Advertisement

Structure and Forces in Liquids and Liquid Mixtures

  • N. H. March
Part of the Physics of Solids and Liquids book series (PSLI)

Abstract

In this chapter, we shall discuss first the statistical mechanical theory of liquids(1), and then of liquid mixtures. The discussion will include the theory of freezing of some simple liquids. This is closely related to the theory of the bulk liquid structure, the main topic of the first part of this chapter. Here, the so-called Born—Green—Yvon hierarchy is the starting point of all structural theories of simple liquids. This hierarchy was also used in the pioneering studies of Kirkwood and his school(2) on the theory of freezing. Modern trends in the theory of both liquid structure and freezing have emphasized the Ornstein—Zernike direct correlation function c (r), which is more directly connected with the interparticle interaction than the liquid pair function g(r), to be defined precisely below. This function c (r) [see equation (3.4.2) below] will therefore be a focal point in this discussion. However, first we shall give an operational definition of the structure factor S(k) of a simple liquid like argon, by summarizing the results for the intensity of X-ray scattering (see Chapter 1 for full details of the diffraction experiments).

Keywords

Liquid Mixture Isothermal Compressibility Collective Mode Concentration Fluctuation Liquid Argon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    See, for example, N. H. March and M. P. Tosi, Atomic Dynamics in Liquids, Macmillan, London (1976).Google Scholar
  2. 2.
    J. G. Kirkwood and E. Monroe, J. Chem. Phys. 9, 514 (1941).CrossRefGoogle Scholar
  3. 3.
    N. Kumar, N. H. March, and A. Wasserman, Phys. Chem. Liq. 11, 271 (1982).CrossRefGoogle Scholar
  4. 4.
    J. L. Yarnell, M. J. Katz, R. G. Wenzel, and S. H. Koenig, Phys. Rev. A 7, 2130 (1973).CrossRefGoogle Scholar
  5. 5.
    G. S. Rushbrooke, Physica 26, 259 (1960).CrossRefGoogle Scholar
  6. 6.
    T. Gaskell, Proc. Phys. Soc. 86, 693 (1965).CrossRefGoogle Scholar
  7. 7.
    M. D. Johnson and N. H. March, Phys. Lett. 3, 313 (1963); M. D. Johnson, P. Hutchinson, and N. H. March, Proc. R. Soc. London, Ser. A 282, 283 (1964).CrossRefGoogle Scholar
  8. 8.
    I. Ebbsjö, G. G. Robinson, and N. H. March, Phys. Chem. Liq. 13, 65 (1983).CrossRefGoogle Scholar
  9. 9.
    P. Schofield, Proc. Phys. Soc. 88, 149 (1966).CrossRefGoogle Scholar
  10. 10.
    P. Bratby, T. Gaskell, and N. H. March, Phys. Chem. Liq. 2, 53 (1970).CrossRefGoogle Scholar
  11. 11.
    P. A. Egelstaff, D. I. Page, and C. R. T. Heard, J. Phys. C 4, 1453 (1971).CrossRefGoogle Scholar
  12. 12.
    U. de Angelis and N. H. March, Phys. Chem. Liq. 6, 225 (1977).CrossRefGoogle Scholar
  13. 13.
    D. Pines, Elementary Excitations in Solids, Benjamin Inc., New York (1963).Google Scholar
  14. 14.
    J. R. D. Copley and J. M. Rowe, Phys. Rev. A 9, 1656 (1974).CrossRefGoogle Scholar
  15. 15.
    C. C. Matthai and N. H. March, Phys. Chem. Liq. 11 207 (1982).CrossRefGoogle Scholar
  16. 16.
    J. E. Enderby, T. Gaskell, and N. H. March, Proc. Phys. Soc. 85, 217 (1965).CrossRefGoogle Scholar
  17. 17.
    R. Eisenshitz and M. J. Wilford, Proc. Phys. Soc. 80, 1078 (1962).CrossRefGoogle Scholar
  18. 18.
    O. J. Kleppa, J. Chem. Phys. 56, 2034 (1972).CrossRefGoogle Scholar
  19. 19.
    J. S. Rowlinson, Liquids and Liquid Mixtures, Cambridge University Press (1969).Google Scholar
  20. 20.
    A. B. Bhatia and D. E. Thornton, Phys. Rev. B 2, 3004 (1970).CrossRefGoogle Scholar
  21. 21.
    R. C. Tolman, The Principles of Statistical Mechanics, Oxford University Press (1938).Google Scholar
  22. 22.
    T. L. Hill, Statistical Mechanics, McGraw-Hill Book Co., New York (1956).Google Scholar
  23. 23.
    A. B. Bhatia, W. H. Hargrove and N. H. March, J. Phys. C 6, 621 (1973).CrossRefGoogle Scholar
  24. 24.
    H. C. Longuet-Higgins, Proc. R. Soc. London, Ser. A 205, 247 (1951).CrossRefGoogle Scholar
  25. 25.
    S. P. McAlister and R. Turner, J. Phys. F 2, L51 (1972).CrossRefGoogle Scholar
  26. 26.
    A. B. Bhatia, Proc. Liquid Metals Conf., Adam Hilger: IOP (1976).Google Scholar
  27. 27.
    A. B. Bhatia and N. H. March, Phys. Lett. A 41, 397 (1972).CrossRefGoogle Scholar
  28. 28.
    P. J. Flory, J. Chem. Phys. 10, 51 (1942).CrossRefGoogle Scholar
  29. 29.
    A. B. Bhatia and N. H. March, J. Phys. F 5, 1100 (1975).CrossRefGoogle Scholar
  30. 30.
    K. Ichikawa and J. C. Thompson, J. Phys. F 4, L 9 (1974).Google Scholar
  31. 31.
    A. R. Miedema, P. F. de Chatel, and F. R. de Boer, Physica B 100, 1 (1980).Google Scholar
  32. 32.
    J. A. Alonso and N. H. March, Phys. Chem. Liq. 11, 135 (1981).CrossRefGoogle Scholar
  33. 33.
    D. I. Page, U. de Angelis, and N. H. March, Phys. Chem. Liq. 12, 53 (1982).CrossRefGoogle Scholar
  34. 34.
    M. Parrinello, M. P. Tosi, and N. H. March, Proc. R. Soc. London, Ser. A 341, 91 (1974).CrossRefGoogle Scholar
  35. 35.
    M. W. Johnson, N. H. March, D. I. Page, M. Parrinello, and M. P. Tosi, J. Phys. C 8, 751 (1975).CrossRefGoogle Scholar
  36. 36.
    M. Parrinello, M. P. Tosi, and N. H. March, J. Phys. C 7, 2577 (1974).CrossRefGoogle Scholar
  37. 37.
    I. Ebbsjö, P. Schofield, K. Sköld, and I. Waller, J. Phys. C 7, 3891 (1974).CrossRefGoogle Scholar
  38. 38.
    T. V. Ramakrishnan and M. Yussouff, Solid State Commun. 21, 389 (1977); Phys. Rev. B 19, 2775 (1979).CrossRefGoogle Scholar
  39. 39.
    A. D. J. Haymet and D. W. Oxtoby, J. Chem. Phys. 74, 2559 (1981).CrossRefGoogle Scholar
  40. 40.
    N. H. March and M. P. Tosi, Phys. Chem. Liq. 11, 129 (1981).CrossRefGoogle Scholar
  41. 41.
    See, for example, R. Lovett, C. Y. Mou, and F. P. Buff, J. Chem. Phys. 65, 570 (1976).CrossRefGoogle Scholar
  42. 42.
    A. B. Bhatia, N. H. March, and M. P. Tosi, Phys. Chem. Liq. 9, 229 (1980).CrossRefGoogle Scholar
  43. 43.
    N. H. March and M. P. Tosi, Phys. Chem. Liq. 11, 79 (1981).CrossRefGoogle Scholar
  44. 44.
    D. G. Triezenberg and R. Zwanzig, Phys. Rev. Lett. 28, 1183 (1972).CrossRefGoogle Scholar
  45. 45.
    N. H. March and M. P. Tosi, Phys. Chem. Liq. 11, 89 (1981).CrossRefGoogle Scholar
  46. 46.
    M. Rovere, M. P. Tosi, and N. H. March, Phys. Chem. Liq. 12, 177 (1982).CrossRefGoogle Scholar
  47. 47.
    B. D’Aguanno, M. Rovere, M. P. Tosi, and N. H. March, Phys. Chem. Liq. 13, 113 (1983).CrossRefGoogle Scholar
  48. 48.
    S. A. Rice et al., J. Chem. Phys. 81 1406 (1984) and other references given there.Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • N. H. March
    • 1
  1. 1.Theoretical Chemistry DepartmentUniversity of OxfordOxfordEngland

Personalised recommendations