The geometry of a heterogeneous catalyst is a crucial parameter in determining its performance. Many cataiytic systems can be described well in terms of fractal geometry. Here we study the rate dependence of various operating conditions in diffusion-reaction processes occuring on fractal rough surfaces, such as catalyst supports, and fractal subsets such as steps and kinks that constitute the active sites in metal crystallites.
In a process of diffusion and reaction in a catalyst with external fractal surface, exposed to a fixed reactant concentration, the catalyst exhibits an increasingly larger area for faster reactions; the overall rate scales as k@&)@-Dt)n
, where k is the first-order reaction rate constant and Ds is the diffusivity in the solid. A subfractal, like a Cantor Set, to which molecules diffuse through a stagnant fluid layer of thickness 6 and react instantaneously with the catalytic set, exhibits an overall rate that scales like 6-Dt ; i.e., this subset is less sensitive to mass transfer resistance than a smooth surface.With finite k, the inverse overall rate can be approximated as the sum of the inverse rates at the two asymptotes of very slow and very fast reactions. A fractai line exposed to a fixed reactant concentration at its enveloping boundary, represents a pore network which is an optimal configuration since porosity is higher at the larger pores.