Editing Martynov Sarkisov
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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 | |||
:<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> | ||
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- | [[Ballone-Pastore-Galli-Gazillo]] closure for hard sphere mixtures). | ||
Charpentier and Jaske | Charpentier and Jaske (Ref. 2) 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)] | |||
''' | #[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)] | ||
#[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/10.1063/1.1365107 Gari Sarkisov "Approximate integral equation theory for classical fluids", Journal of Chemical Physics '''114''' pp. 9496-9505 (2001)] | |||
[[Category: Integral equations]] | [[Category: Integral equations]] |