, Volume 24, Issue 6, pp 517–530 | Cite as

An explicit multicomponent adsorption isotherm model: accounting for the size-effect for components with Langmuir adsorption behavior

  • Tom R. C. Van Assche
  • Gino V. Baron
  • Joeri F. M. DenayerEmail author


The extended Langmuir (EL) model is a popular multicomponent adsorption equilibria model, which can be based on single component Langmuir isotherms fitted on pure component data. Such explicit models are preferred over their implicit counterparts due to a lower computational requirement. An important shortcoming of the EL model is its inability to capture the adsorbate size effect occurring when the saturation capacities of pure component Langmuir isotherms are dissimilar. In contrast, this size effect is captured by the ideal adsorbed solution theory (IAST), which is centered on a set of implicit equations. In this work, we present an explicit multicomponent adsorption model for components with uneven saturation capacities obeying the Langmuir isotherm equation. This model predicts the expected change in selectivity with mixture composition, and even a selectivity reversal at high pressure when the adsorbates have significantly different molecular sizes. The model is extendable to any number of components, reduces to the Langmuir equation for pure components and to the EL equation when all saturation capacities are equal. The newly proposed model can be used to approximate the IAST and upgrade the EL model without introducing new parameters. Especially for binary mixtures, this model (Eqs. 12–14) offers a simple improvement of the EL model in predicting the experimental adsorption of light alkanes on 13X and 5A zeolites. The presented model is also applied to describe phase-changing adsorbents, in combination with the osmotic framework adsorbed solution theory (OFAST).


Adsorption Langmuir Isotherm Multicomponent IAST Model Mixture 



Prof. Verelst and Dr. Deridder are kindfully thanked for their fruitful mathematical discussions.

Supplementary material

10450_2018_9962_MOESM1_ESM.pdf (914 kb)
Supplementary material 1 (PDF 913 KB)


  1. Bousquet, D., Coudert, F.X., Fossati, A.G.J., Neimark, A.V., Fuchs, A.H., Boutin, A.: Adsorption induced transitions in soft porous crystals: An osmotic potential approach to multistability and intermediate structures. J. Chem. Phys. 138, 174706 (2013)CrossRefPubMedGoogle Scholar
  2. Couck, S., Van Assche, T.R.C., Liu, Y.Y., Baron, G.V., Van Der Voort, P., Denayer, J.F.M.: Adsorption and separation of small hydrocarbons on the flexible, vanadium-containing MOF, COMOC-2. Langmuir 31, 5063–5070 (2015)CrossRefPubMedGoogle Scholar
  3. Coudert, F.X.: The osmotic framework adsorbed solution theory: predicting mixture coadsorption in flexible nanoporous materials. Phys. Chem. Chem. Phys. 12(36), 10904 (2010)CrossRefPubMedGoogle Scholar
  4. Coudert, F.X., Jeffroy, M., Fuchs, A.H., Boutin, A., Mellot-draznieks, C.: Thermodynamics of guest-induced structural transitions in hybrid organic: inorganic frameworks. J. Am. Chem. Soc. 130(13), 14294–14302 (2008)CrossRefPubMedGoogle Scholar
  5. Coudert, F.X., Mellot-Draznieks, C., Fuchs, A.H., Boutin, A.: Prediction of breathing and gate-opening transitions upon binary mixture adsorption in metal-organic frameworks. J. Am. Chem. Soc. 131, 11329–11331 (2009)CrossRefPubMedGoogle Scholar
  6. Daems, I., Baron, G.V., Punnathanam, S., Snurr, R.Q., Denayer, J.F.M.: Molecular cage nestling in the liquid-phase adsorption of n-alkanes in 5A zeolite. J. Phys. Chem. C 111, 2191–2197 (2007)CrossRefGoogle Scholar
  7. Danner, R.P., Choi, E.C.F.: Mixture adsorption equilibria of ethane and ethylene on 13X molecular sieves. Ind. Eng. Chem. Res. 17, 248–253 (1978)Google Scholar
  8. Dávila, M., Riccardo, J.L., Ramirez-Pastor, A.J.: Exact statistical thermodynamics of alkane binary mixtures in zeolites: new interpretation of the adsorption preference reversal phenomenon from multisite-occupancy theory. Chem. Phys. Lett. 477(4–6), 402–405 (2009)CrossRefGoogle Scholar
  9. Do, D.D.: Adsorption Analysis: Equilibria and Kinetics. Imperial College Press, London (1998)Google Scholar
  10. Dunne, L.J., Manos, G., Du, Z.: Exact statistical mechanical one-dimensional lattice model of alkane binary mixture adsorption in zeolites and comparison with Monte-Carlo simulations. Chem. Phys. Lett. 377(5–6), 551–556 (2003)CrossRefGoogle Scholar
  11. Dunne, L.J., Furgani, A., Jalili, S., Manos, G.: Monte-Carlo simulations of methane/carbon dioxide and ethane/carbon dioxide mixture adsorption in zeolites and comparison with matrix treatment of statistical mechanical lattice model. Chem. Phys. 359(1–3), 27–30 (2009)CrossRefGoogle Scholar
  12. Erto, A., Lancia, A., Musmarra, D.: A real adsorbed solution theory model for competitive multicomponent liquid adsorption onto granular activated carbon. Microporous Mesoporous Mater. 154, 45–50 (2012)CrossRefGoogle Scholar
  13. Frey, D.D., Rodrigues, A.E.: Explicit calculation of multicomponent equilibria for ideal adsorbed solutions. AIChE J. 40(1), 182–186 (1994)CrossRefGoogle Scholar
  14. García-Pérez, E., Torréns, I.M., Lago, S., Dubbeldam, D., Vlugt, T.J.H., Maesen, T.L.M., Smit, B., Krishna, R., Calero, S.: Elucidating alkane adsorption in sodium-exchanged zeolites from molecular simulations to empirical equations. Appl. Surf. Sci. 252, 716–722 (2005)CrossRefGoogle Scholar
  15. Golshan-Shirazi, S., Guiochon, G.: Use of the LeVan-Vermeulen isotherm model for the calculation of elution band profiles in non-linear chromatography. J. Chromatogr. A 545(1), 1–26 (1991)CrossRefGoogle Scholar
  16. Gomez, L.F., Zacharia, R., Bénard, P., Chahine, R.: Multicomponent adsorption of biogas compositions containing CO2, CH4 and N2 on maxsorb and Cu-BTC using extended Langmuir and Doong–Yang models. Adsorption 21(5), 433–443 (2015)CrossRefGoogle Scholar
  17. Krishna, R., van Baten, J.M.: Separating n-alkane mixtures by exploiting differences in the adsorption capacity within cages of CHA, AFX and ERI zeolites. Sep. Purif. Technol. 60, 315–320 (2008)CrossRefGoogle Scholar
  18. Krishna, R., Van Baten, J.M.: Entropy-based separation of linear chain molecules by exploiting differences in the saturation capacities in cage-type zeolites. Sep. Purif. Technol. 76(3), 325–330 (2011)CrossRefGoogle Scholar
  19. Langmuir, I.: The adsorption of gases on plane surfaces of glass, mica and platinum. J. Am. Chem. Soc. 40(9), 1361–1403 (1918)CrossRefGoogle Scholar
  20. LeVan, M.D., Vermeulen, T.: Binary Langmuir and Freundlich isotherms for ideal adsorbed solutions. J. Phys. Chem. 85(22), 3247–3250 (1981)CrossRefGoogle Scholar
  21. Li, D., Zhou, Y., Shen, Y., Sun, W., Fu, Q., Yan, H., Zhang, D.: Experiment and simulation for separating CO2/N2 by dual-reflux pressure swing adsorption process. Chem. Eng. J. 297, 315–324 (2016)CrossRefGoogle Scholar
  22. Loiseau, T., Serre, C., Huguenard, C., Fink, G., Taulelle, F., Henry, M., Bataille, T., Férey, G.: A rationale for the large breathing of the porous aluminum terephthalate (MIL-53) upon hydration. Chemistry 10, 1373–1382 (2004)CrossRefPubMedGoogle Scholar
  23. Loughlin, K.F., Hasanain, M.A., Abdul-Rehman, H.B.: Quaternary, ternary, binary, and pure component sorption on zeolites 2: light alkanes on Linde 5A and 13X zeolites at moderate to high pressures. Ind. Eng. Chem. Res. 29, 1535–1546 (1990)CrossRefGoogle Scholar
  24. Matoz-Fernandez, D.A., Ramirez-Pastor, A.J.: Adsorption preference reversal phenomenon from multisite-occupancy theory for two-dimensional lattices. Chem. Phys. Lett. 610–611, 131–134 (2014)CrossRefGoogle Scholar
  25. Meyer, C., Hesse, D.: Modelling of coadsorption of different-sized molecules by using methods of statistical thermodynamics. Chem. Eng. Technol. 17, 119–126 (1994)CrossRefGoogle Scholar
  26. Mofahari, M., Salehi, S.M.: Pure and binary adsorption isotherms of ethylene and ethane on zeolite 5A. Adsorption 13, 101–110 (2013)CrossRefGoogle Scholar
  27. Moura, P.A.S., Bezerra, D.P., Vilarrasa-Garcia, E., Bastos-Neto, M., Azevedo, D.C.S.: Adsorption equilibria of CO2 and CH4 in cation-exchanged zeolites 13X. Adsorption 22(1), 71–80 (2016)CrossRefGoogle Scholar
  28. Myers, A.L., Prausnitz, J.M.: Thermodynamics of mixed-gas adsorption. AIChE J. 11(1), 121–127 (1965)CrossRefGoogle Scholar
  29. Nitta, T., Shigetomi, T., Kuro-Oka, M., Katayama, T.: An adsorption isotherm of multi-site occupancy model for homogeneous surface. J. Chem. Eng. Jpn. 17(1), 39–45 (1984)CrossRefGoogle Scholar
  30. Ritter, J.A., Bhadra, S.J., Ebnder, A.D.: On the use of the dual-process Langmuir model for correlating unary equilibria and predicting mixed-gas adsorption equilibria. Langmuir 27, 4700–4712 (2011)CrossRefPubMedGoogle Scholar
  31. Ruthven, D.M.: Principles of Adsorption & Adsorption Processes. Wiley, New York (1984)Google Scholar
  32. Silva, J.A.C., Ferreira, A., Mendes, P.A.P., Cunha, A.F., Gleichmann, K., Rodrigues, A.E.: Adsorption equilibrium and dynamics of fixed bed adsorption of CH4/N2 in binderless beads of 5A zeolite. Ind. Eng. Chem. Res. 54(24), 6390–6399 (2015)CrossRefGoogle Scholar
  33. Swisher, J.A., Lin, L.C., Kim, J., Smit, B.: Evaluating mixture adsorption models using molecular simulation. AIChE J. 59(8), 3054–3064 (2013)CrossRefGoogle Scholar
  34. Tarafder, A., Mazzotti, M.: A method for deriving explicit binary isotherms obeying the ideal adsorbed solution theory. Chem. Eng. Technol. 35(1), 102–108 (2012)CrossRefGoogle Scholar
  35. Valenzuela, D.P., Myers, A.L., Talu, O., Zwiebel, I.: Adsorption of gas mixtures: effect of energetic heterogeneity. AIChE J. 34(3), 397–402 (1988)CrossRefGoogle Scholar
  36. Van Assche, T.R.C., Duerinck, T., Van Der Perre, S., Baron, G.V., Denayer, J.F.M.: Prediction of molecular separation of polar-apolar mixtures on heterogeneous metal-organic frameworks: HKUST-1, Langmuir 30, 7878–7883 (2014)CrossRefPubMedGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Tom R. C. Van Assche
    • 1
  • Gino V. Baron
    • 1
  • Joeri F. M. Denayer
    • 1
    Email author
  1. 1.Department of Chemical EngineeringVrije Universiteit BrusselBrusselsBelgium

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