Diffusion current at the tubular band electrode by the integral equation method

The integral equation method is used to compute the transient diffusion current at the tubular band electrode, a geometry consisting of a band electrode inlaid concentrically around the inside wall of an infinitely long insulating tube. When the ratio mu of diameter-to-width of the tubular band electrode is large (at least 100) the transient current closely resembles that obtained at the planar band electrode, with deviation becoming apparent only at very long time. For mu > 2 the edge effect enhancement of the diffusion current more than compensates for the depletion effect and the limiting current exceeds the Cottrell current at longer times, the net enhancement being proportional to mu. For mu < 2 depletion dominates and the limiting current falls below the Cottrell current, the transient behavior approaching that of the tubular electrode (where the entire tube is the electrode) as mu --> 0. At sufficiently long time, the transient current at each tubular band electrode geometry enters a second region of t(-1/2) dependence (i.e. a second Cottrell region), corresponding to complete depletion of the electroactive species within the solution space encompassed by the electrode and the resulting rectilinear diffusion of the species from each direction within the tube.