Martynov Sarkisov

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

B (ρ, T, r) = - \sum_{i = 1}^{\infty} A_{i} (ρ, T) ϕ^{i} (ρ, T, r)

where $ϕ$ 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 [ω (r)] = - A_{2} ω (r_{12})^{2} = \sqrt{(1 + 2 γ (r))} - γ (r) - 1

where $ω (r)$ 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.

References

Related reading

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

[2] 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)

[1]

[2]

Martynov Sarkisov

References

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