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Statistical mechanics of simple fluids: beyond van der Waals

MAR 01, 1980
Equilibrium properties of dense fluids, notoriously difficult to treat theoretically, can now be understood by reference to model systems, such as a fluid of “hard spheres,” and to calculations on high‐speed computers.

DOI: 10.1063/1.2913994

Joel L. Lebowitz
Eduardo M. Waisman

Dense fluids, defined to include both dense gases and liquids, have the reputation of being especially difficult to deal with theoretically. This reputation is not undeserved. Unlike dilute gases and crystalline solids, which can be thought of as deviants from well understood ideal states, the ideal gas and the ideal harmonic crystal, the dense fluid lies far from any recognizable landmark. This rules out the use of straightforward, convergent or asymptotic, expansions—the all‐purpose tool of the theoretical physicist—and makes even the hardy wince.

References

  1. 1. Several detailed review articles as well as books have appeared in recent years. We list here a few of them and refer the interested reader to these for technical details and further references: J. A. Barker, D. Henderson, Rev. Mod. Phys. 48, 587 (1976). https://doi.org/RMPHAT
    H. C. Andersen, D. Chandler, J. D. Weeks, Advances in Chemical Physics 34, 105 (1976).
    J. P. Hansen, I. R. McDonald, Theory of Simple Liquids, Academic, New York (1976).
    G. Stell in Statistical Mechanics, Part A: Equilibrium Techniques, B. Berne, ed., Plenum, New York (1977). There are also other review articles on liquids in this volume.
    J. S. Rowlinson, Liquids and Liquid Mixtures, Butterworths, London (1969) 2nd Edition.

  2. 2. Physica 73, (1974). This volume contains both technical and historical articles about the subject.

  3. 3. D. Ruelle, Statistical Mechanics: Rigorous Results, Benjamin, New York (1969);
    C. J. Thompson, Mathematical Statistical Mechanics, Macmillan, New York (1972).

  4. 4. See the article by M. J. Klein in reference 2, page 28.

  5. 5. Quoted by S. G. Brush in The Physics Teacher 11, 261 (1973).
    See also S. G. Brush, The Kind of Motion We Call Heat, North Holland, New York (1976).

  6. 6. N. G. van Kampen, Phys. Rev. 135, 362 (1964).https://doi.org/PHRVAO

  7. 7. M. Kac, G. E. Uhlenbeck, P. C. Hemmer, J. Math. Phys. 4, 216 and (1963);
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  8. 8. G. Baker, Phys. Rev. 122, 1477 (1961).

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  10. 10. O. Penrose, J. L. Lebowitz, J. Stat. Phys. 3, 211 (1971).https://doi.org/JSTPBS

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    J. D. Weeks, D. Chandler, H. C. Andersen, 54, 5237 (1976).
    H. C. Andersen, J. D. Weeks, D. Chandler, Phys. Rev. A 4, 1597 (1971);
    H. C. Andersen, J. D. Weeks, D. Chandler, J. Chem. Phys. 57, 2620 (1972).https://doi.org/JCPSA6

  12. 12. L. Verlet, J.‐J. Weis, Phys. Rev. A 5, 939 (1972).

  13. 13. L. S. Ornstein, F. Zernike, Proc. K. Akad. Wet. A 17, 793 (1914).
    English translation can be found in The Equilibrium Theory of Classical Fluids, H. L. Frisch, J. L. Lebowitz, eds., Benjamin, New York (1964).

  14. 14. N. M. Rosenbluth, A. W. Rosenbluth, J. Chem. Phys., 22, 881 (1954).
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  15. 15. H. C. Longuet‐Higgins, B. Widom, Mol. Phys. 8, 549 (1964).

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  17. 17. J. L. Lebowitz, Phys. Rev. A 133, 895 (1964).https://doi.org/PRVAAH

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  20. 20. N. F. Carnahan, K. E. Starling, J. Chem. Phys. 51, 635 (1969).https://doi.org/JCPSA6

  21. 21. H. Reiss, H. L. Frisch, J. L. Lebowitz, J. Chem. Phys. 31, 369 (1959).https://doi.org/JCPSA6

  22. 22. J. K. Percus, G. J. Yevick, Phys. Rev. 136, B290, (1964).

  23. 23. The “super” accuracy of the exponential approximation for Lennard‐Jones tluids may indeed be somewhat fortuitous; see G. Stell, J.‐J. Weis, Phys. Rev., to be published.

More about the Authors

Joel L. Lebowitz. Rutgers University, New Brunswick, N.J..

Eduardo M. Waisman. Systems, Science and Software, San Diego, Cal..

This Content Appeared In
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Volume 33, Number 3

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