Reaction engineering principles of processes catalyzed by fractal solids

Fractals are fascinating objects that can serve as good models for highly p orous materials or for materials of high surface areas, and several models of aggregation, leading to fractal objects, resemble the preparation method s of certain classes of catalysts. Evidence of fractal scaling in catalysts has been accumulating for the past two decades. This review focuses on pro cesses that occur on or within fractal porous objects and addresses such is sues as the scaling properties of such processes and their superiority over processes in random or nonfractal media. A plethora of reaction engineerin g 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, an d reaction, and several continuum models for describing it were suggested, it probably does not describe reaction and pore diffusion in a porous pelle t. 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 dat a. Fractional temporal scaling describes the adsorption process from a clos ed volume. Fractional scaling with respect to the thickness of a stagnant f ilm was derived for instantaneous reaction limited by diffusion through suc h a film. Fractional scaling with respect to the rate constant (k) was show n to apply for several processes of moderate reaction velocities. such as d iffusion 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. w hich lies between the known kinetics-limited (rate similar to k) and diffus ion-limited (k(1)/(2)) asymptotes. Within this domain, the selectivity to a n 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 cata lysts may be less or more sensitive to changes in the operating conditions than nonfractal surfaces. Reduced sensitivity to increasing rate constant i s achieved, for example, in a corrugated fractal catalyst exposed to a fixe d reaction concentration. Comparison of the rates in a pore-fractal catalys t 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 syst em of two parallel reactions may also be better in the pore fractal as desc ribed earlier. Also, the apparent rate of deactivation. when it is a unifor m process, can also be suppressed. Future theoretical work should test the validity of these conclusions in st ochastic three-dimensional fractals. Experimental verification is still lac king, the superiority of pore fractals for several processes of diffusion a nd reaction should serve as an incentive for well-designed experiments.