SCALING APPROACH TO STUDY DIFFUSION AND REACTION PROCESSES ON FRACTAL CATALYSTS

We use simple scaling arguments to predict the behaviour of diffusion and reaction processes taking place in a porous fractal object, modelled by a fractal surface, or over isolated catalyst crystallite, using a fractal subset to represent the distribution of active sites. These scalings are tested then by exact numerical simulations. The analysed processes and scaling are: (a) In a process of reaction and diffusion inside a catalyst with fractal external surface exposed to a fixed reactant concentration the overall reaction rate scales as k(D/k)(d-D(f))/2, where D is the diffusion coefficient, k is the rate constant of a first-order reaction and d is the dimension of the embedding Euclidean space. (b) In a process of diffusion from the bulk, through a stagnant film, towards a fractal surface over which an instantaneous reaction occurs, the overall rate scales as delta-D(f), where D(f) is the surface fractal dimension and delta is the film thickness. This holds for a fractal rough surface as modelled by the Koch curve (D(f) > 1) or for a fractal subset as modelled by the Cantor set (CS). (c) In a process of adsorption on the gaps of a Cantor set (CS) and surface diffusion towards the CS points where instantaneous reaction occurs the rate scales as k(a)(D(s)/k(a))(1-D(f))/2, where D(s) is the surface diffusion coefficient and k(a) is the adsorption constant.