Mesopore-Promoted Transport in Microporous Materials

Quantitating Diffusion Enhancement in Pore Hierarchies

A microporous continuum traversed by a set of mutually perpendicular channels is considered to be a model for a hierarchically porous system of the mesoporous zeolite type. Transient profiles of molecular uptake as determined by kinetic Monte Carlo (kMC) simulation are found to be in excellent agreement with the result attained by the application of the two-region model (the Kärger model) of molecular diffusion. In particular, it is found that, in the two limiting cases referred to as fast exchange and slow exchange, there exist two simple analytical expressions for the rate of molecular uptake and hence for the quantification of transport enhancement in comparison with the purely microporous adsorbent. In the general case, transport enhancement is simply recognized by the reciprocal addition of the expressions in the two limiting cases.

Diffusion and reaction in pore hierarchies by the two-region model

The two-region (“Kärger”) model of diffusion in complex pore spaces is exploited for quantitating mass transfer in hierarchically organized nanoporous materials, consisting of a continuous microporous bulk phase permeated by a network of transport pores. With the implications that the diffusivity in the transport pores significantly exceeds the diffusivity in the micropores and that the relative population of the transport pores is far below that of the micropores, overall transport depends on only three independent parameters. Depending on their interrelation, enhancement of the overall mass transfer is found to be ensured by two fundamentally different mechanisms. They are referred to as the limiting cases of fast and slow exchange, with the respective time constants of molecular uptake being controlled by different parameters. Complemented with reaction terms, the two-region model may equally successfully be applied to the quantitation of the combined effect of diffusion and reaction in terms of the effectiveness factor. Generalization of the classical Thiele concept is shown to provide an excellent estimate of the effectiveness factor of a chemical reaction in hierarchically porous materials, solely based on the intrinsic reaction rate and the time constant of molecular uptake relevant to the given conditions.

Dynamics studied by Quasielastic Neutron Scattering (QENS)

Quasielastic neutron scattering (QENS) allows measurement of the molecular displacements in time and space, from pico- to tens of nanoseconds and from Ångstroms to nanometers, respectively. The method probes dynamics from fast vibrational modes down to slow diffusive motion. Every scattering experiment leads to a dynamic structure factor $$S\left( {\vec Q,\omega } \right)$$ S Q → , ω or its spatial and temporal Fourier transform (van Hove correlation function $$G\left( {\vec r,t} \right)$$ G r → , t ). This shows exactly where the atoms are and how they move. In this manuscript the basics of the QENS method are presented and a few examples highlighting the potentials of QENS are given: (i) diffusion of liquids and gases in nano- and mesoporous materials; (ii) hydrogen dynamics in a high temperature polymer electrolyte fuel cell (HT-PEFC) and (iii) influence of the surface interactions on polymer dynamics in nanopores.

Pulsed field gradient NMR diffusion measurement in nanoporous materials

Labeling in diffusion measurements by pulsed field gradient (PFG) NMR is based on the observation of the phase of nuclear spins acquired in a constant magnetic field with purposefully superimposed field gradients. This labeling does in no way affect microdynamics and provides information about the probability distribution of molecular displacements as a function of time. An introduction of the measuring principle is followed by a detailed description of the ranges of measurements and their limitation. Particular emphasis is given to an explanation of possible pitfalls in the measurements and the ways to circumvent them. Showcases presented for illustrating the wealth of information provided by PFG NMR include a survey on the various patterns of concentration dependence of intra-particle diffusion and examples of transport inhibition by additional transport resistances within the nanoporous particles and on their external surface. The latter information is attained by combination with the outcome of tracer exchange experiments, which are shown to become possible via a special formalism of PFG NMR data analysis. Further evidence provided by PFG NMR concerns diffusion enhancement in pore hierarchies, diffusion anisotropy and the impact of diffusion on chemical conversion in porous catalysts. A compilation of the specifics of PFG NMR and of the parallels with other measurement techniques concludes the paper.

Diffusion in nanopores: inspecting the grounds

This paper provides a general overview of the phenomenon of guest diffusion in nanoporous materials. It introduces the different types of diffusion measurement that can be performed under both equilibrium and non-equilibrium conditions in either single- or multicomponent systems. In the technological application of nanoporous materials for mass separation and catalytic conversion diffusion often has a significant impact on the overall rate of the process and is quite commonly rate controlling. Diffusion enhancement is therefore often a major goal in the manufacture of catalysts and adsorbents.

Understanding the Loading Dependence of Adsorbate Diffusivities in Hierarchical Metal-Organic Frameworks

Using atomistic simulations, we studied the diffusion of n-hexane in a series of isoreticular hierarchical metal-organic frameworks (MOFs) NU-100x. Nonmonotonic diffusivity-loading relationships that depend on the pore sizes were observed, which can be explained by the spatial distribution of adsorbates at different loadings. For one of the MOFs in the series, NU-1000-M, the diffusivity-loading relationship is almost identical to the previously reported results of n-hexane diffusion in the hierarchical self-pillared pentasil (SPP) zeolite. Detailed analysis revealed that the similarity results from their similar micropore and window sizes, which was confirmed by free-energy mapping. The effects of temperature and adsorbate chain length on the diffusion were also studied, which supported our conclusion that the diffusivity in hierarchical nanoporous materials is primarily controlled by the sizes of the micropores and the connecting windows, particularly at relatively low loadings.

Synthesis and Characterisation of Hierarchically Structured Titanium Silicalite-1 Zeolites with Large Intracrystalline Macropores

The successful synthesis of hierarchically structured titanium silicalite-1 (TS-1) with large intracrystalline macropores by steam-assisted crystallisation of mesoporous silica particles is reported. The macropore topology was imaged in 3D by using electron tomography and synchrotron radiation-based ptychographic X-ray computed tomography, revealing interconnected macropores within the crystals accounting for about 30 % of the particle volume. The study of the macropore formation mechanism revealed that the mesoporous silica particles act as a sacrificial macropore template during the synthesis. Silicon-to-titanium ratio of the macroporous TS-1 samples was successfully tuned from 100 to 44. The hierarchically structured TS-1 exhibited high activity in the liquid phase epoxidation of 2-octene with hydrogen peroxide. The hierarchically structured TS-1 surpassed a conventional nano-sized TS-1 sample in terms of alkene conversion and showed comparable selectivity to the epoxide. The flexible synthesis route described here can be used to prepare hierarchical zeolites with improved mass transport properties for other selective oxidation reactions.

Understanding Diffusion in Hierarchical Zeolites with House-of-Cards Nanosheets

Introducing mesoporosity to conventional microporous sorbents or catalysts is often proposed as a solution to enhance their mass transport rates. Here, we show that diffusion in these hierarchical materials is more complex and exhibits non-monotonic dependence on sorbate loading. Our atomistic simulations of n-hexane in a model system containing microporous nanosheets and mesopore channels indicate that diffusivity can be smaller than in a conventional zeolite with the same micropore structure, and this observation holds true even if we confine the analysis to molecules completely inside the microporous nanosheets. Only at high sorbate loadings or elevated temperatures, when the mesopores begin to be sufficiently populated, does the overall diffusion in the hierarchical material exceed that in conventional microporous zeolites. Our model system is free of structural defects, such as pore blocking or surface disorder, that are typically invoked to explain slower-than-expected diffusion phenomena in experimental measurements. Examination of free energy profiles and visualization of molecular diffusion pathways demonstrates that the large free energy cost (mostly enthalpic in origin) for escaping from the microporous region into the mesopores leads to more tortuous diffusion paths and causes this unusual transport behavior in hierarchical nanoporous materials. This knowledge allows us to re-examine zero-length-column chromatography data and show that these experimental measurements are consistent with the simulation data when the crystallite size instead of the nanosheet thickness is used for the nominal diffusional length.

Multiscale adsorption and transport in hierarchical porous materials

This review presents the state-of-the-art of multiscale adsorption and transport in hierarchical porous materials.

Diffusion in nanoporous materials: fundamental principles, insights and challenges

The increasing complexity of nanoporous catalysts and adsorbents presents a challenge to both the experimental measurement and theoretical modeling of transport behavior.

Transport properties of hierarchical micro–mesoporous materials

This work provides an overview of different experimental techniques of diffusion measurements in porous materials and discusses transport properties of several classes of hierarchically organized micro-mesoporous materials.