Coefficient intracrystalline diffusion

Understanding the adsorption, diffusivities and transport limitations of hydrocarbons inside zeolites is important for tailoring zeolites for desired applications. Knowledge about diffusion coefficients of hydrocarbons inside the micropores of zeolites is important in discriminating whether the transport process is micropore or macropore controlled. For example, if the diffusion rate is slow inside zeolite micropores, one can modify the post-synthesis treatment of zeolites such as calcination, steaming or acid leaching to create mesopores to enhance intracrystalline diffusion rates [223]. The connectivity of micro- and mesopores then becomes an... 

A good example for reactant shape selectivity includes the use of catalysts with ERI framework type for selective cracking of linear alkanes, while excluding branched alkanes with relatively large kinetic diameters from the active sites within the narrow 8-MR zeolite channels [61, 62]. Here molecular sieving occurs both because of the low Henry coefficient for branched alkanes and because of the intracrystalline diffusion limitations that develop from slow diffusivities for branched alkane feed molecules. 

These calculated intracrystalline diffusion coefficients are particularly appropriate for comparison with those determined from pulsed field gradient (PFG) NMR experiments. Time-independent equilibrium properties such as adsorbate conformations are also readily accessible. The classical nature of the simulations allows a particle s trajectory to be followed, and from this it is possible to determine all kinds of information, such as how often a particle diffuses through a certain region. 

A new mathematical model based on moment techniques to describe micro- and macropore diffusion is used to study the mass-transfer resistances of Ci to C4 saturated hydrocarbons in H and Na mordenites between 127° C and 272° C. The intracrystalline diffusion coefficient decreases as the number of carbon atoms increases while the energy of activation increases with the number of carbons. The contribution from individual mass-transfer resistances to the overall mass-transfer processes is estimated. 

Second-Order Moment. The linearity of y U /2L vs. l/t/B2 is shown in Figure 4. From the slope of the straight line, the axial dispersion coefficient D can be calculated. With the assumption that kR = Z)Ab, Da and Di can be calculated from the second and third terms in the bracket of the right-hand side of Equation 6 by varying the particle size. The results are given in Table II. As expected, both inter- and intracrystalline diffusion coefficients increase with temperature. The values obtained for Di in Na mordenite are somewhat smaller than those obtained by Satterfield and Frabetti (7) and Satterfield and Margetts (8) which were obtained at a lower temperature. However, Frabetti reported that diffusion co-... 

A method is presented for obtaining the diffusion coefficients of Ci to C4 hydrocarbons on H and Na mordenite by analysis of their chromatographic curves. It is shown that in such a transient device the role of the intercrystalline diffusion may be important for the estimation of the total mass-transfer resistance. The diffusion coefficients decrease with increase in the number of carbon atoms. They are about one order of magnitude smaller on mordenite in the Na form than in the H form. The energies of activation are higher for intracrystalline diffusion than for intercrystalline diffusion. The resistance from intercrystalline diffusion makes an important contribution to the total mass-transfer resistance at low temperature. 

A successful measurement of the intracrystalline diffusion coefficient in zeolites thus requires that the time needed be less than the time available— i.e., that... 

An intriguing aspect of these measurements is that the values of D determined from NMR and from sorption kinetics differ by several orders of magnitude. For example, for methane on (Ca,Na)-A the value of the diffusion coefficient determined by NMR is 2 x 10 5 cm2 sec-, and the value determined for sorption rates only 5 x 10"10 cm2 sec-1. The values from NMR are always larger and are similar to those measured in bulk liquids. The discrepancy, which is, of course, far greater than the uncertainty of either method, remained unexplained for several years, until careful studies (267,295,296) showed that the actual sorption rates are not determined by intracrystalline diffusion, but by diffusion outside the zeolite particles, by surface barriers, and/or by the rate of dissipation of the heat of sorption. NMR-derived results are therefore vindicated. Large diffusion coefficients (of the order of 10-6 cm2 sec-1) can be reliably measured by sorption kinetics... 

Studies of intracrystalline diffusion can delineate factors limiting transport within crystals and hence will aid understanding of molecule sieving and site accessibility in catalysis. One may hope to learn from basic diffusion studies how diffusion coefficients within zeolites are related to ... 

Measurements have been made of tracer or intrinsic diffusion coefficients of water in a number of zeolites. Most refer to crystals nearly saturated with zeolitic water, while smoothed rather than adsorption areas were used in calculating the coefficients. From the temperature dependence of Da or Da, the activation energy, E, may be found using the Arrhenius equations Da = Do exp — E/RT or Da = Do exp — E/RT. Some results for tracer diffusion are summarized in Table VI. (iS). These shed considerable light upon certain aspects of intracrystalline diffusion for small polar molecules ... 

The control of reaction rates by a bulk difiusion process is not usually demonstrable by microscopic observations, but support may be obtained from measurements of diffusion coefficients of appropriate species within the structure concerned. This approach has been invaluable in formulating the mechanisms of oxidation of metals, where rates of reaction have been correlated with rates of transportation of ions across barrier layers of product. Sometimes the paths by which such movements occur correspond to regions of high difi isivity, involving imperfect zones within the barrier layer, compared with normal rates of intracrystalline diffusion across more perfect regions of material [63]. Difiusion measurements have been made for ions in nickel sulfide and it was concluded that the decomposition of NiS is diffiision controlled [50]. 

Lee and Ma (1977) observed that the intracrystalline diffusion coefficients (A) of n-butane, isobutane and 1-butene in the Na-, Ca- and La-forms of synthetic faujasite, determined in a constant volume, decrease in the following order for all three hydrocarbons (table 4) A(La-X) > A(Ca-X) > A(Na-X). This is caused by the... 

With the TEX-PEP technique experiments on the diffusion and adsorption of mixture of n-hexane/2-methylpentane in large silicalite-1 crystals have been performed. By modeling the experimental tracer exchange curves values of intracrystalline diffusion coefficient and adsorption constant were obtained. Slight preference for the adsorption of /t-hexane was found. Diffusivity of -hexane sharply decreases with increasing fraction of its isomer, since the last one occupies channel intersections thus blocking zeolite network. 

Fig. 18 Apparent coefficients of intracrystalline self-diffusion of n-hexane as observed by time- and space-resolved PFG NMR in a bed of zeolite Na-X with restricted ( ) and unrestricted ( ) sorbate supply in dependence on the sorbate concentration. The real diffusivities open symbols) were calculated from these values by using the correspondence presented by Fig. 3. The full line with the indicated error bars represents the range of intracrystalline diffusivities as observed in previous PFG NMR studies with closed sample tubes. From [163] with permission...

Fig. 25 Dependencies of the diffusion coefficients of n-butane in silicalite-1 on the root of mean square displacements at different temperatures and comparison with the results of dynamic MC simulations for a barrier separation of 3 jxm with the assumption that jumps across the barriers occur with an activation energy exceeding that of intracrystalline diffusion by 21.5 kj mol h Filled and open symbols correspond to measurements performed with two different samples of silicalite-1. From [216,217], with permission...

Keipeit, O.P. Baers, M., Determination of the intracrystalline diffusion coefficients of alkanes in H-ZSM-5 zeolite by a transient technique using the temporal-analysis-of-products (TAP) reactor. Chem. Eng. Sci. 53 (1998) pp. 3623-3634. 

The model of Santacesaria et is an extension of the linear driving force model, with fluid side resistance, for a nonlinear multicomponent Langmuir system. It includes axial dispersion, and the combined effects of pore diffusion and external fluid film resistance are accounted for throu an overall rate coefficient. Intracrystalline diffusional resistance is neglected and equilibrium between the fluid in the macfopores and in the zeolite crystals is... 

Xe NMR spectra are simulated from the adsorbate concentration profiles. The fit of experimental with calculated spectra (Fig. 3a) using the adjustable parameter, Tintra, allows the determination of the intracrystalline diffusion coefficient of benzene in HZSM-5 zeolite during its adsorption under constant (saturation) pressure. Dint = 7x10 m s" . This value agrees with that obtained with other techniques and reported in literature [4]. The equilibrium time, too, of 8 and 13 h, depends on the bed length, 5 and 15 mm, respectively. The calculation... 

The intracrystalline diffusion coefficient Dc was considered to be independent of adsorbate concentration in the above analysis of Ruckenstein et al. (1971). However, if the initial quantity of adsorbate admitted to the adsorbent is such that the vapour phase concentration does not remain constant, then account should be taken of the variation of the intracrystalline diffusivity with concentration. This dependence of diffusivity on concentration may be derived by equating the Fickian flux to the thermodynamically defined flux, the latter depending on the product of concentration and the gradient of chemical potential. It then follows (Ruthven 1984, Yang 1987) that the diffusion coefficient is related to adsorbed phase concentration by the equation... 

The validity of eqn. (3) for determining the intracrystalline self-diffusion coefficients from uptake data has been shown for the sorption of benzene by... 

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... 

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