Editing Martynov Sarkisov

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

:<math>B(\rho, T, r)= - \sum_{i=1}^\infty A_i (\rho,T) \phi^i (\rho, T, r)</math>

where <math>\phi</math> is the chosen basis function and <math>A_i</math> 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 <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> 

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).
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
greater than <math>T^*\approx 2.74</math>, thus the Martynov-Sarkisov closure is deficient in the supercritical domain.

==References==
<references/>
'''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/10.1063/1.478276  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]]