Measurement of Micropore Diffusion

For several reasons the rehable measurement of micropore diffusion has proved to be far more difficult than expected. We now know that when the diameter of the diffusing molecule is even shghtly smaller than the pore diameter, diffusion within an ideal micropore is surprisingly fast and difficult to measure by macroscopic methods, since the size of available zeohte crystals is limited. Such fast processes can, however, be measured relatively easily by PFG NMR and QENS. As the molecular diameter of the sorbate approaches (or even exceeds) the minimiun diameter of the pore, the diffusional activa-... 

Fundamentals of sorption and sorption kinetics by zeohtes are described and analyzed in the first Chapter which was written by D. M. Ruthven. It includes the treatment of the sorption equilibrium in microporous sohds as described by basic laws as well as the discussion of appropriate models such as the Ideal Langmuir Model for mono- and multi-component systems, the Dual-Site Langmuir Model, the Unilan and Toth Model, and the Simphfied Statistical Model. Similarly, the Gibbs Adsorption Isotherm, the Dubinin-Polanyi Theory, and the Ideal Adsorbed Solution Theory are discussed. With respect to sorption kinetics, the cases of self-diffusion and transport diffusion are discriminated, their relationship is analyzed and, in this context, the Maxwell-Stefan Model discussed. Finally, basic aspects of measurements of micropore diffusion both under equilibrium and non-equilibrium conditions are elucidated. The important role of micropore diffusion in separation and catalytic processes is illustrated. 

The same method is also applicable, in principle, to the measurement of micropore diffusivities in zeolite crystals but, except when micropore diffusion... 

In the measurement of micropore diffusivities by the uptake rate method it is generally necessary to use an assemblage of microparticles (such as zeolite... 

The dynamic characteristics of adsorbed molecules can be determined in terms of temperature dependences of relaxation times [14-16] and by measurements of self-diffusion coefficients applying the pulsed-gradient spin-echo method [ 17-20]. Both methods enable one to estimate the mobility of molecules in adsorbent pores and the rotational mobility of separate molecular groups. The methods are based on the fact that the nuclear spin relaxation time of a molecule depends on the feasibility for adsorbed molecules to move in adsorbent pores. The lower the molecule s mobility, the more effective is the interaction between nuclear magnetic dipoles of adsorbed molecules and the shorter is the nuclear spin relaxation time. The results of measuring relaxation times at various temperatures may form the basis for calculations of activation characteristics of molecular motions of adsorbed molecules in an adsorption layer. These characteristics are of utmost importance for application of adsorbents as catalyst carriers. They determine the diffusion of reagent molecules towards the active sites of a catalyst and the rate of removal of reaction products. Sometimes the data on the temperature dependence of a diffusion coefficient allow one to ascertain subtle mechanisms of filling of micropores in activated carbons [17]. 

The measured responses were fitted using the characteristic function of micropore diffusion in isotropic spherical particles of uniform size (see the symbols for the measured responses and the best fit curves in Figure 5), The larger the deviation of the data from the best fit the wider is the particle-size distribution (cf Figures 2 and 5). 

Perhaps the most obvious experimental approach to the determination of micropore diffusivities is to measure directly the sorption/desorption rate for an adsorbent particle subjected to a well-defined change in the ambient concentration of sorbate. For an isothermal spherical particle subjected to a step change in sorbate concentration at the external surface at time zero, the ap-... 

The method is in principle applicable also to the measurement of micropore or intracrystalline diffusivities, but the practical difficulties of mounting and sealing a single small zeolite crystal have hitherto prevented such applications. However, these difficulties have been overcome and the results of two studies have been recently reported in which diffusion through a single (iOO /tm) zeolite crystal, mounted in a metal plate, was measured by this method. 

K.S. Panesar, C. Hugon, G. Aubert, P. Judeinstein, J.M. Zanotti, D. SakeUariou, Measurement of self-diffusion in thin samples using a novel one-sided NMR magnet, Microporous Mesoporous Mater. 178 (2013) 79—83. 

Jobic, H., et ah. Measurement of the diffusivity of benzene in microporous silica by quasi-elastic neutron scattering and NMR pulsed-field gradient technique. Adsorption, 1(3), 197-202 (1995). 

The first thing to notice about these results is that the influence of the micropores reduces the effective diffusion coefficient below the value of the bulk diffusion coefficient for the macropore system. This is also clear in general from the forms of equations (10.44) and (10.48). As increases from zero, corresponding to the introduction of micropores, the variance of the response pulse Increases, and this corresponds to a reduction in the effective diffusion coefficient. The second important point is that the influence of the micropores on the results is quite small-Indeed it seems unlikely that measurements of this type will be able to realize their promise to provide information about diffusion in dead-end pores. 

Although microporous membranes are a topic of research interest, all current commercial gas separations are based on the fourth type of mechanism shown in Figure 36, namely diffusion through dense polymer films. Gas transport through dense polymer membranes is governed by equation 8 where is the flux of component /,andare the partial pressure of the component i on either side of the membrane, /is the membrane thickness, and is a constant called the membrane permeability, which is a measure of the membrane s ability to permeate gas. The ability of a membrane to separate two gases, i and is the ratio of their permeabilities,a, called the membrane selectivity (eq. 9). 

Although the systems investigated here exhibited predominantly macropore control (at least those with pellet diameters exceeding 1/8" or 0.32 cm), there is no reason to believe that surface diffusion effects would not be exhibited in systems in which micropore (intracrystalline) resistances are important as well. In fact, this apparent surface diffusion effect may be responsible for the differences in zeolitic diffusion coefficients obtained by different methods of analysis (13). However, due to the complex interaction of various factors in the anlaysis of mass transport in zeolitic media, including instabilities due to heat effects, the presence of multimodal pore size distribution in pelleted media, and the uncertainties involved in the measurement of diffusion coefficients in multi-component systems, further research is necessary to effect a resolution of these discrepancies. 

A diameter of 20 A represents approximately the limiting pore size that can be measured by mercury intrusion. In pores smaller than this, transport becomes increasingly affected by molecule-pore wall interactions, and conventional theories based on molecular and Knudsen diffusion break down. The classification is somewhat arbitrary, however, since the point at which such effects become important also depends on the size of the diffusing molecule. Adsorption equilibrium in microporous adsorbents also depends to some extent on the pore size as well as on the nature of the surface, so control of the pore size distribution is important in the manufacture of an adsorbent for a particular separation. 

Alternatively one can in principle derive both micropore and macropore diffusivities from measurements of the transient uptake rate for a particle (or assemblage of crystals) subjected to a step change in ambient sorbate pressure or concentration. The main problem with this approach is that the overall uptake rate may be controlled by several different processes, including both heat and extraparticle mass transfer as well as intraparticle or intracrystalline diffusion. The intrusion of such rate processes is not always obvious from a cursory examination of the experimental data, and the literature of the subject is replete with incorrect diffusivities (usually erroneously low values) obtained as a result of intrusion of such extraneous effects. Nevertheless, provided that intraparticle diffusion is sufficiently slow, the method offers a useful practical alternative to the Wicke-Kallen bach method. 

An experimental facility was described in Section 4.5.9 (see Figure 4.22) that was used to carry out the characterization of the groups present on the surface of a porous material or the channels and/or cavities of a microporous material applying the FTIR methodology. With this methodology, it is also possible to measure different diffusion coefficients in microporous materials with the help of the FTIR method [87-92], Here, a laboratory-assembled facility similar to that reported in Section 4.5.9 that has two manifolds (Figure 5.31) instead of one, for the introduction of the diffusing molecules, and thus has the capability to deliver two different hydrocarbons to the IR cell, is described [90],... 

Inelastic and quasielastic neutron scattering have special advantages for studying certain of the motional properties of protonated or organic species within zeolites and related microporous materials. These advantages and various experimental methods are outlined, and illustrated by measurements of torsional vibrations and rotational diffusion of tetramethylammonium (TMA) cations occluded within zeolites TMA-sodalite, omega, ZK-4 and S APO-20. 

Madon and Boudart propose a simple experimental criterion for the absence of artifacts in the measurement of rates of heterogeneous catalytic reactions [R. J. Madon and M. Boudart, Ind. Eng. Chem. Fundam., 21 (1982) 438]. The experiment involves making rate measurements on catalysts in which the concentration of active material has been purposely changed. In the absence of artifacts from transport limitations, the reaction rate is directly proportional to the concentration of active material. In other words, the intrinsic turnover frequency should be independent of the concentration of active material in a catalyst. One way of varying the concentration of active material in a catalyst pellet is to mix inert particles together with active catalyst particles and then pelletize the mixture. Of course, the diffusional characteristics of the inert particles must be the same as the catalyst particles, and the initial particles in the mixture must be much smaller than the final pellet size. If the diluted catalyst pellets contain 50 percent inert powder, then the observed reaction rate should be 50 percent of the rate observed over the undiluted pellets. An intriguing aspect of this experiment is that measurement of the number of active catalytic sites is not involved with this test. However, care should be exercised when the dilution method is used with catalysts having a bimodal pore size distribution. Internal diffusion in the micropores may be important for both the diluted and undiluted catalysts. 

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