# 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 $A_i$ 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 [1]), for hard spheres, is

$B[\omega(r)]= - A_2 \omega(r_{12})^2 = \sqrt{(1+2\gamma(r))}-\gamma(r) -1$

where $\omega(r)$ is the thermal potential and $A_2=1/2$. (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 $A_2$ differs drastically from 0.5 for temperatures greater than $T^*\approx 2.74$, thus the Martynov-Sarkisov closure is deficient in the supercritical domain.