Diffusion and catalytic reaction

For the simplest one-dimensional or flat-plate geometry, a simple statement of the material balance for diffusion and catalytic reactions in the pore at steady-state can be made that which diffuses in and does not come out has been converted. The depth of the pore for a flat plate is the half width L, for long, cylindrical pellets is L = dp/2 and for spherical particles L = dp/3. The varying coordinate along the pore length is x ... 

Sorption, Diffusion, and Catalytic Reaction in Zeolites L. Riekert... 

Attaching the catalyst molecules to the electrode surface presents an obvious advantage for synthetic and sensor applications. Catalysis can then be viewed as a supported molecular catalysis. It is the object of the next section. A distinction is made between monolayer and multilayer coatings. In the former, only chemical catalysis may take place, whereas both types of catalysis are possible with multilayer coatings, thanks to their three-dimensional structure. Besides substrate transport in the bathing solution, the catalytic responses are then under the control of three main phenomena electron hopping conduction, substrate diffusion, and catalytic reaction. While several systems have been described in which electron transport and catalysis are carried out by the same redox centers, particularly interesting systems are those in which these two functions are completed by two different molecular systems. 

The rate processes of diffusion and catalytic reaction in simple square stochastic pore networks have also been subject to analysis. The usual second-order diffusion and reaction equation within individual pore segments (as in Fig. 2) is combined with a balance for each node in the network, to yield a square matrix of individual node concentrations. Inversion of this 2A matrix gives (subject to the limitation of equimolar counterdiffusion) the concentration profiles throughout the entire network [14]. Figure 8 shows an illustrative result for a 20 X 20 network at an intermediate value of the Thiele modulus. The same approach has been applied to diffusion (without reaction) in a Wicke-Kallenbach configuration. As a result of large and small pores being randomly juxtaposed inside a network, there is a 2-D distribution of the frequency of pore fluxes with pore diameter. 

SO far only been attained by Monte Carlo simulations. Figure 5 illustrates the situation due to the combined effect of diffusion and catalytic reaction in a single-file system for the case of a monomolecular reaction A B [1]. For the sake of simplicity it is assumed that the molecular species A and B are completely equivalent in their microdynamic properties. Moreover, it is assumed that in the gas phase A is in abimdance and that, therefore, only molecules of type A are captured by the marginal sites of the file. Figure 5 shows the concentration profile of the reaction product B within the singlefile system imder stationary conditions. A parameter of the representation is the probabiUty k that during the mean time between two jump attempts (t), a molecule of type A is converted to B. It is related to the intrinsic reactivity k by the equation... 

This chapter has, hopefully, shown the great potential and vast appHcabiUty of vibrational spectroscopic techniques in the field of science and technology of microporous and mesoporous materials. The diversity of experimental and computational techniques in vibrational spectroscopy as well as the development of modern fadhties and equipment allows us to tackle nowadays problems which seemed to be unsolvable only a short time ago. Thus, the number of reports in the field has increased immensely. Many appHcations became routine work. However, the prospects are still bright. The authors feel that the most promising progress in the role of vibrational spectroscopy in zeoHte research will emerge from further development in computational methods, combination with various other techniques, continued access to the molecular level of processes in microporous and mesoporous materials and last but not least by the extension and perfection of in-situ observations of processes in zeoHtes such as synthesis, modification, diffusion, and catalytic reactions. 

In the opposite case, when diffusion of the substrate is faster than diffusion of electrons, a pure kinetic situation may again arise, resulting in the mutual compensation of electron diffusion and catalytic reaction. 

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