Effectiveness under single-file conditions

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. 

Most importantly, combining the expressions for the intracrystalline mean life time Eq. 23 and the effective self-diffusivity (Eq. 19), in the case of singlefile diffusion the mean time of molecular exchange is found to scale with L, rather than with the dependence typical of normal diffusion. Therefore, under the conditions of single-file diffusion, the exchange rate with zeoUte crystallites decreases even more pronounced with increasing crystal sizes as in the case of normal diffusion. 

In complete agreement with the fact that the product molecules in a singlefile system are prevented from leaving the system by their file neighbors, the concentration profiles in the single-file cases show a much more pronounced tendency of accumulation of the reaction products in the file center than in the case of normal diffusion. Under stationary conditions, the effective reactivity k is related to the intrinsic reactivity k by the equation... 

Thiele moduli. These also appear in the smaller area below the single-file profile curve for /c = 1.27 x 10 in Fig. 5, in comparison to the area under the profile resulting from the conditions of normal diffusion with the same Thiele modulus. By comparing single-file diffusion with ordinary diffusion the prevailing effect is clearly the dramatic enhancement of rintra and hence of the Thiele modulus, leading to a correspondingly dramatic reduction of the effectiveness factor. 

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