Current Distribution on a Rotating Ring‐Disk Electrode below the Limiting Current

Abstract

Ring-disk electrodes have been used in the literature to simulate experimentally the nonuniform current distribution across a rotating disk electrode operated at a fraction of the limiting current. The analogy of a sectioned disk to a ring-disk electrode is difficult to substantiate since both the limiting current and primary current distributions are radically different. Thus a detailed knowledge of the distribution of current and concentrations is developed to compare rationally the differences in nonuniformity for the ring-disk and disk electrodes. Integral measures of the degree of departure from the limiting current and primary current distributions are developed and related to the measurement of throwing power.The ring-disk electrode system is one of the most convenient arrangements of two working electrodes in a common cell. The concentric, rotating electrode structure is relatively easy to fabricate and is available commercially. The device has drawn attention recently, as both the object of theoretical analysis and experimental applications. Bruckenstein and Miller (1) and Smyrl and Newman (4) have performed experiments with ring disks to assess the nonuniform current distribution on a disk electrode utilizing the sectionedelectrode approach. Miller and Bellavance (2) have reported a number of experiments with the system, including measurement of interrupter and steady-state resistances and interactive resistances between the ring and the disk. Smyrl and Newman (3, 4) have presented data for ring-disk electrodes operated at and below the limiting current, along with a detailed analysis demonstrating the limiting current calculations. The primary current distribution was recently computed by Miksis and Newman (5). The limiting current (4, 11) and the primary current (5) densities of a ring electrode are not uniform, so the current density on a ring operated at some fraction of the limiting current, where kinetics also must be taken into account, does not approach the uniform distribution (12) that prevails near the edge of a disk electrode as the fraction of the limiting current approaches unity. The current distribution across a ring-disk electrode tends to be more nonuniform than for an equivalent disk.Newman's (6) approach to the computation of the concentration and current density distributions across a rotating disk electrode has been applied successfully to a number of other electrode geometries (7-9, 24-26). Parrish and Newman (8) investigated the current distributions on two plane parallel electrodes in channel flow, the only application to two interactive working electrodes. The ring-disk geometry contains two working electrodes and can utilize a counierelectrode, which would be considered infinitely far from the working electrodes. The working electrodes interact through the potential distribution, which is described by an elliptic Laplacian equation giving global effects, and through the parabolic concentration boundarylayer equations which allow a downstream influence on the ring electrode by ...

Effect of Water and HF on the Distribution of Discharge Products at Li–O2 Battery Cathode

“…Actually, N k value of 0.47 was obtained experimentally in the O 2 saturated NBu 4 PF 6 DMSO solution at potentials more negative than 2.5 V, where O 2 − is generated with 100% current efficiency at the disk electrode. The smaller values of N k at potentials more positive than 2.5 V should be due to nonuniform current distribution at rotating disk electrode operated at a fraction of limiting current as theoretically explained by Newman et al 30 Potential dependence of N k in solution 4 is essentially the same to that in the O 2 saturated NBu 4 PF 6 DMSO solution up to 2.4 V, showing that the reduction products in solution 4 in this potential region are mainly soluble products such as O 2 − . Decrease of N k in more negative potential region coincided with the decrease of disk current, suggesting the deposition of insulating products on the disk electrode.…”

Ring Electrodes

“…The primary current distribution for a ring electrode can be easily computed following the method outlined by Miksis and Newman (15) for ring-disk electrodes. The technique involves the solution of Laplace's equation which Newman (16) reduced to an extremely useful (17) where ~o is the ohmic potential drop between the surface of the ring electrode and a large counterelectrode which is far enough away from the working electrode so that it does not influence the current distribution, i is the normal component of the current density, K is an elliptic integral of the first kind (18). The use of Eq.…”

“…[3] .) Equation [1] is also used to compute the variation in the ohmic drop extrapolated to the surface of the ring for nonuniform potential distributions, in the same manner as for ring disks (17).…”

“…An integral equation has proven useful for computing analytic and numerical results. The same equations and approach for the concentration boundary layers which were recently applied by Pierini and Newman (17) to ring-disk electrodes are used here for computing the surface concentration when ohmic effects and potential dependent kinetics are included. The results of Levich (3) Figure 3 shows limiting current distributions for rings of various thicknesses computed with Eq.…”

Characteristics of the dropping mercury electrode below the limiting current

“…(14). This gives With this growth rate, the governing equations (7) and (13) for the dropping~mercury electrode below the limiting current can be expressed in dimensionless form as In Eqs. (17) and (18).…”