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Exact Solution of the Percus–Yevick Approximation for Hard Spheres …and Beyond

  • Andrés Santos
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 923)

Abstract

One of the milestones of the statistical-mechanical theory of liquids in equilibrium was the exact analytical solution of the Percus–Yevick integral equation for three-dimensional hard spheres by, independently, Wertheim and Thiele in 1963. The solution was later extended to mixtures, hard hyperspheres in odd dimensions, and sticky hard spheres. This chapter presents some of those solutions within the framework of the rational-function approximation, which lends itself to generalizations beyond the Percus–Yevick approximation.

Keywords

Integral Equation Hard Sphere Virial Coefficient Helmholtz Free Energy Packing Fraction 
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.

References

  1. 1.
    R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1974)zbMATHGoogle Scholar
  2. 2.
    M.S. Wertheim, Phys. Rev. Lett. 10, 321 (1963)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    E. Thiele, J. Chem. Phys. 39, 474 (1963)ADSCrossRefGoogle Scholar
  4. 4.
    M.S. Wertheim, J. Math. Phys. 5, 643 (1964)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    J.L. Lebowitz, Phys. Rev. 133, A895 (1964)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    J.S. Høye, L. Blum, J. Stat. Phys. 16, 399 (1977)ADSCrossRefGoogle Scholar
  7. 7.
    C. Freasier, D.J. Isbister, Mol. Phys. 42, 927 (1981)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    E. Leutheusser, Physica A 127, 667 (1984)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    R.J. Baxter, J. Chem. Phys. 49, 2770 (1968)ADSCrossRefGoogle Scholar
  10. 10.
    J.W. Perram, E.R. Smith, Chem. Phys. Lett. 35, 138 (1975)ADSCrossRefGoogle Scholar
  11. 11.
    B. Barboy, Chem. Phys. 11, 357 (1975)ADSCrossRefGoogle Scholar
  12. 12.
    B. Barboy, R. Tenne, Chem. Phys. 38, 369 (1979)ADSCrossRefGoogle Scholar
  13. 13.
    S.B. Yuste, A. Santos, Phys. Rev. A 43, 5418 (1991)ADSCrossRefGoogle Scholar
  14. 14.
    S.B. Yuste, M. López de Haro, A. Santos, Phys. Rev. E 53, 4820 (1996)ADSCrossRefGoogle Scholar
  15. 15.
    M. López de Haro, S.B. Yuste, A. Santos, in Theory and Simulation of Hard-Sphere Fluids and Related Systems, ed. by A. Mulero. Lecture Notes in Physics, vol. 753 (Springer, Berlin, 2008), pp. 183–245Google Scholar
  16. 16.
    J.R. Solana, Perturbation Theories for the Thermodynamic Properties of Fluids and Solids (CRC Press, Boca Raton, 2013)CrossRefzbMATHGoogle Scholar
  17. 17.
    R.D. Rohrmann, A. Santos, Phys. Rev. E 76, 051202 (2007)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    L. Carlitz, Duke Math. J. 24, 151 (1957)MathSciNetCrossRefGoogle Scholar
  19. 19.
    J. Abate, W. Whitt, Queueing Syst. 10, 5 (1992)MathSciNetCrossRefGoogle Scholar
  20. 20.
    A. Santos, Radial distribution function for hard spheres. Wolfram Demonstrations Project (2013), http://demonstrations.wolfram.com/RadialDistributionFunctionForHardSpheres/
  21. 21.
    H. Reiss, H.L. Frisch, J.L. Lebowitz, J. Chem. Phys. 31, 369 (1959)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    E. Helfand, H.L. Frisch, J.L. Lebowitz, J. Chem. Phys. 34, 1037 (1961)ADSCrossRefGoogle Scholar
  23. 23.
    J.L. Lebowitz, E. Helfand, E. Praestgaard, J. Chem. Phys. 43, 774 (1965)ADSCrossRefGoogle Scholar
  24. 24.
    A. Santos, Phys. Rev. Lett. 109, 120601 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    K.W. Kratky, J. Stat. Phys. 27, 533 (1982)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    S. Labík, J. Kolafa, A. Malijevský, Phys. Rev. E 71, 021105 (2005)ADSCrossRefGoogle Scholar
  27. 27.
    N. Clisby, B.M. McCoy, J. Stat. Phys. 122, 15 (2006)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    R.J. Wheatley, Phys. Rev. Lett. 110, 200601 (2013)ADSCrossRefGoogle Scholar
  29. 29.
    C. Zhang, B.M. Pettitt, Mol. Phys. 112, 1427 (2014)ADSCrossRefGoogle Scholar
  30. 30.
    A.J. Schultz, D.A. Kofke, Phys. Rev. E 90, 023301 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    J. Kolafa, S. Labík, A. Malijevský, Phys. Chem. Chem. Phys. 6, 2335 (2004). See also http://www.vscht.cz/fch/software/hsmd/ CrossRefGoogle Scholar
  32. 32.
    S.B. Yuste, A. Santos, J. Stat. Phys. 72, 703 (1993)ADSCrossRefGoogle Scholar
  33. 33.
    S.B. Yuste, A. Santos, Phys. Rev. E 48, 4599 (1993)ADSCrossRefGoogle Scholar
  34. 34.
    S.B. Yuste, A. Santos, M. López de Haro, J. Chem. Phys. 108, 3683 (1998)ADSCrossRefGoogle Scholar
  35. 35.
    A. Santos, S.B. Yuste, M. López de Haro, J. Chem. Phys. 109, 6814 (1998)ADSCrossRefGoogle Scholar
  36. 36.
    A. Malijevský, S.B. Yuste, A. Santos, J. Chem. Phys. 125, 074507 (2006)ADSCrossRefGoogle Scholar
  37. 37.
    A. Santos, R.D. Rohrmann, Phys. Rev. E 87, 052138 (2013)ADSCrossRefGoogle Scholar
  38. 38.
    M. Mandell, H. Reiss, J. Stat. Phys. 13, 113 (1975)ADSCrossRefGoogle Scholar
  39. 39.
    Y. Rosenfeld, J. Chem. Phys. 89, 4272 (1988)ADSCrossRefGoogle Scholar
  40. 40.
    M. Heying, D. Corti, J. Phys. Chem. B 108, 19756 (2004)CrossRefGoogle Scholar
  41. 41.
    T. Boublík, J. Chem. Phys. 53, 471 (1970)ADSCrossRefGoogle Scholar
  42. 42.
    E.W. Grundke, D. Henderson, Mol. Phys. 24, 269 (1972)ADSCrossRefGoogle Scholar
  43. 43.
    L.L. Lee, D. Levesque, Mol. Phys. 26, 1351 (1973)ADSCrossRefGoogle Scholar
  44. 44.
    G.A. Mansoori, N.F. Carnahan, K.E. Starling, J.T.W. Leland, J. Chem. Phys. 54, 1523 (1971)ADSCrossRefGoogle Scholar
  45. 45.
    M. Barošová, A. Malijevský, S. Labík, W.R. Smith, Mol. Phys. 87, 423 (1996)ADSCrossRefGoogle Scholar
  46. 46.
    M.A. Miller, D. Frenkel, Phys. Rev. Lett. 90, 135702 (2003)ADSCrossRefGoogle Scholar
  47. 47.
    M.A. Miller, D. Frenkel, J. Chem. Phys. 121, 535 (2004)ADSCrossRefGoogle Scholar
  48. 48.
    J. Largo, M.A. Miller, F. Sciortino, J. Chem. Phys. 128, 134513 (2008)ADSCrossRefGoogle Scholar
  49. 49.
    M.A. Miller, D. Frenkel, J. Phys. Condens. Matter 16, S4901 (2004)ADSCrossRefGoogle Scholar
  50. 50.
    A.J. Post, E.D. Glandt, J. Chem. Phys. 84, 4585 (1986)ADSCrossRefGoogle Scholar
  51. 51.
    N.A. Seaton, E.D. Glandt, J. Chem. Phys. 84, 4595 (1987)ADSCrossRefGoogle Scholar
  52. 52.
    N.A. Seaton, E.D. Glandt, J. Chem. Phys. 86, 4668 (1987)ADSCrossRefGoogle Scholar
  53. 53.
    N.A. Seaton, E.D. Glandt, J. Chem. Phys. 87, 1785 (1987)ADSCrossRefGoogle Scholar
  54. 54.
    R.D. Rohrmann, A. Santos, Phys. Rev. E 89, 042121 (2014)ADSCrossRefGoogle Scholar
  55. 55.
    R.O. Watts, D. Henderson, R.J. Baxter, Adv. Chem. Phys. 21, 421 (1971)Google Scholar
  56. 56.
    M.G. Noro, D. Frenkel, J. Chem. Phys. 113, 2941 (2000)ADSCrossRefGoogle Scholar
  57. 57.
    H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971)Google Scholar
  58. 58.
    L.E. Reichl, A Modern Course in Statistical Physics, 2nd edn. (Wiley, New York, 1998)zbMATHGoogle Scholar
  59. 59.
    S. Fishman, M.E. Fisher, Physica A 108, 1 (1981)ADSMathSciNetCrossRefGoogle Scholar
  60. 60.
    A. Malijevský, A. Malijevský, S.B. Yuste, A. Santos, M. López de Haro, Phys. Rev. E 66, 061203 (2002)ADSCrossRefGoogle Scholar
  61. 61.
    A. Malijevský, S.B. Yuste, A. Santos, M. López de Haro, Phys. Rev. E 75, 061201 (2007)ADSCrossRefGoogle Scholar
  62. 62.
    S.B. Yuste, A. Santos, M. López de Haro, J. Chem. Phys. 128, 134507 (2008). Erratum: 140, 179901 (2014)Google Scholar
  63. 63.
    R.D. Rohrmann, A. Santos, Phys. Rev. E 83, 011201 (2011)ADSMathSciNetCrossRefGoogle Scholar
  64. 64.
    R.D. Rohrmann, A. Santos, Phys. Rev. E 84, 041203 (2011)ADSMathSciNetCrossRefGoogle Scholar
  65. 65.
    A. Malijevský, A. Santos, J. Chem. Phys. 124, 074508 (2006)ADSCrossRefGoogle Scholar
  66. 66.
    A. Malijevský, S.B. Yuste, A. Santos, Phys. Rev. E 76, 021504 (2007)ADSCrossRefGoogle Scholar
  67. 67.
    R. Fantoni, A. Giacometti, A. Malijevský, A. Santos, J. Chem. Phys. 131, 124106 (2009)ADSCrossRefGoogle Scholar
  68. 68.
    S.B. Yuste, A. Santos, J. Chem. Phys. 101, 2355 (1994)ADSCrossRefGoogle Scholar
  69. 69.
    L. Acedo, A. Santos, J. Chem. Phys. 115, 2805 (2001)ADSCrossRefGoogle Scholar
  70. 70.
    J. Largo, J.R. Solana, S.B. Yuste, A. Santos, J. Chem. Phys. 122, 084510 (2005)ADSCrossRefGoogle Scholar
  71. 71.
    S.B. Yuste, A. Santos, M. López de Haro, Mol. Phys. 109, 987 (2011)ADSCrossRefGoogle Scholar
  72. 72.
    A. Santos, S.B. Yuste, M. López de Haro, Condens. Matter Phys. 15, 23602 (2012)CrossRefGoogle Scholar
  73. 73.
    A. Santos, S.B. Yuste, M. López de Haro, M. Bárcenas, P. Orea, J. Chem. Phys. 139, 074503 (2013)ADSCrossRefGoogle Scholar
  74. 74.
    R. Fantoni, A. Santos, Phys. Rev. E 84, 041201 (2011)ADSCrossRefGoogle Scholar
  75. 75.
    R. Fantoni, A. Santos, Phys. Rev. E 87, 042102 (2013)ADSCrossRefGoogle Scholar
  76. 76.
    R. Fantoni, A. Santos, J. Chem. Phys. 140, 244513 (2014)ADSCrossRefGoogle Scholar
  77. 77.
    M.A.G. Maestre, R. Fantoni, A. Giacometti, A. Santos, J. Chem. Phys. 138, 094904 (2013)ADSCrossRefGoogle Scholar
  78. 78.
    M. Robles, M. López de Haro, J. Chem. Phys. 107, 4648 (1997)ADSCrossRefGoogle Scholar
  79. 79.
    A. Díez, J. Largo, J.R. Solana, J. Chem. Phys. 125, 074509 (2006)ADSCrossRefGoogle Scholar
  80. 80.
    S.B. Yuste, A. Santos, M. López de Haro, Mol. Phys. 98, 439 (2000)ADSCrossRefGoogle Scholar
  81. 81.
    E. Waisman, Mol. Phys. 25, 45 (1973)ADSCrossRefGoogle Scholar
  82. 82.
    D. Henderson, L. Blum, Mol. Phys. 32, 1627 (1976)ADSCrossRefGoogle Scholar
  83. 83.
    J. Largo, J.R. Solana, L. Acedo, A. Santos, Mol. Phys. 101, 2981 (2003)ADSCrossRefGoogle Scholar
  84. 84.
    A. Lang, G. Kahl, C.N. Likos, H. Löwen, M. Watzlawek, J. Phys. Condens. Matter 11, 10143 (1999)ADSCrossRefGoogle Scholar
  85. 85.
    S. Zhou, J.R. Solana, J. Chem. Phys. 131, 204503 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Andrés Santos
    • 1
  1. 1.Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx)Universidad de ExtremaduraBadajozSpain

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