Skip to main content
Log in

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

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. K.G. Wilson, Rev. Mod. Phys. 55, 583 (1983)

    Article  ADS  Google Scholar 

  2. M.A. Anisimov, Critical Phenomena in Liquids and Liquid Crystals (Gordon and Breach, Philadelphia, 1991)

    Google Scholar 

  3. J.J. Binney, N.J. Dowrick, A.J. Fisher, M.E.J. Newman, The Theory of Critical Phenomena (Clarendon, Oxford, 1992)

    MATH  Google Scholar 

  4. C. Domb, The Critical Point: A Historical Introduction to the Modern Theory of Critical Phenomena (Taylor and Francis, London, 1996)

    Google Scholar 

  5. M.E. Fisher, Rev. Mod. Phys. 70, 653 (1998)

    Article  ADS  Google Scholar 

  6. H.E. Stanley, Rev. Mod. Phys. 71, S358 (1999)

    Article  Google Scholar 

  7. A. Onuki, Phase Transition Dynamics (Cambridge University Press, Cambridge, 2002)

    Book  MATH  Google Scholar 

  8. J.K. Bhattacharjee, S.Z. Mirzaev, U. Kaatze, Rep. Prog. Phys. 73, 066601 (2010)

    Article  ADS  Google Scholar 

  9. R. Folk, G. Moser, Europhys. Lett. 41, 177 (1998)

    Article  ADS  Google Scholar 

  10. R.A. Ferrell, J.K. Bhattacharjee, Phys. Rev. A 31, 1788 (1985)

    Article  ADS  Google Scholar 

  11. H. Strehlow, Rapid Reactions in Solution (VCH, Weinheim, 1992)

    Google Scholar 

  12. R. Behrends, I. Iwanowski, M. Kosmowska, A. Szala, U. Kaatze, J. Chem. Phys. 121, 5929 (2004)

    Article  ADS  Google Scholar 

  13. J. Thoen, J. Hamelin, T.K. Bose, Phys. Rev. E 53, 6264 (1996)

    Article  ADS  Google Scholar 

  14. D.T. Jacobs, S.C. Greer, Phys. Rev. E 54, 5358 (1996)

    Article  ADS  Google Scholar 

  15. P. Urbanowicz, S.J. Rzoska, M. Paluch, B. Sawicki, A. Szulc, J. Zioło, Chem. Phys. 201, 575 (1995)

    Article  ADS  Google Scholar 

  16. L.A. Davidovich, P.K. Khabibullaev, M.G. Khaliulin, Sov. Phys. Acoust. 19, 584 (1974)

    Google Scholar 

  17. S.N. Rao, A.V. Sarma, K.S. Rao, Acustica 41, 37 (1978)

    Google Scholar 

  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. 94

    Google Scholar 

  19. L.I. Lisnyanskii, Y.S. Manucharov, Sov. Phys. Acoust. 22, 33 (1976)

    Google Scholar 

  20. H. Tanaka, Y. Wada, H. Nakajima, Chem. Phys. 75, 37 (1983)

    Article  ADS  Google Scholar 

  21. N. Inoue, H. Takaoka, M. Kato, T. Hasegawa, K. Matsuzawa, Jpn. J. Appl. Phys. 30(Suppl. 30–1), 25 (1991)

    Article  Google Scholar 

  22. S.Z. Mirzaev, U. Kaatze, Chem. Phys. 393, 129 (2012)

    Article  ADS  Google Scholar 

  23. G. Pérez-Sánchez, P. Losada-Pérez, C.A. Cerdeiriña, J. Thoen, J. Chem. Phys. 132, 214503 (2010)

    Article  ADS  Google Scholar 

  24. M. Souto-Caride, J. Troncoso, J. Peliteiro, E. Carballo, L. Romani, Chem. Phys. 324, 483 (2006)

    Article  ADS  Google Scholar 

  25. N.J. Utt, S.Y. Lehman, D.T. Jacobs, J. Chem. Phys. 127, 104505 (2007)

    Article  ADS  Google Scholar 

  26. I.R. Abdelraziq, S.S. Yun, F.B. Stumpf, J. Acoust. Soc. Am. 88, 1831 (1990)

    Article  ADS  Google Scholar 

  27. E. Sada, K. Takahashi, M. Hamada, J. Chem. Eng. Data 22, 279 (1977)

    Article  Google Scholar 

  28. M.L.S. Matos Lopes, C.A. Nieto de Castro, J.V. Sengers, Int. J. Thermophys. 13, 283 (1992)

    Article  ADS  Google Scholar 

  29. G. Zalczer, A. Bourgou, D. Beysens, Phys. Rev. A 28, 440 (1983)

    Article  ADS  Google Scholar 

  30. T. Yin, A. Shi, J. Xie, M. Wang, Z. Chen, X. An, W. Shen, J. Chem. Eng. Data 59, 1312 (2014)

    Article  Google Scholar 

  31. A. Hirtz, W. Lawnik, G.H. Findenegg, Colloids Surf. 51, 405 (1990)

    Article  Google Scholar 

  32. P. Habdas, Temperature and Pressure Studies of Dielectric Permittivity in Near-Critical Binary Mixtures, Ph.D. Thesis (University of Silesia, Katowice, 1999)

  33. B.C. Miller, E.A. Clerke, S.C. Greer, J. Phys. Chem. 87, 1063 (1983)

    Article  Google Scholar 

  34. K. Orzechowski, M. Kosmowska, M. Adamczyk, J. Phys. Chem. B 116, 2492 (2012)

    Article  Google Scholar 

  35. H. Wang, Y. Wu, W. Dong, J. Chem. Termodyn. 37, 866 (2005)

    Article  Google Scholar 

  36. M.I. Aralagruppi, C.V. Jadar, T.M. Aminabhavi, J. Chem. Eng. Data 44, 435 (1999)

    Article  Google Scholar 

  37. M. Dzida, W. Marczak, J. Chem. Thermodyn. 37, 826 (2005)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  39. A. Drozd-Rzosk, S.J. Rzoska, A.R. Imre, Phys. Chem. Chem Phys 6, 2291 (2004)

    Article  Google Scholar 

  40. Y. Miyake, Y. Izumi, Phys. Rev. A 15, 2065 (1977)

    Article  ADS  Google Scholar 

  41. A. Dega-Dałkowska, Chem. Phys. Lett. 107, 575 (1984)

    Article  ADS  Google Scholar 

  42. D. Beyens, S.H. Chen, J.P. Chabrat, L. Letamendia, J. Rouch, C. Vaucamps, J. Phys.(Paris) 38, L-203 (1977)

    Article  Google Scholar 

  43. G.D.J. Phillies, P.J. Chappell, D. Kivelson, J. Chem. Phys. 68, 4031 (1978)

    Article  ADS  Google Scholar 

  44. S.-H. Chen, C.-C. Lai, J. Rouch, P. Tartaglia, Phys. Rev. 27, 1086 (1983)

    Article  ADS  Google Scholar 

  45. N. Fameli, D.A. Balzarini, Phys. Rev. B 75, 064203 (2007)

    Article  ADS  Google Scholar 

  46. S.J. Rzoska, J. Chrapeć, J. Zioło, Int. J. Thermophys. 11, 1087 (1990)

    Article  ADS  Google Scholar 

  47. S.J. Fast, S.S. Yun, J. Acoust. Soc. Am. 81, 1418 (1987)

    Article  ADS  Google Scholar 

  48. S.S. Aliev, P.K. Khabibullaev, Sov. Phys. Acoust. 16, 108 (1970)

    Google Scholar 

  49. Y.S. Manucharov, I.G. Mikhailov, Sov. Phys. Acoust. 20, 176 (1974)

    Google Scholar 

  50. L.A. Davidovich, S. Makhkamov, L. Pulatova, P.K. Khabibullaev, M.G. Khaliulin, Sov. Phys. Acoust. 18, 264 (1972)

    Google Scholar 

  51. A.J. Lui, M.E. Fisher, Phys. A 156, 35 (1989)

    Article  MathSciNet  Google Scholar 

  52. P.C. Hohenberg, B.I. Halperein, Rev. Mod. Phys. 94, 435 (1977)

    Article  ADS  Google Scholar 

  53. M.R. Moldover, G.A. Zimmerli, Phys. Rev. Lett. 82, 920 (1999)

    Article  ADS  Google Scholar 

  54. P. Debye, Polar Molecules (Chemical Catalog, New York, 1929)

    MATH  Google Scholar 

  55. V. Volterra, J.A. Bucaro, T.A. Litovitz, Ber. Bunsenges. Phys. Chem. 75, 309 (1971)

    Google Scholar 

  56. J.V. Champion, D.A. Jackson in Molecular Motions in Liquids, ed. by J. Lascombe(Reidel, Dordrecht, 1974)

  57. M.G. Sceats, J.M. Dawes, J. Chem. Phys. 83, 1298 (1985)

    Article  ADS  Google Scholar 

  58. R. Behrends, U. Kaatze, J. Phys. Chem. A 104, 3269 (2000)

    Article  Google Scholar 

  59. S.S. Aliev, L.E. Kvasova, L.V. Lanshina, K. Parpiev, P.K. Khabibullaev, Sov. Phys. Acoust. 16, 250 (1970)

    Google Scholar 

  60. A.P. Radlinski, L. Barré, D. Espinat, J. Mol. Struct. 383, 51 (1996)

    Article  ADS  Google Scholar 

  61. K. Kawasaki, Ann. Phys. 61, 1 (1970)

    Article  ADS  Google Scholar 

  62. R.A. Ferrell, Phys. Rev. Lett. 24, 1169 (1970)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Udo Kaatze.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mirzaev, S.Z., Kaatze, . Adiabatic Coupling Constant of Nitrobenzene–n-Alkane Critical Mixtures. Evidence from Ultrasonic Spectra and Thermodynamic Data. Int J Thermophys 37, 89 (2016). https://doi.org/10.1007/s10765-016-2095-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10765-016-2095-4

Keywords

Navigation