Limiting current, rotating disk electrode

Derive the Levich equation for the limiting current at the rotating disk electrode [based on combining equations (4-4) and (1-12)]. 

Fig. 3. Steady state concentration profiles of catalyst and substrate species in the film and diffusion layer for for various cases of redox catalysis at polymer-modified electrodes. Explanation of layers see bottom case (S + E) f film d diffusion layer b bulk solution i, limiting current at the rotating disk electrode other symbols have the same meaning as in Fig. 2 (from ref.

Figure 3a is an illustration of the effect of surface overpotential on the limiting-current plateau, in the case of copper deposition from an acidified solution at a rotating-disk electrode. The solid curves are calculated limiting currents for various values of the exchange current density, expressed as ratios to the limiting-current density. Here the surface overpotential is related to the current density by the Erdey Gruz-Volmer-Butler equation (V4) ... 

Mass-transfer rates from limiting-current measurements in well-supported solutions should invariably be correlated with ionic and not with molecular diffusivities. The former can be calculated from limiting-current measurements, for example, at a rotating-disk electrode. 

This value is based on Cu2+ diffusivities calculated Arvia et al. (A5) from limiting-current measurements at a rotating-disk electrode by, with CuS04 concentrations below 0.1 M. In practical applications (e.g., copper refining or electrowinning) higher Cu2+ concentrations are often required, as is also the case in free-convection limiting-current measurements. 

Experimental results obtained at a rotating-disk electrode by Selman and Tobias (S10) indicate that this order-of-magnitude difference in the time of approach to the limiting current, between linear current increases, on the one hand, and the concentration-step method, on the other, is a general feature of forced-convection mass transfer. In these experiments the limiting current of ferricyanide reduction was generated by current ramps, as well as by potential scans. The apparent limiting current was taken to be the current value at the inflection point in the current-potential curve. 

Fig. 9. Logarithmic plot of apparent limiting-current density as a function of current increase rate at a rotating-disk electrode i — apparent limiting current density i, = true steady-state limiting current density di/dt = current increase rate (A cm-2 sec-1) (u = rotation rate (rad sec-1). [From Selman and Tobias (S10).]...

In a detailed rotating-disk electrode study of the characteristic currents were found to be under mixed control, showing kinetic as well as diffusional limitations [Ha3]. While for low HF concentrations (<1 M) kinetic limitations dominate, the regime of high HF concentrations (> 1 M) the currents become mainly diffusion controlled. However, none of the relevant currents (J1 to J4) obeys the Levich equation for any values of cF and pH studied [Etl, Ha3]. According to the Levich equation the electrochemical current at a rotating disk electrode is proportional to the square root of the rotation speed [Le6], Only for HF concentrations below 1 mol 1 1 and a fixed anodic potential of 2.2 V versus SCE the traditional Levich behavior has been reported [Cal 3]. 

A graphite rotating disk electrode maintained at 0.5 V is used to monitor the reaction of Ru(NHj)5 as it is being oxidized by Oj to RulNKj) . The limiting current is proportional to [RufNHj) ] and there is no interference by O2 or the product. The electrode is rotated at 3600 rpm to ensure rapid mixing of reactants within seconds, since reaction times are 20-30 s. See Ref. 333. Square-wave amperometry has been linked to stopped-flow to measure reaction half-lives as short as 5 ms. 

Using the rotating disk electrode, Seliv-anov et al. [214] have investigated the zinc electrodeposition from zincate electrolyte containing polyethylene polyamine. The limiting current density of [Zn(OH)4] ion diffusion through a film of zinc oxides and hydroxides is shown to be responsible for the formation of dark zinc deposits in the potential range from —1.33 to —1.47 V. 

Influence of Rotating Disk Electrode Condition (Stationary or Rotating) on the Diffusion-Layer Thickness and the Limiting Current Density for the Reaction... 

Fig. 8.3. ATafel line. No special effort is made to reduce the limiting current density in case 1 and the Tafel line has a relatively small range, e.g., only 102 times in current density. In case 2, a rotating disk electrode is used to cause an increased limiting current density, and hence a larger range (say, 104 times) of current density.

A rotating disk electrode (RDE) [7] is used to study electrode reactions, because the mass transfer to and from the electrode can be treated theoretically by hydrodynamics. At the RDE, the solution flows toward the electrode surface as shown in Fig. 5.22, bringing the substances dissolved in it. The current-potential curve at the RDE is S-shaped and has a potential-independent limiting current region, as in Fig. 5.6. The limiting current (A) is expressed by Eq. (5.33), if it is controlled by mass transfer ... 

Since the limiting current is proportional to concentration, a rotating-disk electrode can be used for analytical purposes (but almost never is in practice). In summary, the rotating disk electrode is one of the valuable techniques available for the fundamental study of electrode reactions as evidenced by its substantial popularity. 

The first voltammetric methods met are stationary voltammetries performed on a dropping mercury electrode (polarography) or on a solid rotating disk electrode. The limiting current measured is directly proportional to the concentration of the electroactive species in the solution. Experimental potential scan rate is lower than lOrnVs-1. 

The measurement of a molecular diffusion coefficient D by electrochemical techniques is generally done with a rotating disk electrode in the limiting diffusion current condition and application of the Levich s equation [8]. 

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