Cg. Phillips et Ha. Stone, THEORETICAL CALCULATION OF COLLECTION EFFICIENCIES FOR COLLECTOR-GENERATOR MICROELECTRODE SYSTEMS, Journal of electroanalytical chemistry [1992], 437(1-2), 1997, pp. 157-165
Steady-state mass transport is considered in a 'collector-generator' s
ystem of microelectrodes, in which an electroactive species is generat
ed at the surface of one microelectrode (the 'generator') and is trans
ported by diffusion to the surface of another (the 'collector'), where
it reacts. Following its generation, the species may also be consumed
by a homogeneous first-order reaction. Using a form of Green's theore
m, the total current at the collector is obtained as an integral over
the surface of the generator, in which the integrand contains the surf
ace current density, multiplied by a weighting function that can be de
termined by solving a reaction-diffusion problem for the collector mic
roelectrode alone. Therefore, the collection efficiency may be calcula
ted without solving the detailed transport problem in the presence of
both microelectrodes. As an illustration of these ideas, the collectio
n efficiency is calculated numerically as a function of the rate const
ant of the homogeneous reaction, in the mathematically simplest case,
where the current density on the surface of the generator is uniform.
Three geometrical configurations are considered: (i) both collector an
d generator are circular disc microelectrodes of equal radii; (ii) the
collector is a disc and the generator a concentric thin ring and (iii
) the collector is a thin ring and the generator a concentric disc. Co
mparison with asymptotic approximations suggests that the collection e
fficiency is fairly insensitive to the distribution of current at the
generator. Similar results are therefore to be expected in the more ge
neral situation of a non-uniform current density at the generator. Thi
s remains true if generation is enhanced by species produced at the co
llector or by the homogeneous reaction. (C) 1997 Elsevier Science S.A.