Rotating-disc electrode rotation frequency

The last of these is the impedance which has been considered throughout this chapter. We now consider forced convection. For low frequencies the diffusion layer thickness due to the a.c. perturbation is similar to that of the d.c. diffusion layer in these cases convection effects will be apparent in the impedance expressions. For the rotating disc electrode these frequencies are lower than 40 Hz33. For higher frequencies where the two diffusion layers are of quite different thicknesses, the advantage of hydrodynamic electrodes is that transport is well defined with time, as occurs with linear sweep voltammetry. 

C60 has been used to produce solvent-cast and LB films with interesting photoelec-trochemical behavior. A study of solvent-cast films of C60 on Pt rotating disc electrodes (RDEs) under various illumination conditions was reported [284]. Iodide was used as the solution-phase rednctant. The open-circuit potential shifted by 74 mV per decade of illumination intensity from a continuous wave (cw) argon-ion laser. The photocurrent versus power was measured at -0.26 V under chopped illumination (14-Hz frequency, vs. SCE) up to 30 mW cm and was close to linear. The photoexcitation spectrum (photocurrent versus wavelength) was measured at 0.02 V (vs. SCE) from 400 to 800 mn and found to be... 

To appreciate that, experimentally, the best way to perform analyses at the rotated disc electrode (the most popular hydrodynamic electrode) is at a constant rotational frequency and with the face of the disc well below the surface of the liquid. 

Provided that the flow is laminar, and the counter electrode is larger than the working electrode, convective systems yield very reproducible currents. The limiting current at a rotated disc electrode (RDE) is directly proportional to the concentration of analyte, according to the Levich equation (equation (7.1)), where the latter also describes the proportionality between the limiting current and the square root of the angular frequency at which the RDE rotates. 

Another example for the HMRRD electrode is given in Fig. 9 for Fe in alkaline solutions [12, 27]. The square wave modulation of the rotation frequency co causes the simultaneous oscillation of the analytical ring currents. They are caused by species of the bulk solution. Additional spikes refer to corrosion products dissolved at the Fe disc. This is a consequence of the change of the Nemst diffusion layer due to the changes of co. This pumping effect leads to transient analytical ring currents. Besides qualitative information, also quantitative information on soluble corrosion products may be obtained. The size of the spikes is proportional to the dissolution rate at the disc, as has been shown by a close relation of experimental results and calculations [28-30]. As seen in Fig. 7, soluble Fe(II) species are formed in the po-... 

On a RDE, in the absence of a surface layer, the EHD impedance is a function of a single dimensionless frequency, pSc1/3. This means that if the viscosity of the medium directly above the surface of the electrode and the diffusion coefficient of the species of interest are independent of position away from the electrode, then the EHD impedance measured at different rotation frequencies reduces to a common curve when plotted as a function of p. In other words, there is a characteristic dimensionless diffusional relaxation time for the system, pD, strictly (pSc1/3)D, which is independent of the disc rotation frequency. However, if v or D vary with position (for example, as a consequence of the formation of a viscous boundary layer or the presence of a surface film), then, except under particular circumstances described below, reduction of the measured parameters to a common curve is not possible. Under these conditions pD is dependent upon the disc rotation frequency. The variation of the EHD impedance with as a function of p is therefore the diagnostic for... 

Altering the convective rate of transport, e.g. by changing the rotation frequency of a rotating-disc electrode. Experiments in which the convective rate of transport can be altered are known as hydrodynamic techniques. 

Working electrodes which have material reaching them by a form of forced convection are known as hydrodynamic electrodes. There is a wide range of hydrodynamic electrodes rotating-disc electrodes (Albery and Hitchman, 1971), in which the electrode rotates at a fixed frequency and sucks up material to its surface, and channel electrodes (Compton et al., 1993c), over which the electroactive species flows at a fixed volume flow rate, are the primary ones used in the work described in this review (Section 4). 

For details and an exact derivation of the reader is referred to ref. [13]. The derivation also shows that Z is in series with as shown in Fig. 4.13a. Typically, the Warburg impedance leads to a linear increase of Z with rising Z" and the slope is 45° as also shown in Fig, 4.13a. In this case, Z has been calculated assuming an infinite thickness of the diffusion layer. Any convection of the liquid limits the thickness of the diffusion layer. The latter is limited to a well defined value when a rotating disc electrode is used (see Section 4.2.3). In this case, the impedance spectrum is bent off at low frequencies as shown in Fig. 4.13b. The Z branch i.s only linear at its high frequency end where it shows a slope of 45°. 

Fig. 5. Analysis of the experimental steady-state current—potential and impedance-potential data from E = — 650 mV to E = —150 mV for a titanium rotating-disc electrode (45 Hz) in a solution of 3.0 M sulphuric acid at 65°C. (a) Steady state current-potential curve. The potentials are the measured potentials, (b) High-frequency double layer capacity-potential curve. The potentials are the measured potentials.

Fig. 6. Analysis of the experimental steady-state current-potential and impedance-potential data from E = -1300 mV to E = -600 mV for a titanium rotating-disc electrode (45 Hz) in a solution of 2 M perchloric acid, (a) Standard rate constant-potential curve calculated for the hydrogen evolution reaction on titanium assuming that DA = 7.5 x 10-5cm s and E° = —246 mV. The Tafel slope bc = 120 mV and the measured ohmic resistance was 0.3 ohm cm2. The potentials are the "true potentials, (b) Standard rate constant-potential curve calculated for the hydrogen evolution reaction on titanium assuming that DA = 7.5 x 10-5 cms-1 and E° = — 246mV. The Tafel slope bc = 211 mV and the measured ohmic resistance was 0.3 ohm cm2. The potentials are the "true potentials, (c) High-frequency double layer capacity-potential curve obtained from the impedance data. The potentials are the measured potentials.

Figure 5.23 Dependence of the limiting current on the square root of the rotation frequency (rotation per s) on a rotating-disc electrode.

An example is shown in Figure 6.16. The reciprocal current is plotted versus the reciprocal value of the rotation frequency of a rotating disc electrode. The currents taken from the extrapolation to 1/Vf = 0 (rotation frequency/ = 00) are represented versus the potential in Figure 6.17. The current-potential plot shows a current-potential curve in the sub-Tafel region. An approximate current-potential line is shown in Figure 6.17. An approximate value of the charge transfer resistance and of the exchange current density... 

Alternating current polarographic (ACP) limits are set by the frequencies generally applied (f= 10-2000 Hz). Similarly, the limitations of the rotating disc electrode (RDE) are given by the angular rotation rates (6-6000 rad s" ). The slowest chemical reactions may be followed in coulometric analysis (cf. subsection 6.1) lasting usually 10 min and... 

The experimental cell is controlled by a potentiostat/galvanostat, which is also coupled with a frequency response analyzer for EIS measurements. The potentiostat (connected to a computer) measures the WE potential ( ) with respect to the RE, and the current (/) through the CE. The resistor (> 1 Gf2) is internal to the potentiostat and prevents current flow in the RE. The electrochemical cell shown in Figure 3.4(a) can also be used with rotating disc electrodes (RDEs), with the addition of an RDE rotor/controUer. RDE-based experiments do not necessarily mimic the hydrodynamic conditions of CMP, because the fluid velocity prohle at the surface of an RDE (Bard, 2001) is different from that expected for a CMP pad (Thakurta et al., 2002). Nevertheless, certain details of the CMP-related reaction kinetics and the effects of convective mass transfer on such reactions can be examined using RDEs. 

F. Huet, M. Keddam, X. R. Novoa, and H. Takenouti, Frequency and time resolved measurements at rotating ring-disc electrodes for studying localized corrosion,... 

In the model developed, the rates of mass-transfer processes are described in terms of the rotation frequency of a RDE. Under the conditions in which the experiments were performed the electrolyte flow at the surface of the magnetite disc electrode is laminar. Consequently, the quantitative treatment of the mass-transfer process would have to be modified in order use the model to predict the rate of magnetite dissoiution from pipe wails subject to turbulent flow. 

Fig. 8 (a) Rotating ring disc electrode electrode/solution interface at an angular frequency of ca and (b) RDE set-up (Pine Instruments) the RDE is connected to a motor controller that controls the angular velocity of the disc. 

Fig. 9. Polarization curve of an Fe-disc Pt-split-ring electrode with hydrodynamic square wave modulation. In 1 M NaOH with anodic and cathodic scan including capacity of the Fe disc (dashed curve), modulation frequency of rotation co = 0.05 Hz (insert), simultaneous detection of Fe(II) and Fe(III) ions at Pt half rings [12].

This is the same asymptotic modulation frequency dependence as for a small element of a channel electrode, and arises because the concentration boundary layer is the same thickness over the whole of the rotating disc. 

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