The Reaction Dimension in Catalysis on Dispersed Metals

We report that the relation between catalytic activity, a (mol•time⁻¹ •particle⁻¹), and particle size, 2R, of dispersed catalysts obeys in very many cases the following scaling law: a α R^D_R,where D_R, the reaction dimension, is a characteristic parameter of the catalytic reaction which provides quantitative means of comparative evaluation of the degree of structure sensitivity. The observation crosses all catalysis. Examples include hydrogenations, hydrogenolyses, oxidations, isomerizations, and photochemical and electrochemical reactions. Catalysts include Pt, Pd, Ir, Ag, Rh, Fe, Ni, and bimetallic catalysts dispersed on SiO₂, A1₂O₃, TiO₂, MgO, and charcoals. A wide range of D_R values was found: from D_R = 0.2 for ethylene oxidation on Ag/SiO₂, indicating weak dependence of the activity on particle size and a very low proportion of reactive surface sites, through D_R ~ 2 cases indicating structure insensitivity, and up to D_R = 5.8 for ammonia synthesis on Fe/MgO, indicating extreme structure sensitivity. It is suggested that the activity power law reflects a parallel scaling relation in the population of reaction-specific active sites, i.e., that particle size change by a factor of N changes the number of sites by a factor of N^D_R. For D_R< 2 cases it is furthermore suggested that the pattern of distribution of active sites is invariant to the scale changes, i.e., that D_R is the fractal dimension of the reactive subset of surface atoms. Of the many cases presented, two are discussed in some detail, showing the following agreement between experimental drvalues and model-calculated D_R values (reaction: experimental D_R, model D_R)—ethylene oxidation on Ag/SiO₂ to CO₂: 0.71 ±0.16, 0.70 ± 0.04; and to ethylene oxide: 1.16 ± 0.11, 1.18 ± 0.03; methanation on Pd/Si0₂, 2.90 ± 0.15, 2.77 ± 0.09.