Advertisement

Fluids with Long-Range Forces: Toward a Simple Analytic Theory

  • G. Stell
Part of the Modern Theoretical Chemistry book series (MTC, volume 5)

Abstract

There is no reason why one should not be able to develop systematic and accurate approximation schemes in the statistical theory of fluids of such analytic simplicity that their numerical assessment will require no more than an electronic slide rule, paper and pencil, or an expanse of fine sand and a pointed stick. This article is concerned with the description of certain techniques to that end.

Keywords

Monte Carlo Hard Sphere Ionic Solution Core Condition Pade Approximant 
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.
    G. Stell, Remarks on Thermodynamics Perturbation Theory and Related Approximations, SUSB Engineering Report * 182, 1–38 (November 1970).Google Scholar
  2. 2.
    J. C. Rasaiah and G. Stell, Three-body free energy terms and effective potentials in polar fluids and ionic solutions, Chem. Phys. Lett 25, 519–522 (1974).CrossRefGoogle Scholar
  3. 3.
    J. C. Rasaiah, B. Larsen, and G. Stell, Thermodynamic perturbation theory for potentials of multipolar symmetry I, J. Chem. Phys. 63, 722–733 (1975); 64, 913 (1976).Google Scholar
  4. 4.
    B. Larsen, J. C. Rasaiah, and G. Stell, Thermodynamic perturbation theory for potentials of multipolar symmetry II, Mol. Phys (in press).Google Scholar
  5. 5.
    J. S. Hoye, J. L. Lebowitz, and G. Stell, Generalized mean spherical approximations for polar and ionic fluids, J. Chem. Phys 61, 3253–3260 (1974).CrossRefGoogle Scholar
  6. 6.
    G. Stell and S. F. Sun, Generalized mean spherical approximation for charged hard spheres, J. Chem. Phys 63, 5333 (1975).CrossRefGoogle Scholar
  7. 7.
    J. S. Hoye and G. Stell, Ornstein-Zernicke equation with a core condition and direct correlation function of Yukawa form, Mol. Phys 32, 195–207 (1976).CrossRefGoogle Scholar
  8. 8.
    J. S. Hoye, G. Stell, and E. Waisman, Ornstein-Zernicke equation for a two-Yukawa c (r) with a core condition, Mol. Phys 32, 209–230 (1976).CrossRefGoogle Scholar
  9. 9.
    H. L. Lemberg and F. H. Stillinger, Central-force model for liquid water, J. Chem. Phys 62, 1677–1690 (1975).CrossRefGoogle Scholar
  10. 10.
    J. E. Enderby, T. Gaskell, and N. H. March, Asymptotic form of correlation functions in classical fluids and in liquid helium 4, Proc. Phys. Soc 85, 217–221 (1965).CrossRefGoogle Scholar
  11. 11.
    M. D. Johnson, P. Hutchinson, and N. H. March, Ion-ion oscillatory potentials in liquid metals, Proc. Roy. Soc. A 282, 283–302 (1964).CrossRefGoogle Scholar
  12. 12.
    N. D. Mermin, Exact lower bounds for some equilibrium properties of a classical one-component plasma, Phys. Rev 171, 272–275 (1968).CrossRefGoogle Scholar
  13. 13.
    G. Nienhuis and J. M. Deutch, The structure of dielectric fluids III, J. Chem. Phys 56, 1819–1834 (1972).CrossRefGoogle Scholar
  14. 14.
    J. S. Hoye and G. Stell, Statistical mechanics of polar systems: Dielectric constant for dipolar fluids, J. Chem. Phys 61, 562–572 (1974).CrossRefGoogle Scholar
  15. 15.
    G. Stell, Extension of the Ornstein-Zernike theory of the critical region II, Phys. Rev. Bl, 2265–2270 (1970).Google Scholar
  16. 16.
    G. Stell, The Percus-Yevick equation for the radial distribution function of a fluid, Physica 29, 517–534 (1963).CrossRefGoogle Scholar
  17. 17.
    A. Isihara, The Gibbs-Bogoliubov inequality, J. Phys. Al, 539–548 (1968).Google Scholar
  18. 18.
    L. Onsager, Electrostatic interaction of molecules, J. Phys. Chem 43, 189–196 (1939).CrossRefGoogle Scholar
  19. 19.
    O. Penrose, Convergence of fugacity expansions for fluids and lattice gases, J. Math. Phys 4, 1312–1320 (1963).CrossRefGoogle Scholar
  20. 20.
    H. C. Longuet-Higgins and B. Widom, A rigid sphere model for the melting of argon, Mol. Phys 8, 549–556 (1964).CrossRefGoogle Scholar
  21. 21.
    G. S. Rushbrooke, G. Stell and J. S. Hoye, Theory of polar liquids I. Dipolar hard spheres, Mol. Phys 26, 1199–1215 (1973).CrossRefGoogle Scholar
  22. 22.
    D. E. Sullivan, J. M. Deutch, and G. Stell, Thermodynamics of polar lattices, Mol. Phys 28 1359–1371 (1974).CrossRefGoogle Scholar
  23. 23.
    G. N. Patey and J. P. Valleau, Dipolar hard spheres; A Monte-Carlo study, J. Chem. Phys 61, 534–540 (1974).CrossRefGoogle Scholar
  24. 24.
    L. Verlet and J. J. Weis, Perturbation theories for polar fluids, Mol. Phys 28, 665–682 (1974).CrossRefGoogle Scholar
  25. 25.
    I. R. McDonald, Application of thermodynamic perturbation theory to polar and polarizable fluids, J. Phys. C 7, 1225–1236 (1974).CrossRefGoogle Scholar
  26. 26.
    G. N. Patey and J. P. Valleau, Fluids of spheres containing quadrupoles and dipoles: A study using perturbation theory and Monte Carlo computations, J. Chem. Phys. 64, 170 (1976).Google Scholar
  27. 27.
    G. Stell, J. Rasaiah and H. Narang, Thermodynamic perturbation theory for simple polar fluids II, Mol. Phys 27, 1393–1414 (1974).CrossRefGoogle Scholar
  28. 28.
    G. Stell and J. Lebowitz, Equilibrium properties of a system of charged particles, J. Chem. Phys 49, 3706–3717 (1968).CrossRefGoogle Scholar
  29. B. Larsen, Studies in statistical mechanics of electrolytes. I. Equation of state for the restricted primitive model (to appear in J. Chem. Phys,1976).Google Scholar
  30. 30.
    G. Stell and K. C. Wu, Padé approximant for the internal energy of a system of charged particles, J. Chem. Phys 63, 491–498 (1975).CrossRefGoogle Scholar
  31. 31.
    J. L. Lebowitz and J. K. Percus, Mean spherical model for lattice gases with extended hard cores and continuum fluids, Phys. Rev 144, 251–258 (1966).CrossRefGoogle Scholar
  32. 32.
    H. W. Lewis and G. H. Wannier, Spherical model of a ferromagnet, Phys. Rev. 88, 682–683 (1952); errata, 90, 1131 (1953).Google Scholar
  33. 33.
    M. S. Wertheim, Exact solution of the Percus-Yevick integral equation for hard spheres, Phys. Rev. Lett 10, 321–323 (1963).CrossRefGoogle Scholar
  34. 34.
    E. Thiele, Equation of state for hard spheres, J. Chem. Phys 39, 474–479 (1963).CrossRefGoogle Scholar
  35. 35.
    E. Waisman and J. L. Lebowitz, Mean spherical model integral equation of charged hard spheres, J. Chem. Phys 56, 3086–3099 (1972).CrossRefGoogle Scholar
  36. 36.
    M. S. Wertheim, Exact solution of the mean spherical model for fluids of hard spheres with permanent electric dipole moments, J. Chem. Phys 55, 4291–4298 (1971).CrossRefGoogle Scholar
  37. 37.
    E. Waisman, The radial distribution function for a fluid of hard spheres at high densities, Mol. Phys 25, 45–48 (1973).CrossRefGoogle Scholar
  38. 38.
    D. Henderson, G. Stell, and E. Waisman, Ornstein-Zernike equation for the direct correlation function with a Yukawa tail, J. Chem. Phys 62, 4247–4259 (1975).CrossRefGoogle Scholar
  39. 39.
    S. A. Adleman and J. M. Deutch, Exact solution of the mean spherical model for strong electrolytes in polar solvents, J. Chem. Phys 60, 3935–3949 (1974).CrossRefGoogle Scholar
  40. 40.
    L. Blum, Solution of a model for the solvent-electrolyte interactions in the mean spherical approximation, J. Chem. Phys 61, 2129–2133 (1974).CrossRefGoogle Scholar
  41. 41.
    L. Blum, Invariant expansion II: The Ornstein-Zernike equation for nonspherical molecules and an extended solution to the mean spherical model, J. Chem. Phys 57, 1862–1869 (1972).CrossRefGoogle Scholar
  42. 42.
    L. Blum, Invariant expansion III: The general solution of the mean spherical model for neutral spheres with electrostatic interactions, J. Chem. Phys 58, 3295–3303 (1973).CrossRefGoogle Scholar
  43. 43.
    H. C. Andersen, D. Chandler, and J. D. Weeks, Roles of repulsive and attractive forces in liquids: The optimized random phase approximation, J. Chem. Phys 56, 3812 (1972).CrossRefGoogle Scholar
  44. 44.
    J. L. Lebowitz, G. Stell, and S. Baer, Separation of the interaction potential into two parts in treating many-body systems. I, J. Math. Phys 6, 1282–1298 (1965).CrossRefGoogle Scholar
  45. 45.
    G. Stell, J. L. Lebowitz, S. Baer, and W. Theumann, Separation of the interaction potential into two parts in statistical mechanics, II, J. Math. Phys 7, 1532–1547 (1966).CrossRefGoogle Scholar
  46. 46.
    G. Stell, Relation between y-ordering and the mode expansion, J. Chem. Phys 55, 1485–1486 (1971).CrossRefGoogle Scholar
  47. 47.
    G. Stell, Correlation functions and their generating functionals, in: Phase Transitions and Critical Phenomena (C. Domb and M. S. Green, eds.), Vol. 5. Academic Press, London (1976).Google Scholar
  48. 48.
    H. C. Andersen and D. Chandler, Mode expansion in equilibrium statistical mechanics III, J. Chem. Phys 55, 1497–1503 (1971).CrossRefGoogle Scholar
  49. 49.
    P. C. Hemmer, On the van der Waals theory of the vapour-liquid equilibrium IV, J. Math. Phys 5, 75–84 (1964).CrossRefGoogle Scholar
  50. 50.
    E. H. Hauge and P. C. Hemmer, Fluids with weak long-range forces, J. Chem. Phys 43, 323–327 (1966).CrossRefGoogle Scholar
  51. 51.
    J. S. Hoye, Ph.D. thesis, Institutt for Teoretisk Fysikk, NTH, Trondheim, Norway (1973).Google Scholar
  52. 52.
    H. L. Friedman, Ionic Solution Theory, John Wiley and Sons, New York (1962).Google Scholar
  53. 53.
    G. Kelbg, W. Ebeling, and H. Krienke, Zur statistischen Thermodynamik elektrolytischer Lösungen mit grossem Bjerrumparameter II, Z. Phys. Chem. (Leipzig) 238, 76–82 (1968).Google Scholar
  54. 54.
    H. C. Andersen, D. Chandler, and J. D. Weeks, Optimized cluster expansions for classical fluids III, J. Chem. Phys 57, 2626–2631 (1972).CrossRefGoogle Scholar
  55. 55.
    J. M. J. Van Leeuwen, J. Groeneveld, and J. De Boer, New method for the calculation of the pair correlation function, I, Physica 25, 792–808 (1959).CrossRefGoogle Scholar
  56. 56.
    M. S. Green, On the theory of the critical point of a simple fluid, J. Chem. Phys 33, 1403–1409 (1960).CrossRefGoogle Scholar
  57. 57.
    T. Morita and K. Hiroike, A new approach to the theory of classical fluids I, Progr. Theor. Phys 23, 1003–1027 (1960).CrossRefGoogle Scholar
  58. 58.
    E. Meeron, Nodal expansions III, Exact integral equations for particle correlation functions, J. Math. Phys 1, 192–201 (1960).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • G. Stell
    • 1
  1. 1.Department of Mechanics, College of Engineering and Applied SciencesState University of New York at Stony BrookStony BrookUSA

Personalised recommendations