International Journal of Thermophysics

, Volume 18, Issue 5, pp 1217–1235 | Cite as

An analytic expression for the first shell of the radial distribution function

  • H. Touba
  • G. A. Mansoori


A simple analytical expression for the first shell of the radial distribution function (RDF) is proposed. This expression, which has only three adjustable parameters, satisfies all the limiting cases of the hard-sphere RDF at high temperatures, the ideal gas RDF at zero density, the dilute-gas RDF at low densities, and the location of the peak in the first shell. The only requirement is the introduction of a potential function into the model. This theory has been applied to the Lennard Jones, Kihara, and square-well pair intermolecular potential energy functions. The first-shell RDF results are in good agreement with the available computer simulation data for the RDF of the Lennard Jones fluid and the experimental data for argon. By introducing the radius of truncation for the RDF, it is shown that information on the first shell of the RDF is sufficient to predict macroscopic properties of fluids. Calculations of radii of truncation of RDF for various properties indicate that they are always in the range of the first shell of RDF.

Key Words

Kihara potential Lennard-Jones potential radial distribution function thermodynamic properties 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. J. M. Hanley and D. J. Evans,Int. J. Thermophys. 2:1 (1981).CrossRefGoogle Scholar
  2. 2.
    G. A. Mansoori and J. F. Ely,Fluid Phase Equil. 22:253 (1985).CrossRefGoogle Scholar
  3. 3.
    M. S. Wertheim,Phys. Rev. Lett. 10:321 (1963).zbMATHCrossRefADSMathSciNetGoogle Scholar
  4. 4.
    S. Goldman,J. Phys. Chem. 83:3033 (1979).CrossRefGoogle Scholar
  5. 5.
    L. Verlet,Phys. Rev. 165:201 (1968).CrossRefADSGoogle Scholar
  6. 6.
    E. Matteoli and G. A. Mansoori,J. Chem. Phys. 103:4672 (1995).CrossRefADSGoogle Scholar
  7. 7.
    J. L. Yarnell, M. J. Katz, R. G. Wenzel, and S. H. Koenig,Phys. Rev. A 7:2130 (1973).CrossRefADSGoogle Scholar
  8. 8.
    A. K. Soper,Chem. Phys. 107:61 (1986).CrossRefGoogle Scholar
  9. 9.
    J. M. H. Levelt,Physica 26:361 (1960).CrossRefADSGoogle Scholar
  10. 10.
    T. Boublik,J. Chem. Phys. 87:1751 (1987).CrossRefADSGoogle Scholar
  11. 11.
    L. L. Lee,Molecular Thermodynamics of Nonideal Fluids (Butterworths, Boston 1988).Google Scholar
  12. 12.
    L. S. Tee, S. Gotoh, and W. E. Stewart,Ind. Eng. Chem. Fund. 5:363 (1966).CrossRefGoogle Scholar
  13. 13.
    D. Henderson, W. G. Madden, and D. Fitts,J. Chem. Phys. 64:5026 (1976).CrossRefADSGoogle Scholar
  14. 14.
    J. K. Johnson, J. A. Zollweg, and K. E. Gubbins,Mol. Phys. 78:591 (1993).CrossRefGoogle Scholar
  15. 15.
    L. Verlet,Phys. Rev. 159:98 (1967).CrossRefADSGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • H. Touba
    • 1
  • G. A. Mansoori
    • 1
  1. 1.Department of Chemical EngineeringUniversity of Illinois at ChicagoChicagoUSA

Personalised recommendations