Journal of Mathematical Chemistry

, Volume 57, Issue 2, pp 599–608 | Cite as

Theoretical modelling for calculation of the energy densities of adsorption sites using inverse gas chromatography

  • A. Bouhank
  • L. BencheikhEmail author
Original Paper


The inverse gas chromatography is used to determine the energy densities of the adsorption sites of the stationary solid phase. The use of this technique is old and dates back to the 1940s. The many possibilities offered by this method are described in several works. This work is an attempt to explore some adsorption local isotherm models in order to determine the energy density of the adsorption sites. It involves the use of integral equations of the first kind which are known to be numerically instable. These integral equations were solved by two different methods of solution. One is based on the use of Taylor series expansions and the other uses the Stieltjes transform. Some interesting theoretical and numerical results are presented.


Adsorption Integral equations Adsorption isotherms Energy 

List of symbols


Experimentally measured adsorption amount under the equilibrium pressure P and at the absolute temperature T


Langmuir constant


Universal gas constant


Coverage of adsorption sites having adsorption energy ɛ


Minimum and maximum values of the adsorption energy of the system


Dimensionless pressure


Dimensionless energy


  1. 1.
    H. Balard, Langmuir 13(5), 1260 (1997)CrossRefGoogle Scholar
  2. 2.
    A. Ziani, R. Xu, H.P. Schreiber, T. Kobayashi, J. Coating Technol. 71(893), 53 (1999)CrossRefGoogle Scholar
  3. 3.
    E. Díaz, S. Ordóñez, A. Vega, J. Coca, J. Chromatogr. A 1049(1–2), 139 (2004)CrossRefGoogle Scholar
  4. 4.
    E. Papirer, E. Brendle, F. Ozil, H. Balard, Carbon 37(8), 1265 (1999)CrossRefGoogle Scholar
  5. 5.
    A. Boutboul, F. Lenfant, P. Giampaoli, A. Feigenbaum, V. Ducruet, J. Chromatogr. A 969(1–2), 9 (2002)CrossRefGoogle Scholar
  6. 6.
    M. Jaroniec, R. Madey, Physical adsorption on heterogeneous solids, vol. 59 (Elsevier, Amsterdam, 1988)Google Scholar
  7. 7.
    R. Sips, J. Chem. Phys. 16(5), 490 (1948)CrossRefGoogle Scholar
  8. 8.
    R. Sips, J. Chem. Phys. 18(8), 1024 (1950)CrossRefGoogle Scholar
  9. 9.
    U. Landman, E.W. Montroll, J. Chem. Phys. 64(4), 1762 (1976)CrossRefGoogle Scholar
  10. 10.
    S.Z. Roginsky, In CR (Dokl.), Vol. 45 (Acad. Sci. URSS, 1944), p. 61Google Scholar
  11. 11.
    L.B. Harris, Surf. Sci. 10(2), 129 (1968)CrossRefGoogle Scholar
  12. 12.
    J.P. Hobson, Can. J. Phys. 43(11), 1934 (1965)CrossRefGoogle Scholar
  13. 13.
    M.M. Nederlof, W.H. Van Riemsdijk, L.K. Koopal, J. Colloid. Interf. Sci. 135(2), 410 (1990)CrossRefGoogle Scholar
  14. 14.
    J. Jagiełło, J.A. Schwarz, J. Colloid. Interf. Sci. 146(2), 415 (1991)CrossRefGoogle Scholar
  15. 15.
    M. Jaroniec, A.W. Marczewski, Monatsh. Chem. Chem. Monthly 115(8–9), 997 (1984)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Laboratory of Chemical Process Engineering (LCPE), Faculty of TechnologyFerhat ABBAS Setif-1 UniversitySétifAlgeria
  2. 2.Research Center, Industrial Technologies CRTICheraga, AlgiersAlgeria

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