Intracrystalline

Zeolites (section C2.13) are unique because they have regular pores as part of their crystalline stmctures. The pores are so small (about 1 nm in diameter) that zeolites are molecular sieves, allowing small molecules to enter the pores, whereas larger ones are sieved out. The stmctures are built up of linked SiO and AlO tetrahedra that share O ions. The faujasites (zeolite X and zeolite Y) and ZSM-5 are important industrial catalysts. The stmcture of faujasite is represented in figure C2.7.11 and that of ZSM-5 in figure C2.7.12. The points of intersection of the lines represent Si or A1 ions oxygen is present at the centre of each line. This depiction emphasizes the zeolite framework stmcture and shows the presence of the intracrystalline pore stmcture. In the centre of the faujasite stmcture is an open space (supercage) with a diameter of about 1.2 nm. The pore stmcture is three dimensional. 

Also shown are the corresponding curves calculated for the same system assuming a diffusion model in place of the linear rate expression. For intracrystalline diffusion k = 15Dq/v, whereas for macropore diffusion k = 15e /R ) Cq/q ), in accordance with the Glueckauf approximation (21). 

Fig. 15. Theoretical breakthrough curves for a nonlinear (Langmuir) system showing the comparison between the linear driving force (—), pore diffusion (--------------------), and intracrystalline diffusion (-) models based on the Glueckauf approximation (eqs. 40—45). From Ref. 7.

PVF displays several transitions below the melting temperature. The measured transition temperatures vary with the technique used for measurement. T (L) (lower) occurs at —15 to —20 " C and is ascribed to relaxation free from restraint by crystallites. T (U) (upper) is in the 40 to 50°C range and is associated with amorphous regions under restraint by crystallites (63). Another transition at —80° C has been ascribed to short-chain amorphous relaxation and one at 150°C associated with premelting intracrystalline relaxation. 

There are two types of stmctures one provides an internal pore system comprising interconnected cage-like voids the second provides a system of uniform channels which, in some instances, are one-dimensional and in others intersect with similar channels to produce two- or three-dimensional channel systems. The preferred type has two- or three-dimensional channel systems to provide rapid intracrystalline diffusion in adsorption and catalytic apphcations. 

Palygorskite and sepioHte minerals are 2 1 layered phyUosiHcates that differ from the above mentioned clays because the octahedral sheets have significant intracrystalline void space caused by discontinuous octahedral layers. The basal tetrahedral unit is connected to an adjacent inverted basal tetrahedral creating a void space or channel. Charge deficits are balanced by hydrated cations in the intracrystalline space. 

For noncoustaut diffusivity, a numerical solution of the conseiwa-tion equations is generally required. In molecular sieve zeohtes, when equilibrium is described by the Langmuir isotherm, the concentration dependence of the intracrystalline diffusivity can often be approximated by Eq. (16-72). The relevant rate equation is ... 

Tunable Intracrystalline Mesoporosity by Partial Detemplation-Desilication... 

An absolutely different situation occurs in case of polycrystalline adsorbent treated at high temperature in air or in other oxygen containing medium. In this case the volt-ampere analysis exhibits sharply nonlinear VAC, deviations from the Ohm law being observed at anomalously low fields [47]. This indicates an existence of high intracrystalline barriers in such adsorbents. These barriers can be attributed to crys-... 

Namely, the adsorbents of such type are polycrystalline materials with dominant type of intracrystalline contacts in the shape of open bridges enriched in superstoichiometric metal, which is the principal electron donor. Adsorption of oxygen resulting in binding of superstoichiometric metal atoms leads to the change in concentration of free electrons in bridges which results in the change of electric conductivity of the whole adsorbent. 

The propagator is often Gaussian (including the present cases of intracrystalline and long-range diffusion)... 

Introduction of PFG NMR to zeolite science and technology has revolutionized our understanding of intracrystalline diffusion [19]. In many cases, molecular uptake by beds of zeolites turned out to be limited by external processes such as resistances, surface barriers or the finite rate of sorbate supply, rather than by intracrystalline diffusion, as previously assumed [10, 20-24]. Thus, the magnitude of intracrystalline diffusivities had to be corrected by up to five orders of magnitude to higher values [25, 26],... 

Fig. 3.1.6 Temperature dependence of the intraparticle diffusivity of n-octane in an FCC catalyst and the intracrystalline diffusivity of n-octane in large crystals of USY zeolite measured by PFG NMR. The concentration of n-octane in the samples was in all cases 0.62 mmol g 1. Lines show the results of the extrapolation of the intracrystalline diffusivity and of the intraparticle diffusivity of n-octane to higher temperatures, including in particular a temperature of 800 K, typical of FCC catalysis.

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. 

For intracrystalline diffusion paths sufficiently small in comparison with the crystallite radii, the effective diffusivity as defined by Eq. (3.1.6) maybe expanded in a power series [9, 63, 64], leading to... 

Fig. 3.1.11 Relative effective intracrystalline diffusivities D(t)/D0 as function of JDot for n-hexane under single-component adsorption (circles) and for n-hexane (triangles) and tetrafluoromethane (rectangles) under two-...

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