp. 3961-3969    (1999)]
*[http://dx.doi.org/10.1063/1.478276  G. A. Martynov, G. N. Sarkisov and A. G. Vompe "New closure for the Ornstein–Zernike equation" Journal of Chemical Physics '''110''' pp. 3961-3969    (1999)]
#[http://dx.doi.org/10.1063/1.1365107 Gari Sarkisov "Approximate integral equation theory for classical fluids", Journal of Chemical Physics '''114''' pp. 9496-9505  (2001)]
*[http://dx.doi.org/10.1063/1.1365107 Gari Sarkisov "Approximate integral equation theory for classical fluids", Journal of Chemical Physics '''114''' pp. 9496-9505  (2001)]


[[Category: Integral equations]]
[[Category: Integral equations]]

Latest revision as of 12:38, 11 November 2009

Martynov and Sarkisov proposed an expansion of the bridge function in terms of basis functions:

where is the chosen basis function and are the coefficients determined from thermodynamic consistency conditions. The Martynov-Sarkisov closure is based on the expansion of the bridge function in powers of the thermal potential.

The closure in terms of the bridge function (Eq. 16 of [1]), for hard spheres, is

where is the thermal potential and . (This closure formed the basis for the Ballone-Pastore-Galli-Gazzillo closure for hard sphere mixtures). Charpentier and Jaske [2] have observed that the value of differs drastically from 0.5 for temperatures greater than , thus the Martynov-Sarkisov closure is deficient in the supercritical domain.

References[edit]

Related reading