Intracrystalline molecular diffusion

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... 

The classical method of investigation of effects of diffusion on reactions is typically to run a reaction with catalyst particles of various sizes. For zeolites, the resistance of intracrystalline diffusion is normally much larger than that characteristic of molecular diffusion or Knudsen diffusion that could occur in the spaces between the zeolite crystals in a catalyst particle. Thus, the crystal size of the zeolite has to be varied instead of the particle size to determine the effects of diffusion on zeolite-catalyzed reactions. Kinetics of the MTO reaction has been measured with SAPO-34 crystals with identical compositions and sizes of 0.25 and 2.5 pm 89). The methanol conversion was measured as a function of the coke content of the two SAPO-34 crystals in the TEOM reactor. 

In general, for zeolitic self-diffusion at sufficiently high temperatures, the mean molecular displacements outside the crystal are much larger than those inside the zeolites that is to say, long-range self-diffusion, Di.r., is much faster than intracrystalline self-diffusion, Dintra- For observation times comparable with the mean lifetimes of the adsorbed molecules in the individual crystallites, the spin-echo attenuation can be approximated by the superposition of two exponentials of the type of Eq. (6)... 

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. 

Three quantities that have a key function for the understanding of mass transfer in granules are illustrated in Pig. 2 (i) the coefficients of intracrystalline self-diffusion, Dmm, and of (ii) long-range self-diffusion, Du., as well as (iii) the molecular mean lifetime, Tma- The coefficient of long-range self-difffusion is approximated by... 

The molecular root mean square displacement, r t)), of the diffusing molecules during the observation time, t, has to be much smaller than the crystal radius, R, in order to guarantee that the measured r.m.s. displacement reflects the undisturbed intracrystalline self-diffusion. Assuming... 

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... 

KaX than in smaii-port zeolites such as NaCaA. For hydrocarbons in HaX it has been found that the coefficients of intracrystalline self-diffusion decrease with increasing concentration (concentration dependences of type I and II (6).i. By contrast, for not toe high gas phase concentrations (i.e., as long as molecular transfer in the intercrystalline space proceeds by Knudsen diffusion)... 

Covering temperatures from -140 up to 200 C and chain lengths from one to six carbon atoms, the intracrystalline mean life times are found to coincide with the values oi rV 1 r calculated from the nmr self-diffusion coefficients. This clearly indicates that molecular exchange is controlled by intracrystalline self-diffusion, and that for the considered adsorbate-adsorbent systems there are no perceptible surface barriers. 

The variety of diffusion mechanisms involved in intracrystalline molecular mass transfer is most vividly reflected in the different patterns of the concentration dependence of intracrystalline self-diffusion. A classification of the various concentration dependences so far observed by PFG NMR is presented in Fig. 10. 

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 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... 

Studying molecular diffusion in zeolite crystallites is complicated by the small size of the objects of investigation. Inevitable deviations of the real structure of a sample from the ideal one lead to an additional complication of the situation. It is not unexpected, therefore, that in spite of considerable progress in the experimental techniques, there is still some controversy in the imder-standing of intracrystalline zeohtic diffusion (cf. the preceding chapters of this volume). 

Xe NMR spectroscopy of adsorbed xenon, largely used to investigate static properties of porous solids, appears very useful to study the diffusion of coadsorbed molecules when the local concentration of these molecules changes as for example during the adsorption process. Coefficient of intracrystalline molecular transport can be obtained from the simulation of the NMR spectra using the solutions (adsorbate concentration profiles) of the diffusion equations. 

For noncoustaut diffusivity, a numerical solution of the conseiwa-tion equations is generally required. In molecular sieve zeohtes, when equilibrium is described by the Langmuir isotherm, the concentration dependence of the intracrystalline diffusivity can often be approximated by Eq. (16-72). The relevant rate equation is ... 

Introduction of PFG NMR to zeolite science and technology has revolutionized our understanding of intracrystalline diffusion [19]. In many cases, molecular uptake by beds of zeolites turned out to be limited by external processes such as resistances, surface barriers or the finite rate of sorbate supply, rather than by intracrystalline diffusion, as previously assumed [10, 20-24]. Thus, the magnitude of intracrystalline diffusivities had to be corrected by up to five orders of magnitude to higher values [25, 26],... 

The development of composite micro/mesoporous materials opens new perspectives for the improvement of zeolytic catalysts. These materials combine the advantages of both zeolites and mesoporous molecular sieves, in particular, strong acidity, high thermal and hydrothermal stability and improved diffusivity of bulky molecules due to reduction of the intracrystalline diffusion path length, resulting from creation of secondary mesoporous structure. It can be expected that the creation of secondary mesoporous structure in zeolitic crystals, on the one hand, will result in the improvement of the effectiveness factor in hydroisomerization process and, on the other hand, will lead to the decrease of the residence time of products and minimization of secondary reactions, such as cracking. This will result in an increase of both the conversion and the selectivity to isomerization products. 

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