# Martynov Sarkisov

**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]

- ↑ G. A. Martynov; G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics
**49**1495-1504 (1983) - ↑ 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**

- 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)