Skip to main content
SpringerLink
Log in

Possibilities of the Molecular Modeling of Kinetic Processes under Supercritical Conditions

  • IN COMMEMORATION OF ACADEMICIAN V.V. LUNIN: SELECTED CONTRIBUTIONS FROM HIS STUDENTS AND COLLEAGUES
  • Published:
Russian Journal of Physical Chemistry A Aims and scope Submit manuscript

Abstract

Current possibilities of modeling the kinetics of supercritical processes are considered, based on the theory of an absolute rate of the reaction for non-ideal reaction systems, which considers intermolecular interactions that change the effective energy of activation of elementary stages. This allows the theory to describe the rates of elementary stages for arbitrary temperatures and densities of the reagent in different phases. Application of this theory in a wide range of state parameters (pressure and temperature) is examined while calculating elementary bimolecular reactions and dissipative coefficients under supercritical conditions. Generalized dependences within the law of corresponding states are calculated for the compressibility, viscosity, and thermal conductivity coefficients of pure substances and those of the compressibility, self- and mutual diffusion, and viscosity of binary mixtures. The effect density and temperature have on the rates of elementary stages under supercritical conditions is demonstrated for a reaction’s effective energies of activation, diffusion and share coefficients, and equilibrium constants of adsorption. Differences between models with effective parameters and the prospects for developing them by allowing for differences in size and contributions from the vibrational motions of components are described, along with ways of improving the accuracy of describing correlation effects.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.

Similar content being viewed by others

REFERENCES

  1. A. A. Galkin and V. V. Lunin, Russ. Chem. Rev. 74, 21 (2005).

    Article  CAS  Google Scholar 

  2. P. E. Savage, S. Gopalan, T. I. Mizan, et al., AIChE J. 41, 1723 (1995).

    Article  CAS  Google Scholar 

  3. D. Yu. Zalepugin, N. A. Til’kunova, I. V. Chernyshova, and V. S. Polyakov, Sverkhkrit. Flyuidy: Teor. Prakt. 1 (1), 27 (2006).

    Google Scholar 

  4. V. I. Bogdan, A. E. Koklin, and V. B. Kazanskii, Sverkhkrit. Flyuidy: Teor. Prakt. 1 (2), 5 (2006).

    Google Scholar 

  5. S. G. Entelis and R. P. Tiger, Reaction Kinetics in the Liquid Phase (Khimiya, Moscow, 1973) [in Russian].

    Google Scholar 

  6. E. A. Moelwyn-Hughes, The Kinetics of Reactions in Solution (Clarendon, Oxford, 1947).

    Google Scholar 

  7. R. A. Marcus, Ann. Rev. Phys. Chem. 15, 1 (1964).

    Article  Google Scholar 

  8. R. R. Dogonadze and A. M. Kuznetsov, Itogi Nauki Tekh., Ser.: Kinet. Katal. 5, 5 (1978).

    Google Scholar 

  9. A. M. Kuznetsov and J. Ulstrup, Electron Transfer in Chemistry and Biology (Wiley, Chichester, 1999).

    Google Scholar 

  10. Yu. K. Tovbin, Theory of Physicochemical Processes at the Gas–Solid Interface (Nauka, Moscow, 1990; CRC, Boca Raton, FL, 1991).

    Google Scholar 

  11. Yu. K. Tovbin, Prog. Surf. Sci. 34, 1 (1990).

    Article  CAS  Google Scholar 

  12. S. Glasstone, K. J. Laidler, and H. Eyring, The Theory of Rate Processes: The Kinetics of Chemical Reactions, Viscosity, Diffusion, and Electrochemical Phenomena (Van Nostrand, New York, 1941).

    Google Scholar 

  13. S. W. Benson, The Foundations of Chemical Kinetics (McGraw-Hill, New York, 1960).

    Google Scholar 

  14. E. N. Eremin, Principles of Chemical Kinetics (Vysshaya Shkola, Moscow, 1976) [in Russian].

    Google Scholar 

  15. M. I. Temkin, Zh. Fiz. Khim. 11, 169 (1938).

    CAS  Google Scholar 

  16. M. I. Temkin, Zh. Fiz. Khim. 24, 1312 (1950).

    CAS  Google Scholar 

  17. S. L. Kiperman, Introduction to the Kinetics of Heterogeneous Catalytic Reactions (Nauka, Moscow, 1964) [in Russian].

    Google Scholar 

  18. S. L. Kiperman, Foundations of Chemical Kinetics in Heterogeneous Catalysis (Khimiya, Moscow, 1979) [in Russian].

    Google Scholar 

  19. E. A. Guggenheim, Mixtures (Clarendon, Oxford, 1952).

    Google Scholar 

  20. I. P. Prigogine, The Molecular Theory of Solutions (Interscience, Amsterdam, New York, 1957).

    Google Scholar 

  21. N. A. Smirnova, The Molecular Theory of Solutions (Khimiya, Leningrad, 1987) [in Russian].

    Google Scholar 

  22. A. Kruse and E. Dinjus, J. Supercrit. Fluids 39, 362 (2007).

    Article  CAS  Google Scholar 

  23. A. B. Rabinovich and Yu. K. Tovbin, Kinet. Catal. 52, 471 (2011).

    Article  CAS  Google Scholar 

  24. T. L. Hill, Statistical Mechanics. Principles and Selected Applications (McGraw-Hill, New York, 1956).

    Google Scholar 

  25. Yu. K. Tovbin, Zh. Fiz. Khim. 55, 273 (1981).

    CAS  Google Scholar 

  26. Yu. K. Tovbin, Kinet. Katal. 23, 821 (1982).

    CAS  Google Scholar 

  27. Yu. K. Tovbin, Zh. Fiz. Khim. 69, 118 (1995).

    CAS  Google Scholar 

  28. Yu. K. Tovbin, Russ. J. Phys. Chem. A 72, 675 (1998).

    Google Scholar 

  29. N. N. Bogolyubov, Problems of Dynamic Theory in Statistical Physics (Gostekhizdat, Moscow, 1946) [in Russian].

    Google Scholar 

  30. I. Z. Fisher, Statistical Theory of Liquids (Chicago Univ., Chicago, 1964; GIFML, Moscow, 1961).

  31. C. A. Croxton, Liquid State Physics: A Statistical Mechanical Introduction (Cambridge Univ. Press, Cambridge, 1974).

    Book  Google Scholar 

  32. G. A. Martynov, Classical Static Physics. Fluid Theory (Intellekt, Dolgoprudnyi, 2011) [in Russian].

  33. Yu. K. Tovbin, M. M. Senyavin, and L. K. Zhidkova, Russ. J. Phys. Chem. A 73, 245 (1999).

    Google Scholar 

  34. S. Ono, Mem. Fac. Eng. Kyushi. Univ. 10, 190 (1947).

    Google Scholar 

  35. V. K. Fedyanin, Surface Phenomena in Liquids (LGU, Leningrad, 1975), p. 232 [in Russian].

    Google Scholar 

  36. O. Yu. Batalin, Yu. K. Tovbin, and V. K. Fedyanin, Zh. Fiz. Khim. 53, 3020 (1979).

    CAS  Google Scholar 

  37. N. M. Plakida, in Statistical Physics and Quantum Field Theory (Nauka, Moscow, 1973), p. 238 [in Russian].

    Google Scholar 

  38. V. A. Zagrebnov and V. K. Fedyanin, Sov. J. Theor. Math. Phys. 10, 84 (1972).

    Article  Google Scholar 

  39. V. K. Fedyanin, in Theoretical Methods for Describing the Properties of Solutions, Interschool Collection of Scientific Works (Ivanovo, 1987), p. 40 [in Russian].

    Google Scholar 

  40. J. Barker, Lattice Theories of the Liquid State (Pergamon, Oxford, 1963).

    Google Scholar 

  41. M. I. Shakhparonov, Introduction to the Molecular Theory of Solutions (GITTL, Moscow, 1956) [in Russian].

    Google Scholar 

  42. A. G. Morachevskii, N. A. Smirnova, E. M. Piotrovskaya, et al., Thermodynamics of Liquid-Vapour Equilibrium, Ed. by A. G. Morachevskii (Khimiya, Leningrad, 1989) [in Russian].

    Google Scholar 

  43. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954).

    Google Scholar 

  44. Z. Rac and M. F. Collins, Phys. Rev. B 20, 229 (1980).

    Google Scholar 

  45. S. P. J. Rodrigues and F. M. S. S. Fernandes, J. Phys. Chem. 98, 3917 (1994).

    Article  CAS  Google Scholar 

  46. B. V. Egorov, V. N. Komarov, Yu. E. Markachev, and Yu. K. Tovbin, Russ. J. Phys. Chem. A 74, 778 (2000).

    Google Scholar 

  47. Yu. K. Tovbin and V. N. Komarov, Russ. J. Phys. Chem. A 75, 490 (2001).

    Google Scholar 

  48. V. N. Komarov and Yu. K. Tovbin, High Temp. 41, 181 (2003).

    Article  CAS  Google Scholar 

  49. Yu. K. Tovbin, Zh. Fiz. Khim. 61, 2711 (1987).

    CAS  Google Scholar 

  50. Yu. K. Tovbin and V. N. Komarov, Russ. J. Phys. Chem. A 79, 1807 (2005).

    CAS  Google Scholar 

  51. R. C. Reid and T. K. Sherwood, The Properties of Gases and Liquids: Their Estimation and Correlation (McGraw-Hill, New York, San Francisco, etc., 1966).

  52. J. Levelt, Physica (Amsterdam, Neth.) 26, 361 (1960).

  53. V. A. Rabinovich, A. A. Vasserman, V. I. Nedostup, and L. S. Veksler, Thermophysical Properties of Neon, Argon, Krypton, and Xenon (Standartgiz, Moscow, 1976) [in Russian].

    Google Scholar 

  54. E. W. Crain and R. E. Santag, Adv. Cryog. Eng. 11, 379 (1966).

    Article  CAS  Google Scholar 

  55. V. N. Komarov, A. B. Rabinovich, and Yu. K. Tovbin, High Temp. 45, 463 (2007).

    Article  CAS  Google Scholar 

  56. Yu. K. Tovbin, Russ. J. Phys. Chem. A 79, 1903 (2005).

    CAS  Google Scholar 

  57. R. Bird, W. Stewart, and E. Lightfoot, Transport Phenomena (Wiley, New York, 2006).

    Google Scholar 

  58. A. Z. Patashinskii and V. L. Pokrovskii, Fluctuation Theory of Phase Transitions (Nauka, Moscow, 1975) [in Russian].

    Google Scholar 

  59. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Clarendon, Oxford, 1971).

    Google Scholar 

  60. Sh.-K. Ma, Modern Theory of Critical Phenomena (W.A.Benjamin, London, 1976).

  61. Yu. K. Tovbin, Russ. J. Phys. Chem. A 72, 2053 (1998).

    Google Scholar 

  62. Yu. K. Tovbin, A. B. Rabinovich, and E. V. Votyakov, Russ. Chem. Bull. 51, 1667 (2002).

    Article  CAS  Google Scholar 

  63. Yu. K. Tovbin and A. B. Rabinovich, Langmuir 20, 6041 (2004).

    Article  CAS  PubMed  Google Scholar 

  64. Yu. K. Tovbin, Molecular Theory of Adsorption in Porous Solids (CRC, Boca Raton, FL, 2017; Fizmatlit, Moscow, 2012).

  65. D. S. Tsiklis, Dense Gases (Khimiya, Moscow, 1977) [in Russian].

    Google Scholar 

  66. A. I. Cooper, J. Mater. Chem. 10, 207 (2000).

    Article  CAS  Google Scholar 

  67. M. A. McHugh and V. J. Krukonis, Supercritical Fluid Extraction: Principles and Practice (Stoneham, 1994).

  68. A. B. Rabinovich and Yu. K. Tovbin, Russ. Chem. Bull. 59, 1865 (2010).

    Article  CAS  Google Scholar 

  69. E. U. Franck, Ber. Bunsen-Ges. Phys. Chem. 88, 829 (1984).

    Google Scholar 

  70. M. A. Anisimov, V. A. Rabinovich, and V. V. Sychev, Thermodynamics of Critical State (Energoatomizdat, Moscow, 1990) [in Russian].

    Google Scholar 

  71. S. Chapman and T. Cowling, Mathematical Theory of Nonequilibrium Gases (Cambridge Univ. Press, Cambridge, 1953).

    Google Scholar 

  72. E. A. DiMarzio, J. Chem. Phys. 35, 658 (1961).

    Article  CAS  Google Scholar 

  73. S. Chandrasekhar, Liquid Crystals (Cambridge Univ., Cambridge (U.K.), 1977).

    Google Scholar 

  74. I. P. Bazarov and E. V. Gevorkyan, Statistical Theory of Solid and Liquid Crystals (Mosk. Gos. Univ., Moscow, 1983) [in Russian].

    Google Scholar 

  75. Yu. K. Tovbin, Russ. J. Phys. Chem. A 86, 705 (2012).

    Article  CAS  Google Scholar 

  76. M. P. Vukalovich and V. V. Altunin, Thermophysical Properties of Carbon Dioxide (Atomizdat, Moscow, 1965) [in Russian].

    Google Scholar 

  77. S. V. Titov and Yu. K. Tovbin, Russ. Chem. Bull. 60, 11 (2011).

    Article  CAS  Google Scholar 

  78. S. V. Titov and Yu. K. Tovbin, Russ. J. Phys. Chem. A 85, 194 (2011).

    Article  CAS  Google Scholar 

  79. G. M. Bell, J. Phys. C 5, 889 (1972).

    Article  CAS  Google Scholar 

  80. G. M. Bell and D. W. Salt, J. Chem. Soc: Faraday Trans. Pt. 2 72, 76 (1976).

    CAS  Google Scholar 

  81. Water. A Comprehensive Treatise, Ed. by F. Franks (Plenum, New York, London, 1972), Vol. 1.

    Google Scholar 

  82. D. Eizenberg and V. Kautsman, Structure and Properties of Water (Gidrometeooizdat, Leningrad, 1975) [in Russian].

    Google Scholar 

  83. Yu. K. Tovbin and S. V. Titov, Russ. J. Phys. Chem. A 87, 185 (2013).

    Article  CAS  Google Scholar 

  84. Yu. K. Tovbin and E. V. Votyakov, Russ. J. Phys. Chem. A 71, 214 (1997).

    Google Scholar 

  85. Yu. K. Tovbin and S. V. Titov, Sverkhkrit. Flyuidy: Teor. Prakt. 6 (2), 35 (2011).

    Google Scholar 

  86. Yu. K. Tovbin, Small Systems and Fundamentals of Thermodynamics (CRC, Boca Raton, FL, 2019; Fizmatlit, Moscow, 2018).

  87. Yu. K. Tovbin, Russ. J. Phys. Chem. A 92, 1045 (2018).

    Article  CAS  Google Scholar 

  88. Yu. K. Tovbin, Kinet. Catal. 60, 398 (2019).

    Article  CAS  Google Scholar 

  89. E. A. Moelwin-Hughes, The Kinetics of Reactions in Solution (Oxford Univ. Press, London, 1950).

    Google Scholar 

  90. Yu. K. Tovbin, Russ. J. Phys. Chem. A 93, 603 (2019).

    Article  CAS  Google Scholar 

  91. V. V. Brazhkin, A. G. Lyapin, V. N. Ryzhov, K. Trachenko, Yu. D. Fomin, and E. N. Tsiok, Phys. Usp. 55, 1061 (2012).

    Article  CAS  Google Scholar 

  92. I. M. Abdulagatov and P. V. Skripov, Sverkhkrit. Fluidy: Teor. Prakt. 15 (1), 34 (2020).

    Google Scholar 

  93. I. M. Lifshits, Zh. Eksp. Teor. Fiz. 9, 481 (1939).

    CAS  Google Scholar 

  94. I. Z. Fisher, in Many-Body Problems and Plasma Physics (Nauka, Moscow, 1967), p. 204 [in Russian].

    Google Scholar 

  95. I. R. Krichevskii, Phase Equilibria at High Pressures (Goskhimizdat, Moscow, 1963) [in Russian].

    Google Scholar 

  96. I. B. Borovskii, K. P. Gurov, Yu. E. Marchukova, and Yu. E. Ugaste, Interdiffusion Processes in Alloys, Ed. by K. P. Gurov (Nauka, Moscow, 1973) [in Russian].

    Google Scholar 

  97. Yu. K. Tovbin, Russ. J. Phys. Chem. B 5, 256 (2011).

    Article  CAS  Google Scholar 

  98. Yu. K. Tovbin, Russ. J. Phys. Chem. A 85, 238 (2011).

    Article  CAS  Google Scholar 

  99. Yu. K. Tovbin, Russ. J. Phys. Chem. B 6, 716 (2012).

    Article  CAS  Google Scholar 

  100. Yu. K. Tovbin, Russ. J. Phys. Chem. A 91, 403 (2017).

    Article  CAS  Google Scholar 

  101. A. Yu. Nikolaev, A. A. Lazutin, and Yu. K. Tovbin, in Proceedings of the All-Russia Conference on Physicochemical Aspects of Nanomaterial Technologies, Their Properties and Application, Moscow, 2009 (Intellekt Budushch., Obninsk, 2011), p. 121.

  102. S. N. Gaydamaka, V. V. Timofeev, Yu. V. Gur’ev, L. A. Lemenovsky, G. P. Brusova, O. O. Parenago, V. N. Bagratashvili, and V. V. Lunin, Russ. J. Phys. Chem. B 4, 1217 (2010).

  103. I. Barker and D. Henderson, Rev. Mod. Phys. 46, 587 (1976).

    Article  Google Scholar 

  104. Yu. K. Tovbin, Russ. J. Phys. Chem. A 80, 1554 (2006).

    Article  CAS  Google Scholar 

  105. Yu. K. Tovbin, Zh. Fiz. Khim. 61, 2711 (1987).

    CAS  Google Scholar 

  106. Yu. K. Tovbin, Russ. J. Phys. Chem. A 70, 1655 (1996).

    Google Scholar 

  107. J. W. Gibbs, Elementary Principles of Statistical Mechanics (Ox Bow Press, 1981; Nauka, Moscow, 1982).

  108. I. Prigogine and R. Defay, Chemical Thermodynamics (Longmans Green, London, 1954).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, 119991, Moscow, Russia

    Yu. K. Tovbin

Authors
  1. Yu. K. Tovbin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. K. Tovbin.

Additional information

Translated by L. Chernikova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tovbin, Y.K. Possibilities of the Molecular Modeling of Kinetic Processes under Supercritical Conditions. Russ. J. Phys. Chem. 95, 429–444 (2021). https://doi.org/10.1134/S0036024421030225

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0036024421030225

Keywords:

Search

Navigation