(501c) Novel Experimental Technique for the Study of Knudsen Diffusion in Complex Pore Geometries

Knudsen diffusion is a transport mechanism, where the frequency of intermolecular collisions is smaller than the frequency of collisions of gas molecules with the pore walls. It is often the dominant transport mechanism for gases in amorphous mesoporous media, where the pore width is smaller than the mean free path of the diffusing gas molecule. Amorphous mesoporous media have a lot of industrial applications as catalysts and catalysts supports. Many of the processes that use these media involve diffusion limited reactions (e.g. production of vinyl acetate, and catalytic reforming of naphtha) [1],[2].

Amorphous mesoporous media are known to have a disordered porous space with a fractal internal surface on the single pore level [3]. Analytical and computational work by Coppens and co-workers [4],[5] and by Zschiegner et al [6] has indicated that there is a distinct decrease in the Knudsen diffusivity when the fractal roughness of the internal surface of the pores increases. In their work, Coppens and co-workers report temporary trapping effects and confinement effects of the gas molecules inside the surface corrugations of the rough pore that can affect the residence time inside a pore and thus the conversion and selectivity. On the other side, the surface corrugation can also impact the stability of the active sites when these media are used as catalyst support [7]. Therefore, further investigation is necessary to obtain a better understanding of the impact of surface roughness of the pores on diffusion and catalysis.

Here, a new experimental technique has been developed to provide experimental validation of the previous analytical and computational work in a scale-up of a mesopore from the nanometres to a few centimetres using a specially-designed ultra-high vacuum diffusion setup [8]. Ultra-high vacuum conditions enable the study of diffusion for the same Knudsen numbers as the ones that prevail in the mesopores. 3D-printed channels of varying fractal surface roughness represent different single, rough pores, a million times magnified. The vacuum chambers on both sides of the diffusion channel play the role of the gas reservoir often used in single pore model simulations. When introducing nitrogen gas molecules, the self- and transport diffusivity in the Knudsen regime can be obtained from Einstein’s equation and Fick’s law of diffusion respectively. Future work for studies of Knudsen diffusion and reaction under ultra-high vacuum conditions will also be discussed.

References

[1] Coppens, M.-O. The effect of fractal surface roughness on diffusion and reaction in porous catalysts – from fundamentals to practical applications. Catal. Today 53(2), 225–243 (1999).

[2] Coppens, M.-O. & Malek, K. Dynamic Monte-Carlo simulations of diffusion limited reactions in rough nanopores. Chem. Eng. Sci. 58(21), 4787–4795 (2003).

[3] Avnir, D., Farin, D. & Pfeifer, P. Molecular fractal surfaces. Nature 308, 261–263 (1984).

[4] Coppens, M.-O. & Froment, G. F. Knudsen diffusion in porous catalysts with a fractal internal surface. Fractals 03(04), 807–820 (1995).

[5] Malek, K. & Coppens, M.-O. Knudsen self- and Fickian diffusion in rough nanoporous media. J. Chem. Phys. 119(5), 2801–2811 (2003).

[6] Zschiegner, S., Russ, S., Valiullin, R., Coppens, M.-O., Dammers, A. J., Bunde, A. & Kärger, J. Normal and anomalous diffusion of non-interacting particles in linear nanopores. Eur. Phys. J. Spec. Top. 161(1), 109–120 (2008).

[7] Nazari, M., Davoodabadi, A., Huang, D., Luo, T. & Ghasemi, H. Transport Phenomena in Nano/Molecular Confinements. ACS Nano 14(12), 16348–16391 (2020).

[8] Yu, H. Development of A Novel Ultra-High Vacuum Diffusion Apparatus for Investigating Knudsen Diffusion in Complex Pore Channels (2021) (Doctoral thesis, University College London, London, UK). Available from UCL Discovery database.