Reaction engineering principles of processes catalyzed by fractal solids

Moshe Sheintuch*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


Fractals are fascinating objects that can serve as good models for highly porous materials or for materials of high surface areas, and several models of aggregation, leading to fractal objects, resemble the preparation methods of certain classes of catalysts. Evidence of fractal scaling in catalysts has been accumulating for the past two decades. This review focuses on processes that occur on or within fractal porous objects and addresses such issues as the scaling properties of such processes and their superiority over processes in random or nonfractal media. A plethora of reaction engineering problems has been studied. Fractal structures induce unique scaling properties: Diffusion on a fractal media is anomalous and has been extensively investigated; although it may have implications for certain problems of adsorption, surface diffusion, and reaction, and several continuum models for describing it were suggested, it probably does not describe reaction and pore diffusion in a porous pellet. Anomalous temporal or parameter scaling was shown to describe processes of diffusion toward a reactive or adsorbing corrugated fractal surface and, typically, a multifractal description is necessary to characterize the data. Fractional temporal scaling describes the adsorption process from a closed volume. Fractional scaling with respect to the thickness of a stagnant film was derived for instantaneous reaction limited by diffusion through such a film. Fractional scaling with respect to the rate constant (k) was shown to apply for several processes of moderate reaction velocities, such as diffusion toward a diffusion-limited aggregate. Etching of surface and mass fractals also exhibit fractional temporal scaling. Diffusion and reaction in a self-similar pore-fractal network exhibit a new intermediate asymptote, in which the rate is only weakly dependent on k, which lies between the known kinetics-limited (rate ∼ k) and diffusion-limited (k1/2) asymptotes. Within this domain, the selectivity to an undesired slow side reaction, in a system of two parallel reactions, can be suppressed significantly when its order is higher than that of the main fast reaction. These results may have several technical implications. Fractal surface catalysts may be less or more sensitive to changes in the operating conditions than nonfractal surfaces. Reduced sensitivity to increasing rate constant is achieved, for example, in a corrugated fractal catalyst exposed to a fixed reaction concentration. Comparison of the rates in a pore-fractal catalyst with those in a uniform-pore object showed that the rate in the former is superior in the intermediate k-insensitive domain. Selectivities in a system of two parallel reactions may also be better in the pore fractal as described earlier. Also, the apparent rate of deactivation, when it is a uniform process, can also be suppressed. Future theoretical work should test the validity of these conclusions in stochastic three-dimensional fractals. Experimental verification is still lacking; the superiority of pore fractals for several processes of diffusion and reaction should serve as an incentive for well-designed experiments.

Original languageEnglish
Pages (from-to)233-289
Number of pages57
JournalCatalysis Reviews - Science and Engineering
Issue number3
StatePublished - 2001
Externally publishedYes


  • Catalysis
  • Fractals
  • Reaction engineering


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