Skip to main content
Log in

Diffusion in complementary pore spaces

  • Published:
Adsorption Aims and scope Submit manuscript

Abstract

The rate of mass transfer is among the key numbers determining the efficiency of nanoporous materials in their use for matter upgrading by heterogeneous catalysis or mass separation. Transport enhancement by pore space optimization is, correspondingly, among the main strategies of efficiency promotion. Any such activity involves probing and testing of the appropriate routes of material synthesis and post-synthesis modification just as the exploration of the transport characteristics of the generated material. Modelling and molecular simulation is known to serve as a most helpful tool for correlating these two types of activities and their results. The present paper reports about a concerted research activity comprising these three types of activities. Recent progress in producing pore space replicas enabled focusing, in these studies, on “complementary” pore spaces, i.e. on pairs of material, where the pore space of one sample did just coincide with the solid space of the other. We report about the correlations in mass transfer as observable, in this type of material, by pulsed field gradient NMR diffusion studies, with reference to the prediction as resulting from a quite general, theoretical treatment of mass transfer in complementary pore spaces.

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

Access this article

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

Instant access to the full article PDF.

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

  • Auerbach, S.M., Carrado, K.A., Dutta, P.K. (eds.): Handbook of Zeolite Science and Technology. CRC Press, New York (2003)

    Google Scholar 

  • Bunde, A., Havlin, S.: Fractals and Disordered Systems. Springer, Berlin (1996)

    Book  Google Scholar 

  • Cahn, J.W.: Phase separation by spinodal decomposition in isotropic systems. J. Chem. Phys. 42, 93 (1965)

    Article  CAS  Google Scholar 

  • Callaghan, P.T.: Translational dynamics and magnetic resonance. Oxford University Press, Oxford (2011)

    Book  Google Scholar 

  • Cejka, J., Corma, A., Zones, S. (eds.): Zeolites and Catalysis: Synthesis, Reactions and Applications. Wiley, Weinheim (2010)

    Google Scholar 

  • Chmelik, C., Kärger, J.: In-situ study on molecular diffusion phenomena in nanoporous catalytic solids. Chem. Soc. Rev. 39, 4864–4884 (2010)

    Article  CAS  Google Scholar 

  • Chmelik, C., Bux, H., Caro, J., Heinke, L., Hibbe, F., Titze, T., Kärger, J.: Mass transfer in a nanoscale material enhanced by an opposing flux. Phys. Rev. Lett. 104, 85902 (2010)

    Article  Google Scholar 

  • Chmelik, C., Enke, D., Galvosas, P., Gobin, O.C., Jentys, A., Jobic, H., Kärger, J., Krause, C., Kullmann, J., Lercher, J.A., Naumov, S., Ruthven, D.M., Titze, T.: Nanoporous glass as a model system for a consistency check of the different techniques of diffusion measurement. ChemPhysChem 12, 1130–1134 (2011)

    Article  CAS  Google Scholar 

  • Choi, M., Cho, H.S., Srivastava, R., Venkatesan, C., Choi, D.H., Ryoo, R.: Amphiphilic organosilane-directed synthesis of crystalline zeolite with tunable mesoporosity. Nat. Mater. 5, 718–723 (2006)

    Article  CAS  Google Scholar 

  • Coppens, M.O.: Nature Inspired Chemical Engineering (Inaugural Lecture). Delft University Press, Delft (2003)

    Google Scholar 

  • Coppens, M.-O., Froment, G.F.: The effectiveness of mass fractal catalysts. Fractals 5, 493–505 (1997)

    Article  CAS  Google Scholar 

  • Cotts, R.M., Hoch, M.J.R., Sun, T., Markert, J.T.: Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems. J. Magn. Reson. 83, 252–266 (1989)

    CAS  Google Scholar 

  • Cussler, E.L.: Diffusion: Mass Transfer in Fluid Systems. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  • Enke, D., Janowski, F., Schwieger, W.: Porous glasses in the 21st century—a short review. Microporous Mesoporous Mater. 60, 19–30 (2003)

    Article  CAS  Google Scholar 

  • Feil, F., Naumov, S., Michaelis, J., Valiullin, R., Enke, D., Kärger, J., Bräuchle, C.: Single-particle and ensemble diffusivities—test of ergodicity. Angew. Chem. Int. Ed. 51, 1152–1155 (2012)

    Article  CAS  Google Scholar 

  • Galarneau, A., Iapichella, J., Bonhomme, K., Di Renzo, F., Kooyman, P., Terasaki, O., Fajula, F.: Controlling the morphology of mesostructured silicas by pseudomorphic transformation: a route towards applications. Adv. Funct. Mater. 16, 1657–1667 (2006)

    Article  CAS  Google Scholar 

  • Galvosas, P., Stallmach, F., Seiffert, G., Kärger, J., Kaess, U., Majer, G.: Generation and application of ultra-high-intensity magnetic field gradient pulses for NMR spectroscopy. J. Magn. Reson. 151, 260–268 (2001)

    Article  CAS  Google Scholar 

  • Hartmann, S., Brandhuber, D., Hüsing, N.: Glycol-modified silanes: novel possibilities for the synthesis of hierarchically organized (hybrid) porous materials. Acc. Chem. Res. 40, 885–894 (2007)

    Article  CAS  Google Scholar 

  • Heitjans, P., Kärger, J. (eds.): Diffusion in Condensed Matter: Methods, Materials, Models. Springer, Berlin (2005)

    Google Scholar 

  • Inayat, A., Reinhardt, B., Uhlig, H., Einicke, W.-D., Enke, D.: Silica monoliths with hierarchical porosity obtained from porous glasses. Chem. Soc. Rev. 42, 3753 (2013)

    Article  CAS  Google Scholar 

  • Ivanova, I.I., Knyazeva, E.E.: Micro–mesoporous materials obtained by zeolite recrystallization: synthesis, characterization and catalytic applications. Chem. Soc. Rev. 42, 3671 (2013)

    Article  CAS  Google Scholar 

  • Janowski, F., Enke, D.: Porous Glasses. In: Schüth, F., Sing, K.S.W., Weitkamp, J. (eds.) Handbook of Porous Solids, vol. 4, pp. 1432–1542. Wiley, Weinheim (2002)

    Chapter  Google Scholar 

  • Jian, K., Truong, T.C., Hoffman, W.P., Hurt, R.H.: Mesoporous carbons with self-assembled surfaces of defined crystal orientation. Microporous Mesoporous Mater. 108, 143–151 (2008)

    Article  CAS  Google Scholar 

  • Jobic, H., Theodorou, D.: Quasi-elastic neutron scattering and molecular dynamics simulations as complementary techniques for studying diffusion in zeolites. Microporous Mesoporous Mater. 102, 21–50 (2007)

    Article  CAS  Google Scholar 

  • Kainourgiakis, M.E., Kikkinides, E.S., Stubos, A.K., Kanellopoulos, N.K.: Simulation of self-diffusion of point-like and finite-size tracers in stochastically reconstructed Vycor porous glasses. J. Chem. Phys. 111, 2735 (1999)

    Article  CAS  Google Scholar 

  • Kärger, J.: Transport phenomena in nanoporous materials. ChemPhysChem 16, 24–51 (2015)

    Article  Google Scholar 

  • Kärger, J., Heink, W.: The propagator representation of molecular transport in microporous crystallites. J. Magn. Reson. 51, 1–7 (1983)

    Google Scholar 

  • Kärger, J., Kocirik, M., Zikanova, A.: Molecular-transport through assemblages of microporous particles. J. Colloid Interface Sci. 84, 240–249 (1981)

    Article  Google Scholar 

  • Kärger, J., Ruthven, D.M., Theodorou, D.N.: Diffusion in Nanoporous Materials. Wiley, Weinheim (2012)

    Book  Google Scholar 

  • Kärger, J., Binder, T., Chmelik, C., Hibbe, F., Krautscheid, H., Krishna, R., Weitkamp, J.: Microimaging of transient guest profiles to monitor mass transfer in nanoporous materials. Nat. Mater. 13, 333–343 (2014)

    Article  Google Scholar 

  • Kondrashova, D., Valiullin, R.: Freezing and melting transitions under mesoscalic confinement: application of the kossel-stranski crystal-growth model. J. Phys. Chem. C. 119, 4312–4323 (2015)

    Article  CAS  Google Scholar 

  • Lei, Q., Zhao, T., Li, F., Zhang, L., Wang, Y.: Catalytic cracking of large molecules over hierarchical zeolites. Chem. Commun. 16, 1769 (2006)

    Article  Google Scholar 

  • Levitz, P.: Off-lattice reconstruction of porous media: critical evaluation, geometrical confinement and molecular transport. Adv. Colloid Interface Sci. 76–77, 71–106 (1998)

    Article  Google Scholar 

  • Marsh, H., Rodríguez-Reinoso, F.: Activated Carbon. Elsevier, Amsterdam (2006)

    Google Scholar 

  • Mitchell, S., Pinar, A.B., Kenvin, J., Crivelli, P., Kärger, J., Pérez Ramírez, J.: Elucidating the crystal, pore, and active site structure in hierarchically-organized zeolites: state-of-the-art and beyond. Nat. Commun. (2015). doi:10.1038/ncomms9633

    Google Scholar 

  • Möller, K.P., Bein, T.: Mesoporosity—a new dimension for zeolites. Chem. Soc. Rev. 42, 3689 (2013)

    Article  Google Scholar 

  • Monette, L., Grest, G.S., Anderson, M.P.: 3-dimensional Ising system with long-range interactions—a computer model of Vycor glass. Phys. Rev. E 50, 3361 (1994)

    Article  CAS  Google Scholar 

  • Na, K., Choi, M., Ryoo, R.: Recent advances in the synthesis of hierarchically nanoporous zeolites. Microporous Mesoporous Mater. 166, 3–19 (2013)

    Article  CAS  Google Scholar 

  • Nakanishi, K.: Pore structure control of silica gels based on phase separation. J. Porous. Mater. 4, 67 (1997)

    Article  CAS  Google Scholar 

  • Prigogine, I.: The End of Certainty. The Free Press, New York (1997)

    Google Scholar 

  • Reinhardt, B., Enke, D., Syrowatka, F., Nakanishi, K.: Preparation of porous, hierarchically organized glass monoliths via combination of sintering and phase separation. J. Am. Ceram. Soc. 95, 461–465 (2012)

    Article  CAS  Google Scholar 

  • Schmidt, F., Paasch, S., Brunner, E., Kaskel, S.: Carbon templated SAPO-34 with improved adsorption kinetics and catalytic performance in the MTO-reaction. Microporous Mesoporous Mater. 164, 214–221 (2012)

    Article  CAS  Google Scholar 

  • Schneider, D., Kondrashova, D., Valiullin, R., Bunde, A., Kärger, J.: Mesopore-promoted transport in microporous materials. Chem. Ing. Tech. 87, 1794–1809 (2015)

    Article  CAS  Google Scholar 

  • Shakhov, A., Reichenbach, C., Kondrashova, D., Zeigermann, P., Mehlhorn, D., Enke, D., Valiullin, R.: Exploring internal structure of nanoporous glasses obtained by leaching of phase-separated alkali borosilicate glasses. Chem. Ing. Tech. 85, 1734–1741 (2013)

    Article  CAS  Google Scholar 

  • Stallmach, F., Galvosas, P.: Spin echo NMR diffusion studies. Annu. Rep. NMR Spectrosc. 61, 51–131 (2007)

    Article  CAS  Google Scholar 

  • Stallmach, F., Kärger, J.: The potentials of pulsed field gradient nmr for investigation of porous media. Adsorption 5, 117–133 (1999)

    Article  CAS  Google Scholar 

  • Stoltenberg, D., Seidel-Morgenstern, A., Enke, D.: Mesoporöse glasmembranen als modellsysteme zur untersuchung der gasdiffusion durch poröse medien. Chem. Ing. Tech. 82, 829–835 (2010)

    Article  CAS  Google Scholar 

  • Studt, F., Sharafutdinov, I., Abild-Pedersen, F., Elkjær, C.F., Hummelshøj, J.S., Dahl, S., Chorkendorff, I., Nørskov, J.K.: Discovery of a Ni-Ga catalyst for carbon dioxide reduction to methanol. Nat. Chem. 6, 320–324 (2014)

    Article  CAS  Google Scholar 

  • Su, B.L., Sanchez, C., Yang, X.Y. (eds.): Hierarchically Structured Porous Materials. Wiley, Weinheim (2012)

    Google Scholar 

  • Titze, T., Chmelik, C., Kullmann, J., Prager, L., Miersemann, E., Gläser, R., Enke, D., Weitkamp, J., Kärger, J.: Microimaging of transient concentration profiles of reactant and product molecules during catalytic conversion in nanoporous materials. Angew. Chem. Int. Ed. 54, 5060–5064 (2015)

    Article  CAS  Google Scholar 

  • Trogadas, P., Nigra, M., Coppens, M.-O.: Nature-inspired optimisation of hierarchical porous media for catalytic and separation processes. New J. Chem. (2016). doi:10.1039/c5nj03406j

    Google Scholar 

  • Valiullin, R.: Diffusion in nanoporous host systems. Annu. Rep. NMR Spectrosc. 79, 23–72 (2013)

    Article  CAS  Google Scholar 

  • Valiullin, R., Kortunov, P., Kärger, J., Timoshenko, V.: Concentration-dependent self-diffusion of liquids in nanopores: a nuclear magnetic resonance study. J. Chem. Phys. 120, 11804–11814 (2004)

    Article  CAS  Google Scholar 

  • Valiullin, R., Kärger, J., Gläser, R.: Correlating phase behaviour and diffusion in mesopores: perspectives revealed by pulsed field gradient NMR. Phys. Chem. Chem. Phys. 11, 2833–2853 (2009)

    Article  CAS  Google Scholar 

  • Verboekend, D., Mitchell, S., Pérez-Ramírez, J.: Hierarchical zeolites overcome all obstacles: next stop industrial implementation. CHIMIA Int. J. Chem. 67, 327–332 (2013)

    Article  CAS  Google Scholar 

Download references

Acknowledgement

Financial support by the DFG (BU 534/22, KA 953/30) and by “Fonds der Chemischen Industrie” is gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rustem Valiullin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mehlhorn, D., Kondrashova, D., Küster, C. et al. Diffusion in complementary pore spaces. Adsorption 22, 879–890 (2016). https://doi.org/10.1007/s10450-016-9792-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10450-016-9792-y

Keywords

Navigation