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.

(1983 Eq.16 Ref. 1) closure in terms of the bridge function, 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-Gazillo closure for hard sphere mixtures). Charpentier and Jaske (Ref. 2) have observed that the value of $A_{2}$ differs drastically from 0.5 for temperatures greater than $T^{*}\approx 2.74$, thus the MS closure is deficient in the supercritical domain.

References

1. [MP_1983_49_1495]
2. [JCP_2001_114_02284]
3. [JCP_1993_99_03926]
4. [JCP_1999_110_03961]
5. [JCP_2001_114_09496]