Adiabatic Coupling Constant of Nitrobenzene–n-Alkane Critical Mixtures. Evidence from Ultrasonic Spectra and Thermodynamic Data

  • Sirojiddin Z. Mirzaev
  • Udo Kaatze


Ultrasonic spectra of mixtures of nitrobenzene with n-alkanes, from n-hexane to n-nonane, are analyzed. They feature up to two Debye-type relaxation terms with discrete relaxation times and, near the critical point, an additional relaxation term due to the fluctuations in the local concentration. The latter can be well represented by the dynamic scaling theory. Its amplitude parameter reveals the adiabatic coupling constant of the mixtures of critical composition. The dependence of this thermodynamic parameter upon the length of the n-alkanes corresponds to that of the slope in the pressure dependence of the critical temperature and is thus taken another confirmation of the dynamic scaling model. The change in the variation of the coupling constant and of several other mixture parameters with alkane length probably reflects a structural change in the nitrobenzene–n-alkane mixtures when the number of carbon atoms per alkane exceeds eight.


Adiabatic coupling constant Binary liquids Critical demixing Dynamic scaling Ultrasonic spectroscopy 



S. Z. M. gratefully acknowledges a fellowship by the DAAD, Bonn, Germany.


  1. 1.
    K.G. Wilson, Rev. Mod. Phys. 55, 583 (1983)ADSCrossRefGoogle Scholar
  2. 2.
    M.A. Anisimov, Critical Phenomena in Liquids and Liquid Crystals (Gordon and Breach, Philadelphia, 1991)Google Scholar
  3. 3.
    J.J. Binney, N.J. Dowrick, A.J. Fisher, M.E.J. Newman, The Theory of Critical Phenomena (Clarendon, Oxford, 1992)MATHGoogle Scholar
  4. 4.
    C. Domb, The Critical Point: A Historical Introduction to the Modern Theory of Critical Phenomena (Taylor and Francis, London, 1996)Google Scholar
  5. 5.
    M.E. Fisher, Rev. Mod. Phys. 70, 653 (1998)ADSCrossRefGoogle Scholar
  6. 6.
    H.E. Stanley, Rev. Mod. Phys. 71, S358 (1999)CrossRefGoogle Scholar
  7. 7.
    A. Onuki, Phase Transition Dynamics (Cambridge University Press, Cambridge, 2002)CrossRefMATHGoogle Scholar
  8. 8.
    J.K. Bhattacharjee, S.Z. Mirzaev, U. Kaatze, Rep. Prog. Phys. 73, 066601 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    R. Folk, G. Moser, Europhys. Lett. 41, 177 (1998)ADSCrossRefGoogle Scholar
  10. 10.
    R.A. Ferrell, J.K. Bhattacharjee, Phys. Rev. A 31, 1788 (1985)ADSCrossRefGoogle Scholar
  11. 11.
    H. Strehlow, Rapid Reactions in Solution (VCH, Weinheim, 1992)Google Scholar
  12. 12.
    R. Behrends, I. Iwanowski, M. Kosmowska, A. Szala, U. Kaatze, J. Chem. Phys. 121, 5929 (2004)ADSCrossRefGoogle Scholar
  13. 13.
    J. Thoen, J. Hamelin, T.K. Bose, Phys. Rev. E 53, 6264 (1996)ADSCrossRefGoogle Scholar
  14. 14.
    D.T. Jacobs, S.C. Greer, Phys. Rev. E 54, 5358 (1996)ADSCrossRefGoogle Scholar
  15. 15.
    P. Urbanowicz, S.J. Rzoska, M. Paluch, B. Sawicki, A. Szulc, J. Zioło, Chem. Phys. 201, 575 (1995)ADSCrossRefGoogle Scholar
  16. 16.
    L.A. Davidovich, P.K. Khabibullaev, M.G. Khaliulin, Sov. Phys. Acoust. 19, 584 (1974)Google Scholar
  17. 17.
    S.N. Rao, A.V. Sarma, K.S. Rao, Acustica 41, 37 (1978)Google Scholar
  18. 18.
    P.K. Khabibillaev, S.S. Aliev, M.I. Shakhporonov, L.E. Kvasova, in Physics and Physical Chemistry of Liquids, vol. 1, ed. by M.I. Shakhporonov (Moscow State University Press, Moscow, 1973), p. 94Google Scholar
  19. 19.
    L.I. Lisnyanskii, Y.S. Manucharov, Sov. Phys. Acoust. 22, 33 (1976)Google Scholar
  20. 20.
    H. Tanaka, Y. Wada, H. Nakajima, Chem. Phys. 75, 37 (1983)ADSCrossRefGoogle Scholar
  21. 21.
    N. Inoue, H. Takaoka, M. Kato, T. Hasegawa, K. Matsuzawa, Jpn. J. Appl. Phys. 30(Suppl. 30–1), 25 (1991)CrossRefGoogle Scholar
  22. 22.
    S.Z. Mirzaev, U. Kaatze, Chem. Phys. 393, 129 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    G. Pérez-Sánchez, P. Losada-Pérez, C.A. Cerdeiriña, J. Thoen, J. Chem. Phys. 132, 214503 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    M. Souto-Caride, J. Troncoso, J. Peliteiro, E. Carballo, L. Romani, Chem. Phys. 324, 483 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    N.J. Utt, S.Y. Lehman, D.T. Jacobs, J. Chem. Phys. 127, 104505 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    I.R. Abdelraziq, S.S. Yun, F.B. Stumpf, J. Acoust. Soc. Am. 88, 1831 (1990)ADSCrossRefGoogle Scholar
  27. 27.
    E. Sada, K. Takahashi, M. Hamada, J. Chem. Eng. Data 22, 279 (1977)CrossRefGoogle Scholar
  28. 28.
    M.L.S. Matos Lopes, C.A. Nieto de Castro, J.V. Sengers, Int. J. Thermophys. 13, 283 (1992)ADSCrossRefGoogle Scholar
  29. 29.
    G. Zalczer, A. Bourgou, D. Beysens, Phys. Rev. A 28, 440 (1983)ADSCrossRefGoogle Scholar
  30. 30.
    T. Yin, A. Shi, J. Xie, M. Wang, Z. Chen, X. An, W. Shen, J. Chem. Eng. Data 59, 1312 (2014)CrossRefGoogle Scholar
  31. 31.
    A. Hirtz, W. Lawnik, G.H. Findenegg, Colloids Surf. 51, 405 (1990)CrossRefGoogle Scholar
  32. 32.
    P. Habdas, Temperature and Pressure Studies of Dielectric Permittivity in Near-Critical Binary Mixtures, Ph.D. Thesis (University of Silesia, Katowice, 1999)Google Scholar
  33. 33.
    B.C. Miller, E.A. Clerke, S.C. Greer, J. Phys. Chem. 87, 1063 (1983)CrossRefGoogle Scholar
  34. 34.
    K. Orzechowski, M. Kosmowska, M. Adamczyk, J. Phys. Chem. B 116, 2492 (2012)CrossRefGoogle Scholar
  35. 35.
    H. Wang, Y. Wu, W. Dong, J. Chem. Termodyn. 37, 866 (2005)CrossRefGoogle Scholar
  36. 36.
    M.I. Aralagruppi, C.V. Jadar, T.M. Aminabhavi, J. Chem. Eng. Data 44, 435 (1999)CrossRefGoogle Scholar
  37. 37.
    M. Dzida, W. Marczak, J. Chem. Thermodyn. 37, 826 (2005)CrossRefGoogle Scholar
  38. 38.
    P. Losada-Pérez, M. Blesic, G. Pérez-Sánchez, C.A. Cerdeiriña, J. Troncoso, L. Romaní, J. Szydlowski, L.P.N. Rebelo, Fluid Phase Equ. 258, 7 (2007)CrossRefGoogle Scholar
  39. 39.
    A. Drozd-Rzosk, S.J. Rzoska, A.R. Imre, Phys. Chem. Chem Phys 6, 2291 (2004)CrossRefGoogle Scholar
  40. 40.
    Y. Miyake, Y. Izumi, Phys. Rev. A 15, 2065 (1977)ADSCrossRefGoogle Scholar
  41. 41.
    A. Dega-Dałkowska, Chem. Phys. Lett. 107, 575 (1984)ADSCrossRefGoogle Scholar
  42. 42.
    D. Beyens, S.H. Chen, J.P. Chabrat, L. Letamendia, J. Rouch, C. Vaucamps, J. Phys.(Paris) 38, L-203 (1977)CrossRefGoogle Scholar
  43. 43.
    G.D.J. Phillies, P.J. Chappell, D. Kivelson, J. Chem. Phys. 68, 4031 (1978)ADSCrossRefGoogle Scholar
  44. 44.
    S.-H. Chen, C.-C. Lai, J. Rouch, P. Tartaglia, Phys. Rev. 27, 1086 (1983)ADSCrossRefGoogle Scholar
  45. 45.
    N. Fameli, D.A. Balzarini, Phys. Rev. B 75, 064203 (2007)ADSCrossRefGoogle Scholar
  46. 46.
    S.J. Rzoska, J. Chrapeć, J. Zioło, Int. J. Thermophys. 11, 1087 (1990)ADSCrossRefGoogle Scholar
  47. 47.
    S.J. Fast, S.S. Yun, J. Acoust. Soc. Am. 81, 1418 (1987)ADSCrossRefGoogle Scholar
  48. 48.
    S.S. Aliev, P.K. Khabibullaev, Sov. Phys. Acoust. 16, 108 (1970)Google Scholar
  49. 49.
    Y.S. Manucharov, I.G. Mikhailov, Sov. Phys. Acoust. 20, 176 (1974)Google Scholar
  50. 50.
    L.A. Davidovich, S. Makhkamov, L. Pulatova, P.K. Khabibullaev, M.G. Khaliulin, Sov. Phys. Acoust. 18, 264 (1972)Google Scholar
  51. 51.
    A.J. Lui, M.E. Fisher, Phys. A 156, 35 (1989)MathSciNetCrossRefGoogle Scholar
  52. 52.
    P.C. Hohenberg, B.I. Halperein, Rev. Mod. Phys. 94, 435 (1977)ADSCrossRefGoogle Scholar
  53. 53.
    M.R. Moldover, G.A. Zimmerli, Phys. Rev. Lett. 82, 920 (1999)ADSCrossRefGoogle Scholar
  54. 54.
    P. Debye, Polar Molecules (Chemical Catalog, New York, 1929)MATHGoogle Scholar
  55. 55.
    V. Volterra, J.A. Bucaro, T.A. Litovitz, Ber. Bunsenges. Phys. Chem. 75, 309 (1971)Google Scholar
  56. 56.
    J.V. Champion, D.A. Jackson in Molecular Motions in Liquids, ed. by J. Lascombe(Reidel, Dordrecht, 1974)Google Scholar
  57. 57.
    M.G. Sceats, J.M. Dawes, J. Chem. Phys. 83, 1298 (1985)ADSCrossRefGoogle Scholar
  58. 58.
    R. Behrends, U. Kaatze, J. Phys. Chem. A 104, 3269 (2000)CrossRefGoogle Scholar
  59. 59.
    S.S. Aliev, L.E. Kvasova, L.V. Lanshina, K. Parpiev, P.K. Khabibullaev, Sov. Phys. Acoust. 16, 250 (1970)Google Scholar
  60. 60.
    A.P. Radlinski, L. Barré, D. Espinat, J. Mol. Struct. 383, 51 (1996)ADSCrossRefGoogle Scholar
  61. 61.
    K. Kawasaki, Ann. Phys. 61, 1 (1970)ADSCrossRefGoogle Scholar
  62. 62.
    R.A. Ferrell, Phys. Rev. Lett. 24, 1169 (1970)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute of Ion-Plasma and Laser TechnologiesUzbek Academy of SciencesTashkentUzbekistan
  2. 2.Drittes Physikalisches InstitutGeorg-August-Universität GöttingenGöttingenGermany

Personalised recommendations