Colloidal catalysis. Transport versus surface control

Abstract

It has been shown that the flux of material diffusing to the surface of a colloidal particle is greater than to a plane surface of the same area and diffusion layer thickness (δ). Around a small sphere of radius R the effective Nernst layer thickness δ_eff is given by 1//_{δeff =1//R +1//δ . The dependence of δ on radius was established by applying the hydrodynamic theory of Acrivos and Taylor at both large and small Péclet numbers, with a graphical treatment for the intermediate range. At very small radii δ was found to be proportional to R^7/6 and at large radii to R^3/2. It follows that the total flux or mass flow varies inversely with R^2+α(0 ⩽α < 0.17) over the whole range. These findings were applied to redox reactions heterogeneously catalysed at a colloidal metal surface, and equations were derived for surface control, transport control, and mixed surface and transport control. These suggest that plots of 1/RVcat against R should generally be linear, where Vcat is the catalytic rate. This was confirmed by literature data for the reaction between hydrogen ions and methyl viologen radical cations catalysed by platinum and gold sols.}