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CORRESPONDENCE Comments on “Mechanism Discrimination in Heterogeneous Catalytic Reactions: Fractal Analysis” Baoquan Zhang* and Xiufeng Liu School of Chemical Engineering, Tianjin University, Tianjin 300072, People’s Republic of China
Sir: The paper published in Ind. Eng. Chem. Res. by Khorasheh et al.1 dealt with an application of fractal geometry to the mechanism discrimination of heterogeneous reactions over supported metal catalysts. The authors proposed two scaling equations for the singleand dual-site mechanisms of isomerization reaction and performed a two-dimensional computer simulation to verify the two relations. Although the simulation result agrees fairly well with the scaling equations as claimed in the paper, we do believe that the scaling relations themselves were developed on the basis of an inappropriate stand, leading one to further question the conclusions made in the paper. In addition, the authors did not mention some state-of-the-art results of the research related to this article. The relevant problems will be discussed next in detail one by one. On the Scaling Relations In the paper the two scaling equations, eqs 7 and 11, were derived in terms of a commonly used power law, eq 1, which was presented by Avnir and Pfeifer.2 Actually, the number of adsorbed molecules in eq 1, expressed by N, should be calculated in light of experimental data of physisorption if the power of the scaling relation is the fractal dimension of the whole inner surface for solid materials. Even though the method based on physisorption has some weaknesses caused by the effect of the interaction between adsorbed molecules and pore plugging,3,4 it is still a reliable method to determine surface fractality by now.5 The surface fractal dimension usually changes in the range 2 e DS < 3 under the restriction of fractal geometry. Furthermore, the number of adsorbed molecules in eqs 7 and 11, symbolized by NA‚M, is the numerical representation of chemisorption capacity because the chemisorption of reactants comes ahead of the surface reaction in the sequence of elementary steps. It is wellknown that physisorption and chemisorption substantially differ from each other in many properties. For example, physisorption happens at low temperature and the whole surface is accessible to any species available; on the contrary, the chemisorption only occurs at high temperature and the surface, commonly only part of the surface-catalytic sites, is accessible to specific species. So the two quantities, N and NA‚M, cannot be employed interchangeably. However, the two scaling relations in the paper were just obtained by substitution of N for NA‚M. * To whom correspondence should be addressed. Fax: +8622-27403144. E-mail:
[email protected].
The scaling relation for chemisorption describes the influence of the geometry of catalytic sites on the chemisorption capacity. The power of this scaling relation is the so-called chemisorption dimension D h which can take any value in the range 0 e D h < 3 and follow the order D h < DS. For instance, the results of H2 chemisorption on Pt dispersed over silica gel yield a dimension of D h )1.67 ( 0.05, much smaller than the surface fractal dimension of silica gel itself.4 Virtually, the power of the two scaling relations proposed in the paper ought to be D h instead of DS, as the reactant and product molecules can only be adsorbed on catalytic sites and the process temperature is relatively high to make the reaction possible by comparison with physisorption. Mercury Porosimetry Method for Determining Surface Fractal Dimension In addition to the adsorption method, there is another commonly used method based on PSD (pore-size distribution) analysis named the mercury porosimetry method.6-8 This method supplies deep insight of surface fractality in another way, and every so often the predicted results are more reasonable than those by the adsorption method for porous materials such as silica gels.8 However, it was so surprising that the authors did not even mention this method in the paper when they stated the existing methods for the determination of surface fractal dimension on p 362. Complicated Details on Fractal Application to Various Reacting Systems Carberry9 and Farin and Avnir10 introduced a scaling relation to reveal the influence of the geometry of catalytic sites on heterogeneous reactions over dispersed metal catalysts. In fact, the power of this scaling relation, named the reaction dimension, is a complex exponent that counts on more than just the geometry of catalytic sites.10 It would be the same as the chemisorption dimension for isomerization reactions if the geometry should be the sole factor affecting the reaction rate. But the fact is the reaction dimension ranges from 0.7 to 5.8 for various reacting systems investigated already by fitting experimental data.10,11 Some calculated results of the reaction dimension are selected and shown in Table 1. The performance of heterogeneous catalysis is governed by both the geometrical details of the surface and the physicochemical nature of the reacting system. The results of the reaction dimension in Table 1 evidently verify the above argument. The interplay between
10.1021/ie991070l CCC: $19.00 © 2000 American Chemical Society Published on Web 01/07/2000
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Table 1. Some Calculated Results of Reaction Dimension support
reaction
Al2O3 CO hydrogenation (DS ) 2.8-2.9) oxidation of methane SiO2 CO hydrogenation (DS ) 2.9-3.0) a
dispersed temp, metal K Ni Fe Pt Ru Pd Rh Pt Pd
548 513 548 523 673 773 548 523
DR, Ra 2.80, s 3.43, 0.90 1.74, 0.91 3.52, 0.95 4.24, 0.99 2.41, 0.95 1.74, 0.91 2.90, s
Correlation coefficient.
various factors, geometric and physicochemical, is so complicated that the subject needs to be explored further.11,12 The interaction between adsorbed molecules, and between adsorbed molecules and the surface, have a great effect on heterogeneous catalysis in most cases. Another influential factor is the so-called SMSI (strong metal-support interaction). The result of the reaction dimension for the same reaction and support but different dispersed metals, given in Table 1, illustrates the influence of the above factors.11 Besides, there is a strong dependency of activity on specific active sites for some heterogeneous catalytic reactions. Ammonia synthesis over the dispersed Fe/MgO catalyst is a typical example, for which the reaction dimension is 5.8, the biggest value of reaction dimension ever found.10 Strictly speaking, most of the actual heterogeneous reactions over dispersed metal catalysts cannot be represented by the Langmuir-Hinshelwood mechanism. Summary The power of the two scaling relations proposed in the paper should not be the fractal dimension of catalyst surface DS, but instead be the chemisorption dimension D h because the chemisorption of reactant molecules occurs before the surface reaction in the elementary steps. Both the reaction mechanism and the simulation were oversimplified which has little practical value because most of the actual heterogeneous reactions over dispersed metal catalysts, if not all, are governed by both geometrical and physiochemical details. And this over-
simplification may result in absurd conclusions such as the concluding remark “The geometry of a solid medium is a major parameter in determining the reaction rate in catalytic systems” made in the paper. The fractal application in chemical engineering is still immature. Critical discussion in the area is indeed necessary to make the best of this promising tool. The ultimate aim of this letter is just to do something to achieve the above goal. Acknowledgment The authors are greatly indebted to the State Key Laboratory of Chemical Engineering and National Natural Science Foundation of China for supporting the relevant work. Literature Cited (1) Khorasheh, F.; Radnabesh, R.; Kazemeini, M. Mechanism Discrimination in Heterogeneous Catalytic Reactions: Fractal Analysis. Ind. Eng. Chem. Res. 1998, 37, 362-366. (2) Avnir, D.; Farin, D.; Pfeifer, P. Molecular Fractal Surfaces. Nature 1984, 308, 261-163. (3) Klafter, J. Private communication, Dec 1995. (4) Rothschild, W. G. Fractals in Heterogeneous Catalysis. Catal. Rev.-Sci. Eng. 1991, 33, 71-107. (5) Avnir, D.; Farin, D.; Pfeifer, P. A Discussion of Some Aspects of Surface Fractality and of Its Determination. New J. Chem. 1992, 16, 439-449. (6) Friesen, W. I.; Mikula, R. J. Fractal Dimensions of Coal Particles. J. Colloid Interface Sci. 1987, 120, 263-271. (7) Neimark, A. V. Calculating Surface Fractal Dimension of Adsorbents. Adsorpt. Sci. Technol. 1990, 7, 210-219. (8) Zhang, B. Q.; Li, S. F. Determination of the Surface Fractal Dimension for Porous Media by Mercury Porosimetry. Ind. Eng. Chem. Res. 1995, 34, 1383-1386. (9) Carberry, J. J. Structure Sensitivity in Heterogeneous Catalysis: Activity and Yield/Selectivity. J. Catal. 1988, 114, 277283. (10) Farin, D.; Avnir, D. The Reaction Dimension in Catalysis on Dispersed Metals. J. Am. Chem. Soc. 1988, 110, 2039-2045. (11) Zhang, B. Q.; Liu, X. F.; Guo, H. Y. On Reaction Dimension of Heterogeneous Catalysis. In Proceedings of Asia-Pacific Chemical Reaction Engineering Symposium 99, Hong Kong University of Science and Technology, June 1999; pp 503-508. (12) Bennett, C. O.; Che, M. Some Geometric Aspects of Structure Sensitivity. J. Catal. 1989, 120, 293-302.
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