Mean spherical approximation: Difference between revisions

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==References==
==References==
#[http://dx.doi.org/10.1103/PhysRev.144.251  J. L. Lebowitz and J. K. Percus "Mean Spherical Model for Lattice Gases with Extended Hard Cores and Continuum Fluids", Physical Review '''144''' pp. 251 - 258 (1966)]
#[http://dx.doi.org/10.1103/PhysRev.144.251  J. L. Lebowitz and J. K. Percus "Mean Spherical Model for Lattice Gases with Extended Hard Cores and Continuum Fluids", Physical Review '''144''' pp. 251 - 258 (1966)]
#[http://dx.doi.org/10.1007/BF01011750 L. Blum and J. S. Høye "Solution of the Ornstein-Zernike equation with Yukawa closure for a mixture", Journal  of Statistical Physics, '''19''' pp. 317-324 (1978)]
#[http://dx.doi.org/
#[http://dx.doi.org/
#[http://dx.doi.org/
#[JSP_1978_19_0317_nolotengoSpringer]
#[JSP_1980_22_0661_nolotengoSpringer]
#[JSP_1980_22_0661_nolotengoSpringer]
#[http://dx.doi.org/10.1063/1.470724      Der-Ming Duh and A. D. J. Haymet "Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function", Journal of Chemical Physics '''103''' pp. 2625-2633 (1995)]
#[http://dx.doi.org/10.1063/1.470724      Der-Ming Duh and A. D. J. Haymet "Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function", Journal of Chemical Physics '''103''' pp. 2625-2633 (1995)]


[[Category:Integral equations]]
[[Category:Integral equations]]

Revision as of 14:36, 28 February 2007

The Lebowitz and Percus mean spherical approximation (MSA) (1966) (Ref. 1) closure is given by



The Blum and Hoye mean spherical approximation (MSA) (1978-1980) (Refs 2 and 3) closure is given by



and

where and are the total and the direct correlation functions for two spherical molecules of i and j species, is the diameter of 'i species of molecule. Duh and Haymet (Eq. 9 Ref. 4) write the MSA approximation as



where and comes from the WCA division of the Lennard-Jones potential. By introducing the definition (Eq. 10 Ref. 4)



one can arrive at (Eq. 11 in Ref. 4)



The Percus Yevick approximation may be recovered from the above equation by setting .

References

  1. J. L. Lebowitz and J. K. Percus "Mean Spherical Model for Lattice Gases with Extended Hard Cores and Continuum Fluids", Physical Review 144 pp. 251 - 258 (1966)
  2. L. Blum and J. S. Høye "Solution of the Ornstein-Zernike equation with Yukawa closure for a mixture", Journal of Statistical Physics, 19 pp. 317-324 (1978)
  3. [http://dx.doi.org/
  4. [JSP_1980_22_0661_nolotengoSpringer]
  5. Der-Ming Duh and A. D. J. Haymet "Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function", Journal of Chemical Physics 103 pp. 2625-2633 (1995)