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/RV_cat against R should generally be linear, where V_cat 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.