Skip to main content
SpringerLink
Log in

Thermodynamics and Problems of Taking into Account Deformations of Porous Adsorbents

  • PHYSICOCHEMICAL PROCESSES AT THE INTERFACES
  • Published:
Protection of Metals and Physical Chemistry of Surfaces Aims and scope Submit manuscript

Abstract

An adsorbate can simultaneously affect the external and internal surfaces of an adsorbent, changing the volume of a sample with a fixed amount of the adsorbent. This process is discussed from the standpoints of mechanics of continuous media, thermodynamics, and molecular models. The microscopic theory of solids distinguishes between external and internal deformations, which makes it possible to associate mechanical characteristics with adsorption ones. Based on the lattice gas model, the principles of two-level structural models are formulated for deformable porous bodies. They enable the self-consistent description of changes in their volumes and adsorption isotherms as a function of the adsorbate external pressure at a fixed temperature. For the simple presentation of the calculation scheme, it is accepted that the atomic sizes of a solid and components of the adsorbate mobile phase are comparable. The molecular level reflects the volume of molecules and their lateral interaction in the quasi-chemical approximation. The supramolecular level of the model is presented as a granule/grain of a porous material with the set distribution function of different (in size and type) pores connected with each other. A relationship between internal deformations and the nonequilibrium state of a solid is shown. A calculation procedure for local mechanical modules with regard to internal and external deformations characterizing the mechanical properties of solids is exemplified by the compression modulus. The procedure takes into account the effect of the nonequilibrium of an adsorbent on adsorbent isotherms and its volume. The approach proposed can be also applied to related systems in which the adsorption of active mobile solutions by highly dispersed compounds changes their volume.

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

Similar content being viewed by others

REFERENCES

  1. Plachenov, T.G. and Kolosentsev, S.D., Porometriya (Porosimetry), Leningrad: Khimiya, 1988.

    Google Scholar 

  2. Fenelonov, V.B., Poristyi uglerod (Porous Carbon), Novosibirsk: Boreskov Institute of Catalysis Siberian Branch Russ. Acad. Sci., 1995.

  3. Radushkevich, L.V., Osnovnye problemy teorii fizicheskoi adsorbtsii (The Main Problems on Theory of Physical Adsorption), Moscow: Nauka, 1970.

  4. Modelirovanie poristykh materialov (Simulation of Porous Materials), Novosibirsk: Siberian Branch USSR Acad. Sci., 1976.

  5. Kheifets, L.I. and Neimark, A.V., Mnogofaznye protsessy v poristykh telakh (Multi-Phase Processes in Porous Bodies), Moscow: Khimiya, 1982.

  6. Adsorbenty, ikh poluchenie, svoistva i primenenie (Adsorbents, their Synthesizing, Properties, and Application), Leningrad: Nauka, 1985.

  7. Cheremskoi, P.G., Metody issledovaniya poristosti tverdykh tel (Methods for Researching Porosity of Solids), Moscow: Energoatomizdat, 1985.

  8. Karnaukhov, A.P., Adsorbtsiya. Tekstura dispersnykh poristykh materialov (Adsorption. Texture of Disperse Porous Materials), Novosibirsk: Nauka, 1999.

  9. Fenelonov, V.B., Vvedenie v fizicheskuyu khimiyu formirovaniya supramolekulyarnoi struktury adsorbentov i katalizatorov (Introduction to Physical Chemistry for Forming Adsorbents’ and Catalysators’ Supramolecular Structure), Novosibirsk: Siberian Branch Russ. Acad. Sci., 2004.

  10. Hill, T.L., Statistical Mechanics. Principles and Selected Applications, New York: McGraw-Hill, 1956.

    Google Scholar 

  11. Tovbin, Yu.K., Theory of Physical Chemistry Processes at a Gas-Solid Interface, Boca Raton, FL: CRC Press, 1991.

    Google Scholar 

  12. Tovbin, Yu.K., Molecular Theory of Adsorption in Porous Solids, Boca Raton, FL: CRC Press, 2017.

    Book  Google Scholar 

  13. Tovbin, Yu.K., Small Systems and Fundamentals of Thermodynamics, Boca Raton, FL: CRC Press, 2019.

    Google Scholar 

  14. Tovbin, Yu.K., Russ. J. Phys. Chem. A, 2020, vol. 94, no. 2, p. 270.

    Article  CAS  Google Scholar 

  15. Tovbin, Yu.K., Russ. J. Phys. Chem. A, 2020, vol. 94, no. 3, p. 622.

    Article  CAS  Google Scholar 

  16. Landau, L.D. and Lifshits, E.M., Course of Theoretical Physics, vol. 7: Theory of Elasticity, Oxford: Pergamon Press, 1989.

    Google Scholar 

  17. Sedov, L.I., Mekhanika sploshnoi sredy (Mechanics of Continuous Medium), Moscow: Nauka, 1970, vol. 1.

  18. Gibbs, J.W., Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of Thermodynamics, New York: C. Scribner’s Sons, 1902.

    Google Scholar 

  19. Tovbin, Yu.K., Russ. J. Phys. Chem. A, 2014, vol. 88, no. 11, p. 1965.

    Article  CAS  Google Scholar 

  20. Mehrer, H., Diffusion in Solids. Fundamentals, Methods, Materials, Diffusion-Controlled Processes, vol. 155 of Springer Series in Solid-State Sciences, Berlin: Springer, 2007.

  21. Bokshtein, B.S., Bokshtein, S.Z., and Zhukhovitskii, A.A., Termodinamika i kinetika diffuzii v tverdykh telakh (Thermodynamics and Kinetics of Diffusion in Solids), Moscow: Metallurgiya, 1974.

  22. Gurov, K.P., Kartashkin, B.A., and Ugaste, Yu.E., Vzaimnaya diffuziya v mnogofaznykh metallicheskikh sistemakh (Inter-Diffusion in Multi-Phase Metal Systems), Moscow: Nauka, 1981.

  23. Tsivadze, A.Yu. and Fomkin, A.A., Fizicheskaya khimiya adsorbtsionnykh yavlenii (Physical Chemistry of Adsorption Phenomena), Moscow: Granitsa, 2011, pp. 6–40.

  24. Adsorbtsiya, adsorbenty i adsorbtsionnye protsessy v nanoporistykh materialakh (Adsorption, Adsorbents, and Adsorptive Processes in Nano-Porous Materials), Tsivadtse, A.Yu., Ed., Moscow: Granitsa, 2011.

    Google Scholar 

  25. Tovbin, Yu.K., Russ. J. Phys. Chem. A, 2017, vol. 91, no. 9, p. 1621.

    Article  CAS  Google Scholar 

  26. Teodosiu, C., Elastic Models of Crystal Defects, Heidelberg: Springer, 1982.

    Book  Google Scholar 

  27. Smirnov, A.A., Teoriya splavov vnedreniya (Theory of Interstitial Alloys), Moscow: Nauka, 1979.

  28. Khachaturyan, A.G., Teoriya fazovykh perekhodov i struktura tverdykh tel (Theory of Phase Transitions and Structure of Solids), Moscow: Nauka, 1974.

  29. Katsnel'son, A.A. and Olemskoi, A.I., Mikroskopicheskaya teoriya neodnorodnykh struktur (Microscopic Theory of Heterogeneous Structures), Moscow: Moscow State Univ., 1987.

  30. Onami, M., Ivasimidzu, S., Genka, K., Siodzava, K., and Tanaka, K., Vvedenie v mikromekhaniku (Introduction to Micromechanics), Moscow: Metallurgiya, 1987.

  31. Coussy, O., Poromechanics, Chichester: Wiley, 2004.

    Google Scholar 

  32. Shchukin, E.D., Pertsev, A.V., and Amelina, E.A., Kolloidnaya khimiya (Colloid Chemistry), Moscow: Vysshaya Shkola, 1992, p. 416.

  33. Adamson, A.W., Physical Chemistry of Surfaces, New York: Wiley, 1975.

    Google Scholar 

  34. Greg, S.J. and Sing, K.S.W., Adsorption, Surface Area and Porosity, London: Academic, 1982.

    Google Scholar 

  35. Kiselev, A.V., Poshkus, D.P., and Yashin, Ya.I., Molekulyarnye osnovy adsorbtsionnoi khromatografii (Molecular Fundamentals for Adsorptive Chromatography), Moscow: Khimiya, 1986.

  36. Kiselev, A.V., Mezhmolekulyarnye vzaimodeistviya v adsorbtsii i khromatografii (Intermolecular Interactions under Adsorption and Chromatography), Moscow: Vysshaya Shkola, 1986.

  37. Tovbin, Yu.K., Izv. Akad. Nauk, Ser. Khim., 2003, no. 4, p. 827.

  38. Tovbin, Yu.K., Russ. J. Phys. Chem. A, 2015, vol. 89, no. 11, p. 1971.

    Article  CAS  Google Scholar 

  39. Tovbin, Yu.K., Russ. J. Phys. Chem. A, 2016, vol. 90, no. 8, p. 1507.

    Article  CAS  Google Scholar 

  40. Tovbin, Yu.K., Russ. J. Phys. Chem. A, 2013, vol. 87, no. 7, p. 1083.

    Article  CAS  Google Scholar 

  41. Tovbin, Yu.K. and Rabinovich, A.B., Russ. J. Phys. Chem. A, 2014, vol. 88, no. 2, p. 190.

    Google Scholar 

  42. Tovbin, Yu.K., Prot. Met. Phys. Chem. Surf., 2020, vol. 56, no. 4, p. 671.

    Article  Google Scholar 

  43. Tovbin, Yu.K., Senyavin, M.M., and Zhidkova, L.K., Russ. J. Phys. Chem. A, 1999, vol. 73, no. 2, p. 245.

    Google Scholar 

  44. Tovbin, Yu.K., Khim. Fiz., 2002, vol. 21, no. 1, p. 83.

    CAS  Google Scholar 

  45. Moelwyn-Hughes, E.A., Physical Chemistry, London: Pergamon, 1961.

    Google Scholar 

  46. Maradudin, A.A., Theoretical and Experimental Aspects of the Effects of Point Defects and Disorder on the Vibrations of Crystals, New York: Academic, 1966.

    Book  Google Scholar 

  47. Din, P., in Vychislitel’nye metody v teorii tverdogo tela (Computational Methods for Solid-State Theory), Moscow: Mir, 1975, p. 209.

  48. Tovbin, Yu.K., Titov, S.V., and Komarov, V.N., Phys. Solid State, 2015, vol. 57, no. 2, p. 360.

    Article  CAS  Google Scholar 

  49. Leibfried, G., Gittertheorie der mechanischen und thermischen Eigenschaften der Kristalle, Berlin, Heidelberg: Springer, 1955.

    Book  Google Scholar 

  50. Kosevich, A.M., Osnovy mekhaniki kristallicheskoi reshetki (Fundamentals for Mechanics of Crystal Lattice), Moscow: Nauka, 1972.

  51. Tovbin, Yu.K., Russ. J. Phys. Chem. A, 2015, vol. 89, no. 10, p. 1929.

    Article  CAS  Google Scholar 

  52. Avgul', N.N., Kiselev, A.V., and Poshkus, D.P., Adsorbtsiya gazov i parov na odnorodnykh poverkhnostyakh (Gas and Vapor Adsorption on Homogenous Surfaces), Moscow: Khimiya, 1975.

  53. Steele, W., The Interaction of Gases with Solid Surfaces, New York: Pergamon, 1974.

    Google Scholar 

  54. Popov, V.L., Mekhanika kontaktnogo vzaimodeistviya i fizika treniya (Mechanics of Contact Interaction and Friction Physics), Moscow: Fizmatlit, 2013.

  55. Aizikovich, S.M., Aleksandrov, V.M., Belokon’, A.V., Krenev, L.I., and Trubchik, I.S., Kontaktnye zadachi teorii uprugosti dlya neodnorodnykh sred (Contact Problems on Theory of Elasticity for Heterogeneous Media), Moscow: FIZMATLIT, 2006.

  56. Aleksandrov, V.M. and Chebakov, M.I., Vvedenie v mekhaniku kontaktnykh vzaimodeistvii (Introduction to Mechanics of Contact Interactions), Rostov-on-Don: TsVVR, 2007.

  57. Johnson, K.L., Contact Mechanics, Cambridge, London, New York, New Rochelle: Cambridge Univ. Press, 1985.

    Book  Google Scholar 

  58. Guggenheim, E.A., Mixture, Oxford: Oxford Univ. Press, 1952.

    Google Scholar 

  59. Smirnova, N.A., Molekulyarnye teorii rastvorov (Molecular Theories of Solutions), Leningrad: Khimiya, 1987.

  60. Tovbin, Yu.K., Russ. J. Phys. Chem. A, 2012, vol. 86, no. 4, p. 705.

    Article  CAS  Google Scholar 

  61. Tovbin, Yu.K., Prog. Surf. Sci., 1990, vol. 34, nos. 1–4, pp. 1–235.

    Article  CAS  Google Scholar 

  62. Breck, D.W., Zeolite Molecular Sieves: Structure, Chemistry, and Use, New York: Wiley, 1973.

    Google Scholar 

  63. Mackenzie, J.K., Proc. Phys. Soc. Sect. B, 1950, vol. 63, no. 1.

  64. Herring, C., in The Physics of Power Metallurgy, Kingston, W.E., Ed., New York: McGraw-Hill, 1951.

    Google Scholar 

  65. Lifshits, I.M., Izbrannye trudy. Fizika real’nykh kristallov i neuporyadochennykh sistem (Selected Works. Physics of Real Crystals and Disordered Systems), Moscow: Nauka, 1986.

  66. Skorokhod, V.V., Reologicheskie osnovy teorii spekaniya (Rheological Fundamentals for Theory of Sintering), Kiev: Naukova Dumka, 1972.

  67. Geguzin, Ya.E., Makroskopicheskie defekty v metallakh (Macroscopic Defects in Metals), Moscow: Metallurgizdat, 1962.

  68. Manevitch, L.I., Andrianov, I.V., and Oshmyan, V.G., Mechanics of Periodically Heterogeneous Structures, Berlin: Springer, 2002.

    Book  Google Scholar 

  69. Fischer-Cripps, A.C., Introduction to Contact Mechanics, Heidelberg: Springer, 2007.

  70. Cheremskoi, P.G., Pory v tverdom tele (Pores in Solid), Moscow: Energoatomizdat, 1990.

  71. Gokhshtein, A.Ya., Poverkhnostnoe natyazhenie tverdykh tel i adsorbtsiya (Surface Tension in Solids and Adsorption), Moscow: Nauka, 1976.

Download references

Funding

This work was supported by the Russian Foundation for Basic Research, project no. 18-03-00030a.

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. Thermodynamics and Problems of Taking into Account Deformations of Porous Adsorbents. Prot Met Phys Chem Surf 57, 1–16 (2021). https://doi.org/10.1134/S2070205121010196

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070205121010196

Keywords:

Search

Navigation