Rotating ring-disc electrode collection efficiency

The rotating ring—disc electrode (RRDE) is probably the most well-known and widely used double electrode. It was invented by Frumkin and Nekrasov [26] in 1959. The ring is concentric with the disc with an insulating gap between them. An approximate solution for the steady-state collection efficiency N0 was derived by Ivanov and Levich [27]. An exact analytical solution, making the assumption that radial diffusion can be neglected with respect to radial convection, was obtained by Albery and Bruckenstein [28, 29]. We follow a similar, but simplified, argument below. 

Compton and co-workers obtained values of the rate constant for the two-electron reduction of fluroescein at various pH values by ESR transients and electrochemical data. The dependence of the rate constant on pH is shown in Fig. 36 with data from collection efficiency experiments at a rotating ring-disc electrode. The application of electrochemical ESR clearly demonstrates the reduction mechanism to be DISP1. Electrochemical or ESR experiments alone could not make the ECE/DISP1 discrimination independently. 

As may be anticipated, the rotating ring-disc electrode may be more useful for the study of this reaction type. The ring should be set at the potential where the mass-transfer controlled back reaction B — A occurs. The deviation of the measured collection efficiency N = — Iring/ Idisc (cf. section 8.3 in chapter 2) from the value N found in the absence of the chemical step allows the rate constant kf to be determined. For electrode systems with very thin rings and small gaps a fairly simple equation has been suggested [60] ... 

Note that iL depends on Vf1/2 whereas, for the wall-jet electrode, it depends on Vf4. This equation only holds for 0.1 Mass transfer is more efficient than at an RDE however, the electrode has to be smaller. Nevertheless, in applications where it is difficult to fabricate a moving electrode (i.e. photoelectrochemical and semiconductor), it could be very valuable. From the theoretical point of view all that has to be done is replace by 0.98 Vf /r% in all the equations for a rotating disc or ring--disc electrode to obtain the wall-tube analogue. In particular, the steady-state collection efficiency, N0 [eqn. (41)], is the same not only in form but also in numerical value for the same radius ratios [50] (Table 2). 

The rotation of the system induces the laminar flow of the solution with the species produced at the disc along the electrode plane to the ring surrounding the disc. The collection efficiency in this system is defined by the ratio... 

Forced convection (hydrodynamic) generator - collector systems are commonly employed in rotating ring-disc or wall-jet geometries or in channel flow cells to improve collection efficiencies. For macroscopic interelectrode gap systems hydrodynamic agitation can be employed to improve feedback, but for diffusion - dominated nano-gap electrode systems hydrodynamic convection effects usually remain insignificant, whereas heating can be used to enhance the rate of diffusion processes and therefore to improve feedback currents. 

In reactions involving gas evolution, the RRDE can be problematic in that bubbles may become trapped at the centre of the disc electrode. To obviate this, a rotating double ring electrode was suggested [34], The collection efficiency, N0, is given by eqn. (41) if we define... 

If an unstable intermediate or product is formed at the disc, only a fraction will reach the ring, and the ratio i /i will be smaller than N. The extent by which the collection efficiency is decreased is a function of the rate of rotation. The dependence of N on to can be used to evaluate the lifetime (or rate of decomposition) of the unstable intermediate. As in any kinetic measurement of this type, one attempts to design the system for the fastest possible transition time from disc to ring, to allow detection of short-lived intermediates. The gap in commercial RRDEs is of the order of 0.01 cm, but electrodes with substantially narrower gaps have been built. We may be tempted to use modem techniques of microelectronics to construct an RRDE with a very small gap, say, 0.1 Xm. A closer examination of the hydrodynamics involved reveals that this may not work and, in fact, there is little or no advantage in reducing the gap below about 5 0.m. 

Oxygen is reduced at the rotating disc electrode and the potential of the concentric ring is set such that the oxidation of hydrogen peroxide is under mass transfer control. Plots are then made of the inverse of the observed collection efficiency versus the inverse of the square route of the rotation speed (in accordance with normal ROE theory). Linear plots are usually observed. Extrapolating to infinite rotation speed allows the prediction of the maximum possible collection efficiency. This is the maximum amount of hydrogen peroxide produced. In terms of the two possible reduction routes (equations 4 and 5 above) this gives the parameter x which is defined as. 

The crucial parameter for the rotating disc electrode is the collection efficiency N. This determines the fraction of stable product generated with 100% efficiency at the disc electrode that will be collected by the ring, under mass transport control, when there is a mass transport-limiting ring current. In general, under these conditions. 

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