Intracrystalline transport resistances

The existence of intracrystalline transport resistances has been confirmed by PFG NMR self-diffusion measurements of short-chain length alkanes in MFI-type zeolites [216,217] with varying observation time. Figure 25 presents the relevant data obtained with n-butane as a probe molecule. Here, the diffusivities are plotted in a way, which is made possible by the special features of PFG NMR, viz. as a function of the displacements over which the molecular diffusion paths (giving rise to the plotted diffusivities) have been measured. This is achieved on the basis of Eq. 7 by which the measured diffusivities maybe transferred into the mean square displacements covered by the molecules during the observation time. Obviously, in the case of ordinary diffusion, i.e. in the original notion of Eq. 7, the diffusivity depends on neither... 

The concept of transport resistances localized in the outermost regions of NS crystals was introduced in order to explain the differences between intracrystalline self-diffusion coefficients obtained by n.m.r methods and diffusion coefficients derived from non-equilibrium experiments based on the assumption that Intracrystalline transport is rate-limiting. This concept has been discussed during the past decade, cf. the pioneering work [79-81] and the reviews [2,7,8,23,32,82]. Nowadays, one can state that surface barriers do not occur necessarily in sorption uptake by NS crystals, but they may occur if the cross-sections of the sorbing molecular species and the micropore openings become comparable. For indication of their significance, careful analysis of... 

This case study clearly illustrates the usefulness of the ZLD-TEOM technique in determining intracrystalline diffusivities in zeolites, provided that effects of other transport resistances such as the surface barrier are eliminated by varying the crystal size of the zeolites. The measured steady-state diffusivity can be directly used for predicting effects of diffusion in reactions catalyzed by zeolites. More important, the TEOM makes it possible to distinguish the deactivation caused by blockage of the active sites and by increased diffusion resistance caused by blockage of cavities or channels by coke. 

If the calculated value of is equal to the measured intracrystalline lifetime, Tinira, the rate of molecular exchange between different crystals is controlled by the intracrystalline self-diffusion as the rate-limiting process. Any increase of Timn, in comparison with Tf,j L indicates the existence of transport resistances different from intracrystalline mass transport. Under the conditions of TD NMR one has A r. > Antra, thus these resistances can only be brought about by sur ce barriers. The ratio Timra/Tfn L represents, therefore, a direct measure of the influence of surface barriers on molecular transport. 

In addition to the conventional application of nmr pulsed field gradient experiments to self-diffusion studies, it is also possible to determine the intracrystalline molecular life times. Referring to the corresponding classical experiment, this method has been termed nmr tracer desorption technique (7). Together with the self-diffusion measurements it provides an excellent tool for characterizing the transport properties in the intra- and intercrystalline spaces, as well as at the interface between them. So far, the nmr techniques provide the only possibility for a direct determination of the existence and of the intensity of transport resistances at this... 

Figure 6 provides a comparison between measured spectra and theoretical spectra calculated under the assumption that the adsorption/desorption process is controlled by either intracrystalline diffusion (Fig. 6a) or external transport resistances such as surface barriers (Fig. 6b). For simplicity in the calculations, the crystallites have been assumed to be of nearly spherical shape with a concentration-independent transport diffusivity Dj or surface permeability a, respectively. Values of the intracrystalline mean lifetime are therefore given by...

If molecular exchange is controlled by intracrystalline diffusion, then the intracrystalline mean lifetime is given by Eq. (2), where it is assumed that the crystallites may be approximated by spheres (Sec. II.A.). Clearly, coincides with the directly measured Tj ,ra if desorption is controlled by intracrystalline diffusion. If, however, the rate of molecular exchange is additionally reduced by transport resistances at the crystallite boundary (so-called surface barriers), Tji,ra may be much greater than ... 

Abstract As a non-invasive technique, NMR spectroscopy allows the observation of molecular transport in porous media without any disturbance of their intrinsic molecular dynamics. The space scale of the diffusion phenomena accessible by NMR ranges from the elementary steps (as studied, e.g., by line-shape analysis or relaxometry) up to macroscopic dimensions. Being able to follow molecular diffusion paths from ca. 100 nm up to ca. 100 xm, PPG NMR has proven to be a particularly versatile tool for diffusion studies in heterogeneous systems. With respect to zeolites, PFG NMR is able to provide direct information about the rate of molecular migration in the intracrystalline space and through assemblages of zeolite crystallites as well as about possible transport resistances on the outer surface of the crystallites (surface barriers). 

The quantitative information provided by PPG NMR about the existence of additional transport resistances on the external surface of the zeolite crystallites (surface barriers) results from a comparison of the values for the intracrystalline mean life time determined directly (viz. Tintra) by an analysis of the time dependence of the spin-echo attenuation (and, hence, of the propagator), and determined indirectly (viz. tP ) from the intracrystalline diffusivity on the assumption that molecular exchange between different crystallites is controlled by intracrystalhne diffusion. On the additional assumption that the shape of the crystallites may be approximated by spheres with a mean square radius (R ) one has in the latter case [87,103]... 

In all the transient concentration profiles considered so far (Figs. 36, 42, 45, 46, 48, and 50), in no case did the boundary concentration immediately assume the equilibrium value. The consequences of this finding on the relation between the transport resistances exerted by the intracrystalline bulk phase and by the crystal surface on the overall uptake and release behavior will be... 

If the intracrystalline diffusional resistance for certain components could be neglected compared to resistances of other types, then the solution to the system of transport equations for a biporous pellet reduces to the macropore diffusion equation (8), in conjunction with the equilibrium relationship, eqs. (15)-(16). For an effective macropore diffusion coefficient, it holds ... 

Micropore mass transfer resistance of zeoUte crystals is quantified in units of time by r /Dc, where is the crystal radius and Dc is the intracrystalline diffusivity. In addition to micropore resistance, zeolitic catalysts may offer another type of resistance to mass transfer, that is resistance related to transport through the surface barrier at the outer layer of the zeoHte crystal. Finally, there is at least one additional resistance due to mass transfer, this time in mesopores and macropores Rp/Dp. Here Rp is the radius of the catalyst pellet and Dp is the effective mesopore and macropore diffusivity in the catalyst pellet [18]. 

The first hypothesis seems unlikely to be true in view of the rather wide variation in the ratio of carbon dioxide s kinetic diameter to the diameter of the intracrystalline pores (about 0.87, 0.77 and 0.39 for 4A, 5A and 13X, respectively (1J2)). The alternative hypothesis, however, (additional dif-fusional modes through the macropore spaces) could be interpreted in terms of transport along the crystal surfaces comprising the "walls" of the macropore spaces. This surface diffusion would act in an additive manner to the effective Maxwell-Knudsen diffusion coefficient, thus reducing the overall resistance to mass transfer within the macropores. 

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. 

The combined application of PFG NMR self-diffusion and tracer desorption experiments has thus proved to be an effective tool for studying the hydrothermal stability of A-type zeolites with respect to their transport properties [186]. It turns out that with commercial adsorbent samples there are considerable variations in hydrothermal stability between different batches of product and even between different pellets from the same batch. As an example. Fig. 24 shows the distribution curves [A(Tin,ra) versus Ti ,r.j] measured with ethane as a probe molecule at 293 K for two different samples of commercial 5A zeolites. Evidently batch 1 is more resistant to hydrothermal deterioration, because the lengthening of Tjn,ra is less dramatic than with batch 2. Since the intracrystalline diffusivity was the same for all samples, the deterioration can be attributed to the formation of a surface barrier. 

The main focus of this volume is on imderstanding the transport of molecules in microporous solids such as zeolites and carbon molecular sieves, and the kinetics of adsorption/desorption. This subject is of both practical and theoretical interest, since the performance of zeohte-based catalysts and adsorbents is strongly influenced by resistances to mass transfer and intracrystalline diffusion. However, at an even more basic level, the performance of microporous catalysts and adsorbents depends on favorable adsorption equilibria for the relevant species, so a general imderstanding of the fundamentals of adsorption equilibrium is a necessary prerequisite for understanding kinetic behavior. This chapter is intended to provide a concise summary of the general principles of adsorption equiHbriiun and of the main features of sorption kinetics in microporous solids, which generally depend on a combination of both equilibriiun and kinetic properties. 

Fig. 56 Correlation between the actual boundary concentration (Csurf) and the relative uptake (m) at the corresponding instant of time. Three different cases are shown the mass transport is essentially limited by intracrystalline diffusion (la/D = 100), by surface barriers la/D = 0.01), and both by intracrystalline diffusion and surface resistance la/D = 1)...

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