Diffusion, crystallite diameters

For root mean square displacements 1 much less than the mean crystallite diameters,the thus determined self-diffusion coefficient exclusively refers to migration in the intracrystalline space. In the opposite limiting case of large molecular displacements one obtains the coefficient of long-range self-diffusion (Di.v.). This quantity is related to the relative... 

Figure 9 Concentration dependence of the self-diffusion coefficient of /j-hexane in zeolite NaX with mean crystallite diameters of 55 p-m (O), 20 xm([ 1), 15 xm ( 0 ), and 4 p.m (A) at 293 K. The proton resonance frequencies were 60 MHz (open symbols) and 16.6 MHz (full symbols), corresponding to external magnetic fields of 1.41 and 0.39 T, respectively. The error bars indicate the uncertainty in the diffusivities and concentrations. (From Ref. 108.)...

Once the molecular root mean square displacements observed by PFG NMR are much larger than the mean crystallite diameters, a direct measurement of the rate of mass transfer through the assemblage of zeolite crystallites becomes possible. This rate is represented by the coefficient of long-range diffusion... 

Figure 29 PFG NMR diffusivity data for w-butane in an assemblage of zeolite NaX with a mean crystallite diameter of about 16 xm and a sorbate concentration of 80 mgg represented by the quantity Dc = /(6 ) (open symbols). Observation times are / = 50 ms (V), 100 ms (A), and 200 ms (Q)- In addition, comparison with values for determined according to Eq. (45). For >>, f iong-range coincides with...

Figure 30 Effective diffusivity of Aj-butane in zeolite NaX, both in a loose assemblage ( ) and after compaction under a pressure of 2.5 MPa (O)- The mean crystallite diameter is 5 p,m for a sorbate concentration of about 80 mgg. (From Ref. 193.)...

D li can be used directly. The method outlined here aims at predicting the permeation of membranes from kinetic modeling carried out on the corresponding powders. In this case, the characteristic length of difiusion is not the same. For the membrane application, the length corresponds to the thickness of the membrane, whereas for powder it corresponds to the crystallite size. The mean crystallite diameter corresponding to an accessible surface determined by N2 adsorption measurements at 77 K was used in the calculation of the value of the vacancy diffusion coefficient. 

The hydrogenation of para-substituted anilines over rhodium catalysts has been investigated. An antipathetic metal crystallite size effect was observed for the hydrogenation of /Moluidinc suggesting that terrace sites favour the reaction. Limited evidence was found for catalyst deactivation by the product amines. Catalysts with pore diameters less than 13.2 nm showed evidence of diffusion control on the rate of reaction but not the cis trans ratio of the product. 

Zeolite crystal size can be a critical performance parameter in case of reactions with intracrystalline diffusion limitations. Minimizing diffusion limitations is possible through use of nano-zeolites. However, it should be noted that, due to the high ratio of external to internal surface area nano-zeolites may enhance reactions that are catalyzed in the pore mouths relative to reactions for which the transition states are within the zeolite channels. A 1.0 (xm spherical zeolite crystal has an external surface area of approximately 3 m /g, no more than about 1% of the BET surface area typically measured for zeolites. However, if the crystal diameter were to be reduced to 0.1 (xm, then the external surface area becomes closer to about 10% of the BET surface area [41]. For example, the increased 1,2-DMCP 1,3-DMCP ratio observed with decreased crystallite size over bifunctional SAPO-11 catalyst during methylcyclohexane ring contraction was attributed to the increased role of the external surface in promoting non-shape selective reactions [65]. 

As in many other anthracitic substances, diffuse bands also appear near 43° and 80° 26. These represent two-dimensional (hk) reflections only since the turbostratic disorder of graphitic layers which characterizes amorphous carbons does not permit (hkl) three-dimensional atomic planes other than (001). Hirsch (19) proposed that the position of the (11) band was a function of carbon content of the sample, related to the crystallite layer diameter (L ). With increasing rank, the (11) reflection shifts towards smaller 26 values, representing greater bond lengths and larger crystallite size. Using values... 

Since offretite is a large-pore structure, intergrowth of offretite in the erionite phase would be expected to affect the adsorption properties. Table II compares adsorption capacities for natural and synthetic erionite with Zeolite A (Ca) and synthetic faujasite (Na) (4.8 Si02/Al203). As expected, the more dense erionite structure shows lower capacity (5). There is substantial agreement between natural and synthetic erionite capacity the difference shows in adsorption rates (D/r ). The low apparent diffusivity of n-parafBns in erionite is somewhat a mystery since there does not appear to be that much difference in pore dimensions between erionite and zeolite A as predicted from their structures (6). The difference cannot be attributed to crystallite size since the natural erionite sample (laths, 0.5 /x diameter or less) has finer crystallite size than any of the synthetic materials (1-5 /x). 

ZSM-11 zeolite is controlledj at least partially, by intracrystalline diffusion. Indeed, the zeolite channel diameter (5.6 A) is i aller than the critical diameter of m-xylene, mesitylene and naphthalene ( 7.4, 8.4 and 7.4 A, respectively). In the case of m-xylene and mesitylene (Fig lb) the first peak at low temperature is mostly due to the desorption of m-xylene and mesitylene adsorbed on the external surface [9], with Tm values (temperature corresponding to peak maximum of the TPD curve) similar to the Tm value for naphthalene sorbed on HZSM-11 zeolite. The second peaks are mostly due to the interaction of m-xylene and mesitylene which partially penetrated in the channels of the zeolites. The TPD of naphthalene sorbed on HZSM-11 zeolite (N1 in Fig. Ic) shows that N did not interact above 298 C, with Tm value close to 198 C. Because the zeolite channel diameter in H-ZSM-11 type zeolite is smaller than the critical size of N, the interaction is only possible with the external sites. Thus, the desorption of N would be mostly due to the N adsorbed on the external surface of the zeolite crystallites. In the case of H Y zeolite, the TPD result for naphthalene (N2 in Fig.lc) shows two peaks. The second one, at high temperatine (high Tm value), corresponds to the desorption of N sorbed in the intracrystalline voids of the large pore HY zeolite, which may easily accommodate naphthalene molecules. 

HZSM-5 zeolite catalysts show high shape selectivity, because they have very fine micro pores within its crystallite [1], The pore diameter is almost equal to sizes of mono-aromatic molecules [2]. HZSM-5 catalysts are typical solid-acid catalysts, and their acid sites are distributed not only within but also on the outer surface of the crystallite [1,3]. Therefore, the shape selectivity of HZSM-5 zeolite is affected strongly by the size of the crystallite, the intracrystalline diffusivities of hydrocarbons and acidic properties within and on the outer surface of the crystallite [4-7],... 

Thus, it can be concluded that the diffuslvities are dependent on the pore size of HZSM-5 zeolites and the weight, length and minimum diameter of the diffusing hydrocarbon molecule. However, there is no available method to predict the diffuslvities within the IIZSM-5 zeolite crystallite. Hence, a estimation method is developed in the next section. 

---