Martynov Sarkisov

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

$B(\rho ,T,r)=-\sum _{i=1}^{\infty }A_{i}(\rho ,T)\phi ^{i}(\rho ,T,r)$

where $\phi$ is the chosen basis function and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_i} 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 ), for hard spheres, is

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B[\omega(r)]= - A_2 \omega(r_{12})^2 = \sqrt{(1+2\gamma(r))}-\gamma(r) -1}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \omega(r)} is the thermal potential and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_2=1/2} . (This closure formed the basis for the Ballone-Pastore-Galli-Gazzillo closure for hard sphere mixtures). Charpentier and Jaske have observed that the value of $A_{2}$ differs drastically from 0.5 for temperatures greater than Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T^*\approx 2.74} , thus the Martynov-Sarkisov closure is deficient in the supercritical domain.

References

Related reading

• G. Sarkisov and D. Tikhonov "Martynov–Sarkisov integral equation for the simple fluids" Journal of Chemical Physics 99 pp. 3926-3932 (1993)
• 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)
• Gari Sarkisov "Approximate integral equation theory for classical fluids", Journal of Chemical Physics 114 pp. 9496-9505 (2001)