Journal of Statistical Physics

, Volume 79, Issue 3–4, pp 569–583 | Cite as

The general solution of the binding mean spherical approximation for pairing ions

  • L. Blum
  • O. Bernard
Articles

Abstract

The mean spherical approximation (MSA) for an arbitrary mixture of charged hard spheres with saturating bonds is solved in the Wertheim formalism. Only pairs are allowed. It is shown that the general solution is given in terms of two scaling parameters and the set of binding fractions. One of the scales is the screening parameter, and the other is a coupling parameter analogous to that of the simple MSA, but that now is found solving a cubic equation. Therefore the full solution requires solvingm+2 nonlinear algebraic equations for a system withm components. A brief discussion of the thermodynamics is given.

Key Words

Ionic mixtures mean spherical approximation dimerizing ions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. K. Percus and G. Yevick,Phys. Rev. B 136:290 (1964).Google Scholar
  2. 2.
    J. L. Lebowitz and J. K. Percus,Phys. Rev. 144:251 (1966).CrossRefGoogle Scholar
  3. 3.
    E. Waisman and J. L. Lebowitz,J. Chem. Phys. 52:4307 (1970).CrossRefGoogle Scholar
  4. 4.
    L. Blum,Mol. Phys. 30:1529 (1975).Google Scholar
  5. 5.
    L. Blum and J. S. Høye,J. Phys. Chem. 81:1311 (1977).CrossRefGoogle Scholar
  6. 6.
    L. Blum,Chem. Phys. Lett. 26:200 (1974);J. Chem. Phys. 61:2129 (1974).CrossRefGoogle Scholar
  7. 7.
    S. A. Adelman and J. M. Deutch,J. Chem. Phys. 60:3935 (1974).CrossRefGoogle Scholar
  8. 8.
    L. Blum,J. Stat. Phys. 18:451 (1978).CrossRefGoogle Scholar
  9. 9.
    L. Blum and D. Q. Wei,J. Chem. Phys. 87:555 (1987).CrossRefGoogle Scholar
  10. 10.
    L. Blum and R. W. Fawcett,J. Phys. Chem. 96:408 (1992).CrossRefGoogle Scholar
  11. 11.
    L. Blum, F. Vericat, and R. W. Fawcett,J. Chem. Phys. 96:3039 (1992).CrossRefGoogle Scholar
  12. 12.
    Y. Rosenfeld and L. Blum,J. Phys. Chem. 89:5149 (1985).CrossRefGoogle Scholar
  13. 13.
    Y. Rosenfeld and L. Blum,J. Chem. Phys. 85:1556 (1986).CrossRefGoogle Scholar
  14. 14.
    L. Onsager,J. Phys. Chem. 63:189 (1939).CrossRefGoogle Scholar
  15. 15.
    E. Meeron,J. Chem. Phys. 26:804 (1957);28:630 (1958).CrossRefGoogle Scholar
  16. 16.
    Y. Rosenfeld,Phys. Rev. A 35:938 (1987).CrossRefGoogle Scholar
  17. 17.
    K. C. Ng,J. Phys. Chem. 61:2680 (1974).CrossRefGoogle Scholar
  18. 18.
    L. Blum and A. H. Narten,J. Chem. Phys. 56:5197 (1972); A. H. Narten, L. Blum, and R. H. Fowler,J. Chem. Phys. 60:3378 (1974).CrossRefGoogle Scholar
  19. 19.
    E. Waisman, J. S. Høye, and G. Stell,Chem. Phys. Lett. 32:209 (1976).Google Scholar
  20. 20.
    L. Blum, J. N. Herrera, and F. Vericat,J. Stat. Phys. 66:249 (1992).CrossRefGoogle Scholar
  21. 21.
    N. Bjerrum,K. Dan. Vidensk. Felsk. Math. Fys. Medd. 7:9 (1926).Google Scholar
  22. 22.
    Yu. V. Kalyuzhnyi, M. F. Holovko, and A. D. Haymet,J. Chem. Phys. 95:9151 (1991).CrossRefGoogle Scholar
  23. 23.
    Yu. V. Kalyuzhnyi and M. F. Holovko,Mol. Phys. 80:1165 (1994).Google Scholar
  24. 24.
    Yu. V. Kalyuzhnyi and V. Vlachy,Chem. Phys. Lett. 215:518 (1993).CrossRefGoogle Scholar
  25. 25.
    W. Ebeling and M. Grigo,J. Sol. Chem. 11:151 (1982).CrossRefGoogle Scholar
  26. 26.
    T. Cartailler, P. Turq, L. Blum, and N. Condamine,J. Phys. Chem. 96:6766 (1992).CrossRefGoogle Scholar
  27. 27.
    A. Tani and D. Henderson,J. Chem. Phys. 79:2390 (1983).CrossRefGoogle Scholar
  28. 28.
    H. R. Corti, R. Fernandez Prini, and L. Blum,J. Chem. Soc. Faraday Trans. 82:921 (1986).CrossRefGoogle Scholar
  29. 29.
    H. R. Corti, R. Fernandez Prini, and L. Blum,J. Chem. Phys. 87:3052 (1987).CrossRefGoogle Scholar
  30. 30.
    P. T. Cummings and G. Stell,Mol. Phys. 51:253 (1984);55:33 (1985);60:1315 (1987); S. H. Lee, P. T. Cummings, and G. Stell,Mol. Phys. 62:65 (1987).Google Scholar
  31. 31.
    G. Stell, SUNYCEAS Report No. 460 (March 1985); S. H. Lee, J. C. Rasaiah, and P. T. Cummings,J. Chem. Phys. 83:317 (1985); J. C. Rasaiah and S. H. Lee,J. Chem. Phys. 83:5870, 6396 (1985); S. H. Lee and J. C. RasaiahJ. Chem. Phys. 86:983 (1987); J. C. Rasaiah, J. Zhu, and S. H. Lee,J. Chem. Phys. 91:495, 505 (1989).Google Scholar
  32. 32.
    G. Stell and Y. Zhou,J. Chem. Phys. 91:3618 (1989).CrossRefGoogle Scholar
  33. 33.
    J. N. Herrera and L. Blum,J. Chem. Phys. 94:5077 (1991).CrossRefGoogle Scholar
  34. 34.
    J. Zhu and J. C. Rasaiah,J. Chem. Phys. 94:3141 (1991).CrossRefGoogle Scholar
  35. 35.
    J. N. Herrera and L. Blum,J. Chem. Phys. 94:6190 (1991).CrossRefGoogle Scholar
  36. 36.
    M. S. Wertheim,J. Stat. Phys. 35:19–35 (1984);42:459–477 (1984).CrossRefGoogle Scholar
  37. 37.
    M. S. Wertheim,J. Chem. Phys. 85:2929 (1985);87:7323 (1987);88:1214 (1988).CrossRefGoogle Scholar
  38. 38.
    M. F. Holovko and Yu. V. Kalyuzhnyi,Mol. Phys. 73:1145 (1991); Yu. V. Kalyuzhnyi, I. A. Protsykevytch, and M. F. Holovko,Chem. Phys. Lett. 215:1 (1993).Google Scholar
  39. 39.
    L. Blum and Y. Rosenfeld,J. Stat. Phys. 63:1177 (1991).CrossRefGoogle Scholar
  40. 40.
    E. S. Yakub,Mol. Phys. 77:845 (1992).Google Scholar
  41. 41.
    Yu. V. Kalyuzhnyi and G. Stell,Mol. Phys. 78:1247 (1993).Google Scholar
  42. 42.
    R. J. Baxter,J. Chem. Phys. 52:4559 (1970).CrossRefGoogle Scholar
  43. 43.
    M. S. Wertheim,J. Math. Phys. 5:643 (1964).CrossRefGoogle Scholar
  44. 44.
    L. Blum and J. S. Høye,J. Phys. Chem. 81:1311 (1977).CrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • L. Blum
    • 1
  • O. Bernard
    • 2
  1. 1.Department of PhysicsUniversity of Puerto RicoRio Piedras
  2. 2.Laboratoire de Physicochimie Théorique, URA 503Université Bordeaux ITalence CedexFrance

Personalised recommendations