Intracrystalline self-diffusivities

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... 

Figure 5) NMR intracrystalline self-diffusion coefficient Di ( ) and NMR desorption diffusivity Dd of methane sorbed in ZSM5 with increasing coking time, (reproduced with the permission from reference 18)...

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... 

As Fig. 25 shows, the intracrystalline self-diffusion coefficient of methane in ZSM-5 is between coefficients in zeolites NaCaA and NaX (5,71,114,115,). This order can be interpreted in terms of the minimum apertures of the zeolite channels, which are approximately 0.45, 0.55, and 0.75 nm for 5A, ZSM-5, and X-type zeolites. Due to the hydrophobic nature of ZSM-5, the mobility of water in ZSM-5 considerably exceeds the mobility in zeolites NaA and NaX. A change in the Si02/Al203 ratio of ZSM-5 does not alter the self-diffusion coefficient of methane. On the contrary, for water in ZSM-5 an increase in the self-diffusion coefficients with decreasing A1 concentrations in the framework is indicated. 

For a number of adsorbate-adsorbent systems it has been found that the intracrystalline self-diffusion of a highly mobile component is drastically reduced by the presence of a second, strongly coadsorbed component. By combining these self-diffusion measurements with a computer simulation of... 

A reduction of the intracrystalline self-diffusion coefficient, Dintra, of a probe molecule (e.g., methane) as measured by PFG NMR has to be regarded as proof of the existence of coke, modifiers, etc. in the volume phase of the zeolite crystal. 

Figure 34 shows that both the intracrystalline self-diffusivity Dimra (as measured by PFG NMR) and the effective self-diffusivity Deff (as derived from TD NMR) decrease with increasing phosphorus content. The continu-... 

Fig. 34. Intracrystalline self-diffusion coefficient Dimm (A) and effective seif-diffusion coefficient ( ) of methane in HZSM-5 modified by impregnation with H3PO4. The starting self-diffusion coefficient is 8.9 X 10" m s" (6 CH4 per u.c., 293 K) 130).

Flo. 37. NMR intracrystalline self-diffusion coefficient Dm, (a) and effective self-diffusivity Dcir ( ) of methane in HZSM-5 crystals that were coked for different times by n-hexane cracking (131-133). Before loading with methane (9.2 CHa per u.c.), the coked ZSM-5 crystals were carefully outgassed at 623 K and 10 Pa. The remaining carbonaceous residues were defined as coke. Amounts of coke after different times on stream 1 h, 0.8 wt% C 2 h, 1.3 wt% C 6 h, 3.2 wt% C 16 h, 4.8 wt% C. The starting self-diffusion coefficient is 8.1 x 10" m s . ... 

Hence, the nmr pulsed iield gradient technique could be applied to study the difiusion behaviour of a large variety of adsorbate molecules. The data for intracrystalline self-diffusion are summarized in the review <6), In the following, we shall restrict ourselves to the discussion of experimental results referring to the existence of surface barriers. 

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. 

In the present case, the intracrystalline mean life times should be compared with a value of Ti lrou ,f = 0,007 ms, which results from inserting the mean crystallite radius and the intracrystalline self-diffusion coefficient (- 10 nrs ) at the given temperature and concentration (15) into Equation 10. Since in the nmr measurement is found to be much less than 0.2 ms,... 

Table I. Comparison of the Intracrystalline Mean Life Times t and the Quantities linu.0 1, calculated on the Basis of the Coefficients of Intracrystalline Self-Diffusion for Aromatic Compounds in Zeolite NaX...

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. 

Figure 28 Values for the coefficients of intracrystalline self-diffusion (A) and for the apparent diffusivity determined from NMR tracer desorption curves ( 1) at 293 K...

Figure 32 Values for the coefficients of (a) intracrystalline self-diffusion of the two components in /i-heptane-benzene mixtures in NaX at 400 K and (b) long-range selfdiffusion at 361 K, plus the separation factors calculated from them. (From Refs. 145, 163, and 165.)...

Fig. 10 The different patterns of concentration dependence of intracrystalline self-diffusivities as determined from PFG NMR measurements. From Keil et al. [232], based on experimental data from Karger and Pfeifer [202]...

Fig. 16 Coefficient of intracrystalline self-diffusion of methane in zeolite (o) Na75,Ca-X, >) Na30,Ca-X, and ( ) Na-X determined by PFG NMR. The numbers inserted in the symbols indicate the concentration in molecules per supercage. From [152] with permission...

Fig. 17 Intracrystalline self-diffusivity of methane ( 2 molecules per supercage, at 25 °C) as a function of the amount of co-adsorbed molecules per window . The solid lines are predictions based on the effective medium approximation of percolation theory with / denoting the ratio of the transition rates through blocked and open windows. From [158] with permission...

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. 3 Types of concentration dependence of the intracrystalline self-diffusion coefficient [20]...

Figure 8 shows the self-diffusion coefficients, Db, of methane, ethane and propane as a function of soibate loading at various temperatures. These corrected diffusion coefficients were calculated from Equation 12 using diffusion coefficients obtained fi m both sorption and desorption half-cycles. These diffusion coefficients were identical. The corrected, Db, diffusion coefficients in Figure 8 are <5 smaller than the intracrystalline self-diffusion coefficients measured directly by NMR which are also included in this figure and are in close agreement with the corrected diffusion coefficients obriuned by the full FR method. 

FIGURE 5.17. Results of tracer desorp-lion study of diffusion of CjH in 5A zeolite crystals showing effect of crystal size and dehydration temperature. Filled symbols represent NMR (PFG) intracrystalline self-diffusivities. Open symbols represent tracer desorption diffusivities. Earlier self-diffusivity data for larger crystals (—) and uptake rate data > [/)(,... 

Despite the large difference in the apparent diffusivities derived from uptake rate measurements, measurements of the intracrystalline self-diffusivity (for C2H6-5A) by the NMR (PFG) method show little difference between the large laboratory synthesized crystals and the small Linde crystals, thus favoring the surface barrier hypothesis. The increase in activation energy, which is observed for this system on severe hydrothermal pretreatment of the smaller crystals, is also consistent with a change from intracrystalline diffusion to surface barrier control. Detailed sorption rate studies with the system n-butane-5A, however, support the opposite conclusion that the differences in... 

Pfeifer. H., et al.. Concentration dependence of intracrystalline self-diffusion in zeolites, Adsorpt. Sci. Technol.. 2(4), 229-240(1985). 

Intracrystalline self-diffusion of methane adsorbed in NaA zeolite was deduced from proton spin-spin relaxation measurements. It was found that, for filling factors of up to 3 molecules per cage, the data were described by ... 

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