Chronoamperometry for reversible charge transfers at cylindrical wire electrodes: Theory for DO ≠ DR, and a highly accurate computation of the current

Semi-analytical modelling of transient experiments at cylindrical wire or fiber electrodes is hindered by the unavailability of numerical procedures for calculating special functions arising in the models. A theory is developed, of the chronoamperometric Faradaic current for a reversible charge transfer reaction at a cylindrical electrode. Arbitrary potential steps and unequal diffusion coefficients (delta = D-O/D-R not equal 1) are assumed. Two procedures (written in C++) are designed, for computing a special function occurring in the theory. One procedure is computationally inexpensive, but has a low accuracy (relative error moduli close to 2% in the worst case, when -0.5 <= log (delta) <= 0.5). The second is more expensive, but highly accurate (relative error moduli close to 4 x 10(-14) in the worst case, when -3 <= log (delta) <= 3). Numerical experiments demonstrate that the effect of delta not equal 1 on the current is not negligible, even for delta not much different from unity. Therefore, the theory presented should be taken into account in experimental investigations. The code for the procedures is freely available.

Automated summary

The study develops a theory on chronoamperometric Faradaic current at cylindrical electrodes, with two procedures designed to compute special functions in the theory. Numerical experiments show that the effect of unequal diffusion coefficients on the current is significant, even when the difference is small.