Skip to main content
SpringerLink
Log in

Adsorption and desorption in confined geometries: A discrete hopping model

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at different rates, and are strongly influenced by the concentration-dependent transport diffusion. Analytical solutions for the transport and self-diffusion are given for systems of length 1 and 2 and for a zero-range process. In the last situation the self- and transport diffusion can be calculated analytically for any length.

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. C.P. Brangwynne, G.H. Koenderink, F.C. MacKintosh, D.A. Weitz, Trends Cell Biol. 19, 423 (2009)

    Article  Google Scholar 

  2. M. Muthukumar, C.Y. Kong, Proc. Natl. Acad. Sci. USA 103, 5273 (2006)

    Article  ADS  Google Scholar 

  3. J. Kärger, D.M. Ruthven, D.N. Theodorou, Diffusion in Nanoporous Materials (Wiley-VCH, 2012)

  4. O.M. Yaghi, M. O’Keeffe, N.W. Ockwig, H.K. Chae, M. Eddaoudi, J. Kim, Nature 423, 705 (2003)

    Article  ADS  Google Scholar 

  5. M.E. Davis, Nature 417, 813 (2002)

    Article  ADS  Google Scholar 

  6. J.E. Galván-Moya, T. Altantzis, K. Nelissen, F.M. Peeters, M. Grzelczak, L.M. Liz-Marzán, S. Bals, G. Van Tendeloo, ACS Nano 8, 3869 (2014)

    Article  Google Scholar 

  7. J. Kärger, T. Binder, C. Chmelik, F. Hibbe, H. Krautscheid, R. Krishna, J. Weitkamp, Nature Mater. 13, 333 (2014)

    Article  ADS  Google Scholar 

  8. E. Beerdsen, D. Dubbeldam, B. Smit, Phys. Rev. Lett. 96, 044501 (2006)

    Article  ADS  Google Scholar 

  9. B. Smit, T.L.M. Maesen, Chem. Rev. 108, 4125 (2008)

    Article  Google Scholar 

  10. R. Krishna, Chem. Soc. Rev. 41, 3099 (2012)

    Article  Google Scholar 

  11. R. Zwanzig, J. Phys. Chem. 96, 3926 (1992)

    Article  Google Scholar 

  12. D. Reguera, J.M. Rubí, Phys. Rev. E 64, 061106 (2001)

    Article  ADS  Google Scholar 

  13. P.S. Burada, P. Hänggi, F. Marchesoni, G. Schmid, P. Talkner, Chem. Phys. Chem. 10, 45 (2009)

    Google Scholar 

  14. P. Kalinay, J.K. Percus, Phys. Rev. E 74, 041203 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  15. I. Santamaría-Holek, Z.J. Gryzwna, J.M. Rubi, Eur. Phys. J. Special Topics 222, 129 (2013)

    Article  ADS  Google Scholar 

  16. J.C.N. Carvalho, K. Nelissen, W.P. Ferreira, G.A. Farias, F.M. Peeters, Phys. Rev. E 85, 021136 (2012)

    Article  ADS  Google Scholar 

  17. D.A. Reed, G. Ehrlich, Surf. Sci. 102, 588 (1981)

    Article  ADS  Google Scholar 

  18. S.M. Auerbach, Int. Rev. Phys. Chem. 19, 155 (2000)

    Article  Google Scholar 

  19. T. Becker, K. Nelissen, B. Cleuren, B. Partoens, C. Van den Broeck, Phys. Rev. Lett. 111, 110601 (2013)

    Article  ADS  Google Scholar 

  20. C. Chmelik, H. Bux, J. Caro, L. Heinke, F. Hibbe, T. Titze, J. Kärger, Phys. Rev. Lett. 104, 085902 (2010)

    Article  ADS  Google Scholar 

  21. D.M. Ruthven, Principles of adsorption and adsorption processes (John Wiley and Sons, Inc., 1984)

  22. M. Tsotsalas, P. Hejcik, K. Sumida, Z. Kalay, S. Furukawa, S. Kitagawa, J. Am. Chem. Soc. 135, 4608 (2013)

    Article  Google Scholar 

  23. D. Reguera, G. Schmid, P.S. Burada, J.M. Rubí, P. Reimann, P. Hänggi, Phys. Rev. Lett. 96, 130603 (2006)

    Article  ADS  Google Scholar 

  24. P.K. Ghosh, V.R. Misko, F. Marchesoni, F. Nori, Phys. Rev. Lett. 110, 268301 (2013)

    Article  ADS  Google Scholar 

  25. P. Malgaretti, I. Pagonabarraga, J.M. Rubi, J. Chem. Phys. 138, 194906 (2013)

    Article  ADS  Google Scholar 

  26. S. Martens, A.V. Straube, G. Schmid, L. Schimansky-Geier, P. Hänggi, Phys. Rev. Lett. 110, 010601 (2013)

    Article  ADS  Google Scholar 

  27. S. Martens, G. Schmid, A.V. Straube, L. Schimansky-Geier, P. Hänggi, Eur. Phys. J. Special Topics 222, 2453 (2013)

    Article  ADS  Google Scholar 

  28. E. Beerdsen, B. Smit, D. Dubbeldam, Phys. Rev. Lett. 93, 248301 (2004)

    Article  ADS  Google Scholar 

  29. C. Tunca, D.M. Ford, Chem. Eng. Sci. 58, 3373 (2003)

    Article  Google Scholar 

  30. D.M. Ruthven, Nat. Phys. Sci. 232, 70 (1971)

    Article  ADS  Google Scholar 

  31. F.G. Pazzona, P. Demontis, G.B. Suffritti, J. Chem. Phys. 131, 234703 (2009)

    Article  ADS  Google Scholar 

  32. F.G. Pazzona, P. Demontis, G.B. Suffritti, J. Chem. Phys. 131, 234704 (2009)

    Article  ADS  Google Scholar 

  33. M. Esposito, Phys. Rev. E 85, 041125 (2012)

    Article  ADS  Google Scholar 

  34. F.G. Pazzona, P. Demontis, G.B. Suffritti, J. Phys. Chem. C 117, 349 (2013)

    Article  Google Scholar 

  35. J. Kärger, D.M. Ruthven, Diffusion in Zeolites and Other Microporous Solids (John Wiley & Sons, Inc., New York, 1992)

  36. T. Becker, K. Nelissen, B. Cleuren, B. Partoens, C. Van den Broeck, Phys. Rev. E 90, 052139 (2014)

    Article  ADS  Google Scholar 

  37. R. Gomer, Rep. Prog. Phys. 53, 917 (1990)

    Article  ADS  Google Scholar 

  38. M.R. Evans, T. Hanney, J. Phys. A: Math. Gen. 38, R195 (2005)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  39. E. Levine, D. Mukamel, G.M. Schütz, J. Stat. Phys. 120, 759 (2005)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  40. A. Asselah, R. Brito, J.L. Lebowitz, J. Stat. Phys. 87, 1131 (1997)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  41. J. Kärger, C. Chmelik, L. Heinke, R. Valiullin, Chem. Ing. Tech. 82, 779 (2010)

    Article  Google Scholar 

  42. J. Crank, The mathematics of diffusion (Oxford university press, 1979)

  43. D.R. Garg, D.M. Ruthven, Chem. Eng. Sci. 27, 417 (1972)

    Article  Google Scholar 

  44. R. Krishna, R. Baur, Sep. Purif. Technol. 33, 213 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Hasselt University, 3590, Diepenbeek, Belgium

    T. Becker, K. Nelissen, B. Cleuren & C. Van den Broeck

  2. Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, 2020, Antwerpen, Belgium

    K. Nelissen & B. Partoens

Authors
  1. T. Becker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Nelissen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Cleuren
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. B. Partoens
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. C. Van den Broeck
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Becker.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Becker, T., Nelissen, K., Cleuren, B. et al. Adsorption and desorption in confined geometries: A discrete hopping model. Eur. Phys. J. Spec. Top. 223, 3243–3256 (2014). https://doi.org/10.1140/epjst/e2014-02330-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2014-02330-8

Keywords

Search

Navigation