(122a) Diffusion in Nanopores Under the Microscope

In his reflections on “Past Progress and Future Challenges in Adsorption Research” at the turn to the new millennium [1], Professor Douglas Ruthven characterizes the relevance of the first technique of microscopic diffusion measurement by saying “The measurement of micropore diffusion in zeolite crystals and other microporous solids has proved a far more challenging task than might have been anticipated. The development during the 1970s of the pulsed field gradient nuclear magnetic resonance (PFG NMR) technique for measuring self-diffusion under equilibrium conditions proved a major milestone. Remarkably, the key developments were made by Professor Pfeifer and his students at the University of Leipzig in East Germany.” We consider it equally important to emphasize that all this progress did, to a large extent, benefit from the support and advice which, in turn, we had the privilege and pleasure to receive from Professor Ruthven. Some highlights in this cooperation shall be presented in this talk, which is co-authored by the fellow-combatants of his stays in Leipzig.

Deviating from, e.g., the gravimetric method commonly applied in former time for diffusion measurement in zeolites, PFG NMR permits following the diffusion path of guest molecules over distances much shorter than the crystal diameter, enabling the truly “microscopic” measurement. The introduction of microimaging by interference and IR microscopy gave rise to a dramatic enhancement in measurement performance since now, with the option of recording transient concentration profiles, diffusion phenomena could as well be studied under non-equilibrium conditions – as reviewed in, e.g., ref. [2]. Owing to the small size of the samples (namely single crystals rather than beds of crystals, corresponding with maximum surface-to-volume ratios), microimaging offers the additional advantage that, notably during fast ad- and desorption, corrupting influences due to the final rate of heat release may, in general, be ruled out [3].

As the main outcome of microscopic diffusion measurements, zeolite morphology was found to notably deviate, as a rule, from the regular pattern as generally implied on analyzing the outcome of gravimetric – or, more generally, of “macroscopic” – diffusion measurement. These deviations were, in addition, found to dramatically depend on the way of synthesis and sample pretreatment. As a main constituent of these deviations, transport resistances (“barriers”) acting in addition to the diffusion resistance of the genuine pore network were found to exist both on the external surface of the individual crystals/particles [4] and in their interior [5]. It is worthwhile mentioning that, after PFG NMR has over decades been exclusively applied to studying the dynamics of guest molecules, now such measurements have become also possible with exchangeable cations [5].

In our joint search for a model system which, upon investigation by both microscopic and macrsocopic techniques, gave rise to a compatible set of diffusion data, we were finally successful on considering cyclo- and n-hexane in nanoporous glass [6]. This material proved an excellent host in also subsequent applications. Thus, using dispersed nickel as a catalyst, nanoporous glass appeared as the system of choice in demonstrating the ability of IR microimaging for the one-shot determination of effectiveness factors during catalytic reaction, in the given case for the hydrogenation of benzene to cyclohexane [7]. Nanoporous glass did, further on, serve as an ideal host system for the direct observation of “uphill diffusion”, namely of ethane towards increasing ethane concentration within zeolite DDR, “driven” by the concentration gradient of the second component, propene, [8] and for demonstrating the validity of Fick’s law by direct experimental evidence, notably in also such cases where, in the literature, this validity is put under question [9].

The potentials of microimaging will, most likely, notably transgress the limits so far encountered during its application. This might, among others, in particular concern the investigation of the dynamics of phase transitions between the gaseous and liquid and the liquid and frozen states in mesopores. First investigations along these lines with mesoporous silicon [10] revealed substantial deviations between the common view on their structure and reality [11].

1. D.M. Ruthven, Past Progress and Future Challenges in Adsorption Research, Ind. Eng. Chem. Res. 39 (2000) 2127–2131.
2. J. Kärger, and D.M. Ruthven, Diffusion in nanoporous materials: Fundamental principles, insights and challenges, New J. Chem. 40 (2016) 4027–4048.
3. L. Heinke, C. Chmelik, P. Kortunov, D.B. Shah, S. Brandani, D.M. Ruthven, and J. Kärger, Analysis of thermal effects in infrared and interference microscopy: n-Butane-5A and methanol-ferrierite systems, Microporous Mesoporous Mater. 104 (2007) 18–25.
4. F. Hibbe, J. Caro, C. Chmelik, A. Huang, T. Kirchner, D. Ruthven, R. Valiullin, and J. Kärger, Monitoring molecular mass transfer in cation-free nanoporous host-crystals of type AlPO-LTA, J. Am. Chem. Soc. 134 (2012) 7725–7732.
5. S. Beckert, F. Stallmach, H. Toufar, D. Freude, J. Kärger, and J. Haase, Tracing Water and Cation Diffusion in Hydrated Zeolites of Type Li-LSX by Pulsed Field Gradient NMR, J. Phys. Chem. C 117 (2013) 24866–24872.
6. C. Chmelik, D. Enke, P. Galvosas, O.C. Gobin, A. Jentys, H. Jobic, J. Kärger, C. Krause, J. Kullmann, J.A. Lercher, S. Naumov, D.M. Ruthven, and T. Titze, Nanoporous glass as a model system for a consistency check of the different techniques of diffusion measurement, ChemPhysChem 12 (2011) 1130–1134.
7. T. Titze, C. Chmelik, J. Kullmann, L. Prager, E. Miersemann, R. Gläser, D. Enke, J. Weitkamp, and J. Kärger, Microimaging of transient concentration profiles of reactant and product molecules during catalytic conversion in nanoporous materials, Angew. Chem. Int. Ed. 54 (2015) 5060–5064.
8. A. Lauerer, T. Binder, C. Chmelik, E. Miersemann, J. Haase, D.M. Ruthven, and J. Kärger, Uphill diffusion and overshooting in the adsorption of binary mixtures in nanoporous solids, Nat. Comms. 6 (2015) 7697.
9. T. Titze, A. Lauerer, L. Heinke, C. Chmelik, N.E.R. Zimmermann, F.J. Keil, D.M. Ruthven, and J. Kärger, Transport in nanoporous materials including MOFs: The applicability of Fick’s laws, Angew. Chem. Int. Ed. 54 (2015) 14580–14583.
10. A. Lauerer, P. Zeigermann, J. Lenzner, C. Chmelik, M. Thommes, R. Valiullin, and J. Kärger, Micro-imaging of liquid–vapor phase transition in nano-channels, Microporous Mesoporous Mater. 214 (2015) 143–148.
11. D. Kondrashova, A. Lauerer, D. Mehlhorn, H. Jobic, A. Feldhoff, M. Thommes, D. Chakraborty, C. Gommes, J. Zecevic, P. de Jongh, A. Bunde, J. Kärger, and R. Valiullin, Scale-dependent diffusion anisotropy in nanoporous silicon, Scientific reports 7 (2017) 40207.