Effects of surface rates for the series reaction A→ B→ C on successive separated spherical sites

A steady - state series reaction A →B → C, consisting of a first reaction A →B on sphere 1 of radius a1 with first order kinetic rate constant kA and reactant diffusivity DA, followed by a second reaction B → C on sphere 2 of radius a2 with a first order kinetic rate constant kB and a B chemical species diffusivity DB, occurs on two discrete chemically active spheres a center - to – center distance d apart. The twin spherical harmonic expansion method with a Neumann iterative solution of the coefficient equations is used to generate a rigorous solution for the rate of series reaction in terms of an expansion in the inverse dimensionless center - to - center sphere separation d ̅(=d⁄((a_1+a_2 ))) up to the inverse thirteenth power. The expansion coefficients depend on three dimensionless parameters (γ,λ_A,λ_B), where the dimensionless inverse surface kinetic constants are λ_A=D_A⁄a_1 kA on sphere 1, λ_B=D_B⁄(a_2 k_B ) on the sphere 2, while the geometry enters as the radius ratio γ=a_1⁄a_2 . Using these results an equivalent site kinetic change is imposed, first to λ_Aon site 1, then to λ_Bon site 2, to determine which site is more influential for the overall series reaction rate. Effects of γ geometry modification at several fixed kinetic surface site rates are examined. When either one of reactive spheres is diffusion controlled, various levels of λ kinetic controls at the other site or γ site geometries are generated to study the effects of site kinetics or geometry control on the series reaction rate. As the “other site” reaction rate also increases toward diffusion control, inflection points are observed to develop as precursors to a local maximum on the series reaction rate versus sphere separation curves. An application to the isomerization of n-pentane is presented