(94f) Experimental Determination and Quantification of the Rate-Determining Steps of Diffusion in Nanoporous Materials in the Focus of an Iupac Initiative

Nanoporous materials are at the heart of numerous technologies of matter upgrading by mass separation and conversion, driven by the intimate interaction between the guest molecules and the internal surface of these materials. The thus accomplished gain in value-added products, obviously, can never be faster than allowed by the rate of mass exchange between the interior of these materials and their surroundings. Detailed knowledge about the diffusion paths covered by the involved molecules from the outside into the material interior and vice versa with the respective rates is thus among the key requirements for a knowledge–based enhancement of the performance of these techniques, including their environmentally friendly execution.

The diffusion paths of the guest molecules in such nanoporous systems during their technological application are, as a rule, quite complex. They include mass transfer through the genuine pore space within the individual nanoporous crystals/particles and within the (notably more voluminous) pore space between these crystals/particles in the pellets/beads, into which, as a rule, they are aggregated, just as passages through the respective boundaries, i.e. through the external surface of the individual crystals/particles and of the pellets/beads.

Depending on the system under study, each of these steps in the diffusion path might, in principle, be the rate-determining one for the overall process of mass exchange between the interior of these materials and their surroundings. As a consequence of the huge differences in the time and space scales over which these various steps occur, there is no way to explore reliably the influence of all these limiting factors by the application of a single measurement technique.

Measurements by following the rate of molecular uptake or release by a bed of nanoporous crystals as the conventional way for gaining information on diffusion in nanoporous materials are therefore generally subject to influence by a variety of parameters. They may include the intracrystalline diffusivity, the permeability through the surface of these crystals, the diffusivity through the bed of crystals and, in addition, also the rate of heat exchange with the surroundings – easily giving rise to misinterpretations [1,2]. A thorough understanding of the theoretical formalism required for the correct interpretation of the experimental results is therefore of great importance.

The risk of misinterpretation obviously decreases, the more “microscopic” the applied measurement techniques are, corresponding to a parallel decrease in the number of possibly influencing parameters as generally observed in such cases. Examples include the combined application of the Zero Length Column (ZLC) Technique (as a release experiment operating “with a minimum” of nanoporous crystals) and Pulsed Field Gradient (PFG) NMR (allowing the recording of diffusion paths down to the range of micrometers) [3] and the direct determination of surface permeabilities by the measurement of transient concentration profiles via microimaging close to the crystal boundary [4].

It is, on the other hand, a great advantage of the “macroscopic” methods such as uptake measurements [5] and the study of adsorption columns dynamics [6] that, as a rule, they operate under conditions that are much closer to the conditions of the technical exploitation of the material under study and that the equipments needed for their application are easy to access. This is often in marked contrast to microscopic measurement methods such as Quasi-Elastic Neutron Scattering [7] or Single-Molecule Observation [8], which necessitate the availability of often quite complex equipments, which are not readily available and, in addition, often require quite specialized experience.

Regardless of the specific importance of each individual measurement technique on its own, which actually suggests their joint use, this high degree of specialization meant that they were developed separately and not in conjunction with each other, which entails the risk that the representatives of the different techniques see themselves as competitors rather than as partners.

To counteract this problem, an IUPAC Task Group (Project Details - IUPAC | International Union of Pure and Applied Chemistry) was formed in 2015, with the aim of providing “a first comprehensive set of guidelines for measurements and reporting of diffusion properties of chemical compounds in nanoporous materials serving for catalytic, mass separation and other relevant purposes” [9,10]. In the course of the Task Group’s activities, contact was established between the representatives of the individual measurement techniques, as a result of which a manuscript was prepared under the title “Diffusion in Nanoporous Materials with Special Consideration of the Measurement of the Determining Parameters”, which is currently under review as an IUPAC Technical Report to serve exactly the objective defined for the IUPAC Task Group [11].

With reference to the draft of this IUPAC Technical Report we would like to use the opportunity of this year’s AIChE Annual Meeting for presenting a first overview of the outcome of this initiative with a detailed presentation of the various types of information provided by the different techniques for experimentally studying molecular diffusion in nanoporous host materials, including the representation of their uniqueness and complementarity, with particular emphasis on their strengths and the hidden traps of misinterpretation.

References

[1] D.M. Ruthven, Past Progress and Future Challenges in Adsorption Research, Ind. Eng. Chem. Res. 39 (2000) 2127–2131.

[2] J. Kärger, The Random Walk of Understanding Diffusion, Ind. Eng. Chem. Res. 41 (2002) 3335–3340.

[3] S. Brandani, D.M. Ruthven, and J. Kärger, Concentration Dependence of Self-Diffusivity of Methanol in NaX Zeolite Crystals, Zeolites 15 (1995) 494–495.

[4] J. Cousin Saint Remi, A. Lauerer, C. Chmelik, I. Vandendael, H. Terryn, G.V. Baron, Denayer, Joeri F. M., and J. Kärger, The Role of Crystal Diversity in Understanding Mass Transfer in Nanoporous Materials, Nat. Mater. 15 (2015) 401–406.

[5] J.-Y. Wang, E. Mangano, S. Brandani, and D.M. Ruthven, A Review of Common Practices in Gravimetric and Volumetric Adsorption Kinetic Experiments, Adsorption 27 (2021) 295–318.

[6] N.S. Wilkins, A. Rajendran, and S. Farooq, Dynamic Column Breakthrough Experiments for Measurement of Adsorption Equilibrium and Kinetics, Adsorption 27 (2021) 397–422.

[7] M. Kruteva, Dynamics Studied by Quasielastic Neutron Scattering (QENS), Adsorption 27 (2021) 875–889.

[8] J.J.E. Maris, D. Fu, F. Meirer, and B.M. Weckhuysen, Single-Molecule Observation of Diffusion and Catalysis in Nanoporous Solids, Adsorption 27 (2021) 423–452.

[9] R. Valiullin, Can Random Motion Look the Same from Different Perspectives? Chem. Intern. 38 (2015) 24.

[10] J. Kärger, D.M. Ruthven, and R. Valiullin, Diffusion Research with Nanoporous Material: More Than Just a Random Walk? Chem. Intern. 43 (2021) 25–29.

[11] J. Kärger, R. Valiullin, S. Brandani, J. Caro, C. Chmelik, Br. F. Chmelka, M.-O. Coppens, S. Farooq, D. Freude, H. Jobic, M. Kruteva, E. Mangano, R. Pini, W. S. Price, A. Rajendran, P. I. Ravikovitch, G. Sastre, R. Q. Snurr, A. G. Stepanov, S. Vasenkov, Y. Wang, B. M. Weckhuysen, Diffusion in Nanoporous Materials with Special Consideration of the Measurement of the Determining Parameters, submitted as the draft of an IUPAC Technical Report to Pure Appl. Chem.