Cg. Phillips et Ha. Stone, THE STEADY-STATE CURRENT FOR A RING-LIKE MICROELECTRODE UNDER NON-DIFFUSION-CONTROLLED CONDITIONS, Journal of electroanalytical chemistry [1992], 396(1-2), 1995, pp. 277-283
The steady-state current for a 'ring-like' microelectrode is considere
d, when the electrode reaction rate is not sufficiently large that the
diffusion of the electroactive species is the rate-limiting transport
process. This regime is particularly relevant for micro-ring electrod
es (which the present formulation includes), because the criterion for
diffusion-limited transport is much more stringent for a thin micro-r
ing electrode than for a micro-disc of comparable size. First an appro
ximate solution is presented for the steady-state current for a ring-l
ike microelectrode, valid for any value of the electrode reaction rate
provided the ring is thin. For the special case of a thin, plane-moun
ted micro-ring electrode, numerical results are given and the surface
current density distribution is shown. In this case the total current
is found to be in close agreement with a semi-empirical approximation
due to A. Szabo (J. Phys. Chem., 91 (1987) 3108). A micro-ring electro
de with an arbitrary ratio of inner to outer radius is then considered
, and the steady-state current is calculated numerically as a function
of the electrode reaction rate for a range of geometries, extending f
rom a complete disc to a thin ring.