Diffusion single file

It is known that the displacement of single particle in single-file diffusion follows the time dependence r2(t) °c t n. Hence the tracer diffusion coefficient vanishes at long times for diffusion on an infinitely long lattice. However, MC simulations show that the collective... 

Since the fraction of empty sites in a zeolite channel determines the correlation factor (Section 5.2.2), as is well known from single-file diffusion in the pores of a membrane, the strong dependence of the diffusion coefficients on concentration can be understood. This is why a simple Nernst-Planck type coupling of the diffusive fluxes (see, for example, [H, Schmalzried (1981)]) is also not adequate. Therefore, we should not expect that sorption and desorption are symmetric processes having identical kinetics. Surveys on zeolite kinetics can be found in [A. Dyer (1988) J. Karger, D.M. Ruthven (1992)]. 

J. KSrger, Single File Diffusion, Ch. 7 in Molecular Sieves Science and Technology, H.G. Karge and J. Weitkamp eds., Wiley-VCH (2002). 

The first term on the right-hand side of the equation denotes the friction between species the second term represents friction between a species and the surface. and )Ji+i are the Maxwell-Stefan diffusivities. The first term on the right side is often referred to as an exchange term that represents the probability of molecules exchanging places on the surface. Since this exchange is not likely to occur in narrow zeolite channels, it is commonly neglected. This is called single-file diffusion. 

FIGURE 10.24 Model of the prevention of secondary reactions by single-file diffusion in tnicroporous membranes. (Adapted from Lange, C., Storck, S Tesche, B and Maier, W.F., J. Catal, 175, 280, 1998.)... 

It is evident that, in the cases of single-file diffusion and barrier-limited molecular exchange, a suitable definition of the Thiele modulus cannot be based on eq. 1. These cases may also be covered, however, if the Thiele modulus is expressed in terms of the... 

It has been demonstrated by numerical simulations [9] that, with this definition, eq. 2 provides a reasonable order-of-magnitude estimate of the effectiveness factor also in the case of single-file diffusion. While in the case of ordinary diffnsion the intracrystalline mean life time may be easily correlated with the crystal size and the internal mobility [11], similar analytical expressions for single-file diffusion have not been established. The rule-of-thumb given in Ref. [10] on the basis of a few first numerical simulations turned out to be of rather limited validity in recent more refined considerations [12]. 

For single file diffusion mechanism, with no possible counter-exchange between adsorbed species, these equations simplify to... 

Por single file diffusion mechanism, it is assumed that no coimter-exchange is possible between the adsorbed solutes i and j. For single file diffusion mechanism the Pick surface diffusivity matrix is given by ... 

For small por s with a pore diameter of about the same size as the molecular diameter (situation b2 in Fig. 9.20) counter-exchange will not take place and terms with D12 are absent. This is the so-called single file diffusion for which can be written [89] ... 

If single file diffusion prevails the single component permeation data (which determine D,) and single component adsorption data are sufficient to predict the binary fluxes via Eq. (9.52). 

As iff 1 increases so should the degree of saturation at which Z>ab begins to deviate significantly from D. The phenomenon of single-file diffusion is, of course, excluded if Ifi > 1. 

It is worthwhile to note that under conditions of single-file diffusion, the definition of the Thiele modulus... 

With this more general equation, representation of the effectiveness factor in terms of the Thiele modulus also becomes possible for single-file diffusion. As an example. Fig. 16 shows the result of a computer simulation of diffusion and reaction within a single-file system consisting of A = 100 sites for different occupation numbers in comparison with the dependence... 

These simple model calculations illustrate the dramatic effect of micropore filling on catalytic performance. Since dilution by pentane does not increase the rate of hexane in Mordenite. The experiments by Spivey and Bryant indicate that diffusion has to be explicitly considered. It is likely that not only the higher heat of adsorption of alkanes in Mordenite compared to Faujasite, but ultimately the one dimensional stracture and resulting single file diffusion are responsible for the unique behavior of the Mordenite catalyst. 

Effect of single-file diffusion on the hydroisomerization of 2,2-dimethylbutane on platinum loaded H-mordenite... 

The effect of single-file diffusion limitation on the rate of an irreversible first order catalytic reaction was studied both theoretically and experimentally. A rate equation was derived using a relation between the effective diffusion constant and the concentration of adsorbed molecules under single-file conditions which is valid on the time scale of catalytic reactions. The hydroisomerization of 2,2-dimethylbutane on platinum loaded large crystallites of H-Mordenite was used as a test reaction to verify the theoretical results. 

Single file diffusion, effect on catalysis 28-0-05 K-01 Singlet molecular oxygen 27-P-ll... 

Effect of single-file diffusion on the hydroisomerization of 2,2-dimethylbutane on platinum loaded H-mordenite F.J.M.M. de Gauw, J. van Grondelle and R.A. vanSanten... 

Anomalous diffusion is also possible in microporous solids. For instance, it is possible for molecules to be confined in a channel system in which they cannot pass each other, and this will obviously affect molecular displacement in a time interval. This case is termed single-file diffusion , and the mean square displacement in a time t is then given... 

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