Configurational diffusion molecules

Fig. 56. Model computation for the demetallation rate as a function of pore size and time on stream for first-order kinetics and configurational diffusion of a 12.5-A-diameter metal-bearing molecule (Rajagopalan and Luss, 1979).

Restricted transport or, by a different name, configurational diffusion [13] occurs when the diffusing molecules are comparable in size to the pores within which they diffuse. This happens, for example, in hydrodemetallation over alumina-supported Co-Ni catalysts [14]. The observation that the effective diffusivity depends on the fourth power of the molecule-to-pore size ratio is important, but it is not yet evident how to correlate complex pore size distributions with effective diffusivities in the configurational... 

Extensive manifestations of configurational diffusion can be seen in catalytic zeolites. The landmark measurements by Gorring [16] of the diffusion coefficients of alkanes (in potassium T zeolites) as a function of their carbon number are shown in Fig. 4, indicating over two orders of magnitude of change in diffusivity, with a minimum at C-8 and a maximum at C-12 for unexplained reasons. Similarly, spectacular effects for more complex molecules have been observed by Haag and Chen [17] and are shown in Fig. 5. Although we do not yet have a workable correlation between zeo-... 

In zeolitic materials, where the molecules are of pore size dimensions, activated configurational diffusion... 

The activation energy for gas translational diffusion represents the energy barrier that a molecule has to overcome upon moving from one channel intersection to the other. The order of magnitude can be calculated from the difference in potential field in a channel and in an intersection. The transition from Knudsen to configurational diffusion depends on the size of the molecule with respect to the zeolite channels and the proportions of the molecule (ratio of length to diameter), as is shown in Fig. 11 for ZSM-S and zeolite-A. 

Figure 11 Transition from Knudsen diffusion to configurational diffusion in ZSM-5 and 5A as a function of the ratio between the minimum kinetic diameter of the molecule and the maximum channel diameter of the zeolite at 300 K. The ratio between the length and the kinetic diameter of the diffusing molecule was taken to be 1.25. (Adapted from Ref. 37.)...

Activated surface diffusion or configurational diffusion occurs in molecules with a diameter larger than 60% of the pore diameter, as is the case in pervaporation with zeolite membranes [113]. Diffusion is an activated process and the diffusivity follows an Arrhenius-type equation ... 

Within micropores, surface forces are dominant and an adsorbed molecule never escapes completely from the force field of the surface. Diffusion within this regime has been called configurational diffusion, intra-crystalline diffusion, micropore diffusion, or simply surface diffusion. The Maxwell-Stefan formulation, which is generally accepted for diffusion in the bulk fluid phase, can be extended to describe surface diffusion by considering the vacant sites to be a (n + l)-th pseudospecies on the surface [38,47,49-52]. Using the Maxwell-Stefan diffusion formulation, the following relationship was obtained for surface diffusion. 

Molecular-sieve membranes can yield high separation factors by permitting small molecules to diffuse while essentially excluding or severely restricting the accessibility of larger molecules (Figure 9.2(d)). This type of diffusion, where the pores are of molecular size, has been referred to as shape selective or configurational diffusion. 

Configurational diffusion (where molecules are of the same size as the pores) mainly in zeoUtes Surface diffusion... 

On the other hand, our knowledge of configurational diffusion in zeolites is far from being adequate. While Fick s law on diffusion has been commonly used to obtain diffusion coefficients in zeolites, there is experimental data such as the window or cage effect observed in erionite which cannot be interpreted by such equations. Data on diffusion of high molecular weight molecules in zeolites are almost nonexistent. Discrepancies also remain unresolved between diffusion coefficients determined by NMR and uptake data (22-23). Needless to say, much remains to be investigated, Uoth in theory (24-25) and in experimental measurement (26). 

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