Diffusion tracer desorption

Comparison between xf a as determined on the basis of Eq. (3.1.15) from the microscopically determined crystallite radius and the intracrystalline diffusivity measured by PFG NMR for sufficiently short observation times t (top left of Figure 3.1.1), with the actual exchange time xintra resulting from the NMR tracer desorption technique, provides a simple means for quantifying possible surface barriers. In the case of coinciding values, any substantial influence of the surface barriers can be excluded. Any enhancement of xintra in comparison with x a, on the other side, may be considered as a quantitative measure of the surface barriers. 

It is worth noting that within a range of 20 %, five different methods of analyzing the crystallite size, viz., (a) microscopic inspection, (b) application of Eq. (3.1.7) for restricted diffusion in the limit of large observation times, (c) application of Eq. (3.1.15) to the results of the PFG NMR tracer desorption technique, and, finally, consideration of the limit of short observation times for (d) reflecting boundaries [Eq. (3.1.16)] and (e) absorbing boundaries [Eq. (3.1.17)], have led to results for the size of the crystallites under study that coincide. 

Fast Tracer Desorption There are many zeolitic systems in which intracrystalline diffusion is too slow to measure directly by the PFG method. A modification of this method which makes it possible, under certain conditions, to measure much slower diffusion processes has recently been introduced by Karger(28,29),... 

With the development of the fast tracer desorption NMR method a more detailed investigation of these systems became possible. A study of diffusion of C2H6 in 5A by this method showed no significant surface barrier, even when the sieve was dehydrated at 600°C under conditions similar to those used commercially(28,29). 

B. Self-Diffusion Measurements by the NMR Tracer Desorption Technique... 

From the NMR tracer desorption and self-diffusion data (second and third lines of Table I), one obtains the relation Timm > TmlL. In the example given, intercrystalline molecular exchange is limited, therefore, by transport resistances at the surface of the individual crystals. Combined NMR and high-resolution electron microscopy studies 54) suggest that such surface barriers are caused by a layer of reduced permeability rather than by a mere deposit of impenetrable material on the crystal surface, although that must not be the case in general. 

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... 

For a direct check of the existence or non-existence of surface barriers we have applied the nmr tracer desorption technique. For a few selected systems, Table I gives a comparison between the mtracrvstaiiine mean life times a,and the quantities T ,n., l J 1 calculated from the coefficients oi intra-crystalline diffusion on the basis of Equation 11. The order of - magnitude agreement between these quantities indicates that under the given conditions in fact a substantial influence of surface barriers on molecular transport may be excluded,... 

During mesityiene coking, the carbonaceous compounds are found to be exclusively deposited on the outer surface. For n-hexane, two stages of the coke deposition become visible At shorter coking times n-hexane is mainiy deposited in the intracrystalline space, tnus simultaneously affecting a retardation of intracrystaliine diffusion ana tracer desorption. In a second stage, similar to the behaviour observed with mesityiene, coke is predominantly deposited on the crystallite surface. 

Equivalently, one may investigate the existence of a surface barrier by comparing the intracrystalline diffusivity as determined by PEG NMR with a quantity derived from the NMR tracer desorption curve assuming intracrystalline diffusion control. In the absence of significant surface barriers, one should find Dj .a > whereas the existence of a barrier will give Di ,ra > f des ... 

Figure 22 gives a comparison of the results of NMR tracer desorption studies and self-diffusion measurements on short chain length paraffins in zeolite NaX [48]. For illustration, the complete tracer desorption curves are also given at selected temperatures. Covering the range from — 140 to 200°C and chain lengths from one to six carbon atoms, the intracrystalline mean lifetimes are found to coincide with values of calculated via Eq. (2) from the NMR self-diffusion co-... 

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. 

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...

It is noteworthy that, in principle, each of these time constants may be determined by the PFG NMR method Xj-rys,, which is identical with Xi ,ra " and Xpciict directly from the measurement of the coefficients of intracrystalline and of long-range diffusion, and x harr by combining the result of the NMR tracer desorption measurements (Xjn, see Sec. III.C.) with Xj ,ra , using the equation Timra + x barr Since in the NMR measurements a wide range of... 

From Eq. (2), the measured diffusivities may be used to determine the mean lifetime of the reactant and product molecules within the individual crystallites under the assumption that the molecular exchange is exclusively controlled by intracrystalline diffusion. These values, being of the order of 30 ms, are found to agree with the real intracrystalline mean lifetime directly determined by NMR tracer desorption studies (208], so that any influence of crystallite surface barriers may be excluded. From an analysis of the time dependence of the intracrystalline concentration of the reactant and product molecules, the intrinsic reaction time constant is found to be on the order of 10 s. This value is much larger than the intracrystalline mean lifetimes determined by PFG NMR, and thus any limiting influence of mass transfer for the considered reaction may be excluded. In agreement with this conclusion, the size of the applied crystallites was found to have no influence on the conversion rates in measurements with a flow reactor (208]. 

A plot of the relative intensity of the broad constituent versus the observation time (i.e. the separation between the two field gradient pulses) contains information which is analogous to that of a tracer exchange experiment between a particular crystallite containing e.g. labelled molecules and the unlabelled surroundings. Therefore, this way of analysis of PFG NMR data of zeolitic diffusion has been termed the NMR tracer desorption technique [60]. The first statistical moment ( time constant ) of the NMR tracer desorption curve represents the intracrystalline mean lifetime Tintra of the molecules under study. 

The size of these crystals and the conditions of dehydration are essentially similar to those used in the preparation of commercial 5A adsorbents. It is remarkable that the diffusional activation energy determined from the tracer desorption results for the small crystals dehydrated at high temperature (2.8 kcal/molc) is almost the same as the value determined from the earlier adsorption rate measurements with small commercial Linde crystals (3.0 kcal/mole). The absolute values of the diffusivities for the severely de-... 

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 > [/)(,... 

Tracer diffusivities are often determined using the thin-source method. Self-diffusivities are often obtained from the diffusion couple and the sorption methods. Chemical diffusivities (including interdiffusivity, effective binary diffusivity, and multicomponent diffusivity matrix) may be obtained from the diffusion-couple, sorption, desorption, or crystal dissolution method. 

In tracer ZLC (TZLC) [28,51,58] the experiment is similar to the standard method, but the monitored species is the deuterated form of the sorbate. This introduces an additional cost for the material and the requirement for an online mass spectrometer. The advantages are the eUmination of all possible heat effects, strict Unearity of the equiUbrium between the fluid phase and the adsorbed phase, and the possibility of measuring directly the tracer diffusivities (which shoifld be the same as the microscopically measured self-diffusivity) over a wide range of loading. To reduce the costs the carrier is prepared with a mixture of pure and deuterated hydrocarbons. It has been shown that small imbalances in the concentration of the carrier and the purge streams do not affect the desorption dynamics [58]. 

Eq. 21 with Eq. 23 results as the solution of the corresponding differential equation of normal diffusion with the appropriate initial and boundary conditions. These relations hold with the adequate interpretation of D as a self-diffusivity or a transport diffusivity, respectively, for both tracer exchange between the initially adsorbed species A by species B and the relative uptake in an adsorption experiment. It should be noted that Eq. 21 also describes the molecular uptake by single-file systems, since with respect to adsorption/desorption there are no differences between single-file systems and systems which permit normal diffusion. 

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