Intracrystalline mean lifetimes

Since for a large variety of samples the shape of the zeolite crystallites tends to be even closer to that of a sphere, in general, Eq. (2) represents a reasonable estimate. It is used again in Sec. II.C., where another (microscopic) method to determine intracrystalline mean lifetimes is introduced. 

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 ... 

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-... 

Tabic 3 Comparison of Values for the Intracrystalline Mean Lifetime and the Quantity, Calculated on the Basis of the Coefficients of Intracrystalline Self-... 

Figure 23 shows results from a systematic study dealing with the influence of a hydrothermal pretreatment of granulated zeolite NaCaA on the three main transport parameters accessible by PFG NMR the coefficients of intracrystalline and long-range diffusion, as well as the intracrystalline mean lifetimes [145,... 

Figure 23 Coefficients of (a) intracrystalline and (b) long-range self-diffusion, and (c) intracrystalline mean lifetimes Tj , and (d) Timra " for methane in granulated zeolite NaCaA at 293 K. Also, comparison with (e) the breakthrough capacities for a petroleum raffinate and (0 the specific retention volume for /i-pentane all plotted against the temperature of hydrothermal pretreatment applied over a time interval of 7 h (0) and 14 h (O), respectively. (From Ref. 175.)...

Figure 26 compares values for the intracrystalline mean lifetime and Tin,ra " for methane in ZSM-5 type crystallites after different coking times and of the values of [145,187]. Depending on the applied coking compound,... 

Figure 26 Values for the intracrystalline mean lifetime Tjn, (f l, ) and the quantity T n,r " (A. A) versus time on stream for methane at 296 K and a sorbate concentration of 12 molecules per unit cell, in H-ZSM-5 coked by n-hexane (Filled symbols) and mesitylene (open symbols). (From Ref. 145.)...

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. 

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)... 

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... 

Comparison of mean intracrystalline lifetimes. For this kind of data evaluation, it is useful to introduce the first statistical moment... 

The absence of additional diffusion barriers at the crystal surface (coke, modifiers, etc.) can be assumed if the experimentally determined mean intracrystalline lifetimes, Timra (measured by TD NMR), and the corresponding calculated data, rSitra [according to Eq. (10)], coincide. The rSim data are calculated by using the self-diffusion coefficients, Dimra (measured by PFG NMR), and crystal radii, R, assuming the adsorption/desorption process to be diffusion controlled. 

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