Transport in Nanoporous Materials Including MOFs: The Applicability of Fick's Laws.

Diffusion in nanoporous host-guest systems is often considered to be too complicated to comply with such "simple" relationships as Fick's first and second law of diffusion. However, it is shown herein that the microscopic techniques of diffusion measurement, notably the pulsed field gradient (PFG) technique of NMR spectroscopy and microimaging by interference microscopy (IFM) and IR microscopy (IRM), provide direct experimental evidence of the applicability of Fick's laws to such systems. This remains true in many situations, even when the detailed mechanism is complex. The limitations of the diffusion model are also discussed with reference to the extensive literature on this subject.

Uphill diffusion and overshooting in the adsorption of binary mixtures in nanoporous solids.

Under certain conditions, during binary mixture adsorption in nanoporous hosts, the concentration of one component may temporarily exceed its equilibrium value. This implies that, in contrast to Fick's Law, molecules must diffuse in the direction of increasing rather than decreasing concentration. Although this phenomenon of 'overshooting' has been observed previously, it is only recently, using microimaging techniques, that diffusive fluxes in the interior of nanoporous materials have become accessible to direct observation. Here we report the application of interference microscopy to monitor 'uphill' fluxes, covering the entire period of overshooting from initiation until final equilibration. It is shown that the evolution of the profiles can be adequately predicted from the single-component diffusivities together with the binary adsorption equilibrium data. The guest molecules studied (carbon dioxide, ethane and propene) and the host material (ZSM-58 or DDR) are of practical interest in relation to the development of kinetically selective adsorption separation processes.

Micro-Imaging by Interference Microscopy: A Case Study of Orientation-Dependent Guest Diffusion in MFI-Type Zeolite Host Crystals.

Because of the small particle size, orientation-dependent diffusion measurements in microporous materials remains a challenging task. We highlight here the potential of micro-imaging by interference microscopy in a case study with MFI-type crystals in which, although with different accuracies, transient concentration profiles in all three directions can be observed. The measurements, which were performed with "rounded-boat" shaped crystals, reproduce the evolution patterns of the guest profiles recorded in previous studies with the more common "coffin-shaped" MFI crystals. The uptake and release patterns through the four principal faces (which in the coffin-shaped crystals extend in the longitudinal direction) are essentially coincident and there is no perceptible mass transfer in the direction of the long axis. The surface resistances of the four crystal faces through which mass transfer occurs are relatively small and have only a minor effect on the mass transfer rate. As a result of the pore structure, diffusion in the crystallographic c direction (which corresponds to the direction of the long axis) is expected to be much slower than in the transverse directions. This could explain the very low rate of mass transfer observed in the direction of the long axis, but it is also possible that the small end faces of the crystal may have high surface resistance. It is not possible to distinguish unequivocally between these two possibilities. All guest molecules studied (methyl-butane, benzene and 4-methyl-2-pentyne) show the same orientation dependence of mass transfer. The long 4-methyl-2-pentyne molecules would be expected to propagate at very different rates through the straight and sinusoidal channels. The coinciding patterns for uptake through the mutually perpendicular crystal faces therefore provide clear evidence that both the coffin shaped crystals and the rounded-boat-shaped crystals considered in this study, must be intergrowths rather than pure single crystals.

Nanoporous glass as a model system for a consistency check of the different techniques of diffusion measurement.

The remarkable differences in the guest diffusivities in nanoporous materials commonly found with the application of different measuring techniques are usually ascribed to the existence of a hierarchy of transport resistances in addition to the diffusional resistance of the pore system and their differing influence due to the differing diffusion path lengths covered by the different measuring techniques. We report diffusion measurements with nanoporous glasses where the existence of such resistances could be avoided. Molecular propagation over diffusion path lengths from hundreds of nanometers up to millimeters was thus found to be controlled by a uniform mechanism, appearing in coinciding results of microscopic and macroscopic diffusion measurement.

The nature of surface barriers on nanoporous solids explored by microimaging of transient guest distributions.

Nanoporous solids are attractive materials for energetically efficient and environmentally friendly catalytic and adsorption separation processes. Although the performance of such materials is largely dependent on their molecular transport properties, our fundamental understanding of these phenomena is far from complete. This is particularly true for the mechanisms that control the penetration rate through the outer surface of these materials (commonly referred to as surface barriers). Recent detailed sorption rate measurements with Zn(tbip) crystals have greatly enhanced our basic understanding of such processes. Surface resistance in this material has been shown to arise from the complete blockage of most of the pore entrances on the outer surface, while the transport resistance of the remaining open pores is negligibly small. More generally, the revealed correlation between intracrystalline diffusion and surface permeation provides a new view of the nature of transport resistances in nanoporous materials acting in addition to the diffusion resistance of the regular pore network, leading to a rational explanation of the discrepancy which is often observed between microscopic and macroscopic diffusion measurements.

Combining macroscopic and microscopic diffusion studies in zeolites using NMR techniques.

In this study the zero length column (ZLC) technique is extended to the case where the decay of the adsorbed phase concentration is observed directly by nuclear magnetic resonance (NMR). An adsorption-desorption apparatus compatible with a 400-MHz NMR spectrometer was developed. It operates with nitrogen or helium as the inert purge gas. The column of the adsorbent material is placed in the sensitive region of the superconducting magnet and the rf coil of the NMR spectrometer. The time scales of the adsorption and desorption processes depend on concentration, temperature and crystal shape and are found to be in the range of 1-10 min. From the desorption branch, the non-equilibrium ZLC-NMR measurements yield intracrystalline diffusion coefficients in the range of 10(-13) to 10(-11) m2/s for different alkanes in silicalite-1. These values are always found to be smaller than the values measured by pulsed field gradient NMR under equilibrium condition indicating that there must be additional transport resistance at the external surface of these silicalite-1 zeolite crystals.