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Hard-sphere fluid-to-solid transition and the virial expansion

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Abstract

An exhaustive Padé approximant study of the Mayer virial series expansion is carried out for the classical hard-sphere system. As one increases the order of the different approximants a clear tendency is seen to reproduce both the random close packing divergence of the fluid branch as well as its instability (towards the crystalline phase) at the spinodal point.

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References

  1. J. E. Mayer and M. G. Mayer,Statistical Mechanics (2nd ed.) (Wiley, New York, 1977).

    Google Scholar 

  2. G. E. Uhlenbeck, inThe T. Y. Wu Festschrift, S. Fujita, ed. (Gordon & Breach, New York, 1978).

    Google Scholar 

  3. K. W. Kratky,Physica (Utrecht) A87:584 (1977).

    Google Scholar 

  4. C. A. Rogers,Proc. Lond. Math. Soc. 8:609 (1958);Packing and Covering (Cambridge U.P., Cambridge, 1964).

    Google Scholar 

  5. J. L. Lebowitz and O. Penrose,J. Math. Phys. 5:841 (1964).

    Google Scholar 

  6. F. H. Ree,Phys. Rev. 155:84 (1967).

    Google Scholar 

  7. L. V. Woodcock,J. Chem. Soc. Faraday Trans. II 72:1667 (1976); inStructure and Mobility in Mobility in Molecular and Atomic Glass, J. M. O'Reilly and M. Goldstein, eds., Annals N.Y. Acad. Sci. Vol. 371 (N.Y. Acad. Sci., New York, 1981), p. 274.

    Google Scholar 

  8. J. G. Kirkwood, E. K. Maun, B. J. Alder,J. Chem. Phys. 18:1040 (1950); B. J. Alder and T. E. Wainwright,J. Chem. Phys. 31:459 (1959);Phys. Rev. Lett. 18:968 (1959);Phys. Rev. A 1:18 (1970); W. W. Wood and J. D. Jacobson,J. Chem. Phys. 27:1207 (1957).

    Google Scholar 

  9. J. A. Barker and D. Henderson,Rev. Mod. Phys. 48:587 (1976).

    Google Scholar 

  10. T. D. Lee,Phys. Rev. 87:404 (1952).

    Google Scholar 

  11. C. N. Yang and T. D. Lee,Phys. Rev. 87:410 (1952).

    Google Scholar 

  12. J. Gammel,J. Math. Anal. Appl. 43:694 (1973);Rocky Mtn. J. Math. 4:203 (1974).

    Google Scholar 

  13. S. Katsura,Adv. Phys. 12:391 (1963).

    Google Scholar 

  14. M. Alexanian and D. E. Wortman,Phys. Rev. 143:96 (1966); A. Baram and M. Luban,J. Phys. C12:L659 (1979).

    Google Scholar 

  15. G. A. Baker, Jr. and P. Graves-Morris,Padé Approximants, inEncycl. of Math. and its Applications, G.-C. Rota, ed. (Addison-Wesley, Reading, Massachusetts, 1981), Vols. 13 and 14.

    Google Scholar 

  16. V. C. Aguilera-Navarro, M. Fortes, M. de Llano, and A. Plastino,J. Chem. Phys. 76:749 (1982).

    Google Scholar 

  17. J. D. Bernal,Nature 188:910 (1960).

    Google Scholar 

  18. V. M. Visscher and J. E. Gubernatis, inDynamical Properties of Solids, G. K. Horton and A. A. Maradudin, eds. (North-Holland, Amsterdam, 1980).

    Google Scholar 

  19. R. O. Watts and I. J. McGee,Liquid State Chemical Physics (Wiley, New York, 1976).

    Google Scholar 

  20. J. G. Kirkwood,J. Chem. Phys. 3:300 (1935).

    Google Scholar 

  21. G. S. Rushbrooke and H. I. Scoins,Phil. Mag. 42:582 (1951).

    Google Scholar 

  22. K. U. Co, J. J. Kozak, and K. D. Luks,J. Chem. Phys. 66:581 (1977).

    Google Scholar 

  23. J. K. Percus and G. J. Yevick,Phys. Rev. 110:1 (1958).

    Google Scholar 

  24. T. Morita,Prog. Theor. Phys. 20:920 (1958).

    Google Scholar 

  25. G. Stell,Physica (Utrecht) 29:517 (1963); S. A. Rice and J. Lekner,J. Chem. Phys. 42:3559 (1965).

    Google Scholar 

  26. Y. T. Lee, F. H. Ree, and T. Ree,J. Chem. Phys. 48:3506 (1968);55:234 (1971).

    Google Scholar 

  27. W. G. Hoover and F. H. Ree,J. Chem. Phys. 49:3609 (1968).

    Google Scholar 

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On leave from Instituto de Física Teorica, Sao Paulo, Brasil.

Supported by ININ & CONACyT.

On leave from Universidad Nacional, La Plata, Argentina CONICET.

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Aguilera-Navarro, V.C., Fortes, M., de Llano, M. et al. Hard-sphere fluid-to-solid transition and the virial expansion. J Stat Phys 32, 95–104 (1983). https://doi.org/10.1007/BF01009422

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  • DOI: https://doi.org/10.1007/BF01009422

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