Martynov Sarkisov: Difference between revisions

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'''Martynov''' and '''Sarkisov''' proposed
'''Martynov''' and '''Sarkisov''' proposed
an expansion of the Bridge function in terms of basis functions:
an expansion of the [[bridge function]] in terms of basis functions:


:<math>B(\rho, T, r)= - \sum_{i=1}^\infty A_i (\rho,T) \phi^i (\rho, T, r)</math>
:<math>B(\rho, T, r)= - \sum_{i=1}^\infty A_i (\rho,T) \phi^i (\rho, T, r)</math>
Line 7: Line 7:
[[thermodynamic consistency]] conditions.
[[thermodynamic consistency]] conditions.
The Martynov-Sarkisov closure is based on
The Martynov-Sarkisov closure is based on
the expansion of the [[Bridge function]] in powers of the thermal potential.
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 sphere model | hard sphere]]s, is
(1983 Eq.16  Ref. 1) closure in terms of  the bridge function,  for [[hard sphere model | hard sphere]]s, is

Revision as of 16:03, 21 March 2007

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.

(1983 Eq.16 Ref. 1) closure in terms of the bridge function, for hard spheres, is

where is the thermal potential and . (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 differs drastically from 0.5 for temperatures greater than , thus the Martynov-Sarkisov closure is deficient in the supercritical domain.

References

  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)
  3. G. Sarkisov and D. Tikhonov "Martynov–Sarkisov integral equation for the simple fluids" Journal of Chemical Physics 99 pp. 3926-3932 (1993)
  4. 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)
  5. Gari Sarkisov "Approximate integral equation theory for classical fluids", Journal of Chemical Physics 114 pp. 9496-9505 (2001)