Electrode rotating disc

The rotating disc electrode (RDE) is one of the most popular hydrodynamic electrodes due to its relatively easy fabrication, commercial availability and facile surface regeneration. Moreover, the corresponding simulation problem can be reduced to a single spatial dimension. 

Note that in the case of more complicated mechanisms, the corresponding kinetic terms must be added in Eq. (8.6) as studied in Chapters 5 and 6. The boundary value problem of the RDE problem is given by 

The above mathematical problem can be written in dimensionless form by defining the dimensionless variables  

Considering a uniform spatial grid with an interval AY, the spatial derivatives can be discretised as 

The RDE problem has been solved successfully making use of the explicit method [9]. Within this approach, according to Eq. (8.17) the concentration of species j at the point in solution i at the timestep k can be calculated directly from the previous profile, from 

The thickness of the diffusion layer on a rotating-disc electrode is given by the equation 

D is the diffusion coefficient, v = tj/p the kinematic viscosity, the ratio between viscosity and density, and co = 27i/the rotation velocity with /the rotation frequency. With typical values for the constants in Eq. (5.37) the thickness of the diffusion layer is of the order of 10 cm. 

Inserting Eq. (5.37) into Eq. (5.5) gives the equation for the current density on a rotating-disc electrode 

The equations derived for the rotating-disc electrode are limited for laminar flow. The Reynolds number was introduced as a measure for the transition to turbulent flow (Section 5.1). For the rotating disc the Reynolds number is given by the equation 

For a rotating-disc electrode with a radius r = 1 cm in an aqueous electrolyte (kinematic viscosity of water 0.01 cm s at 20 °C) the critical rotation rate is 10,000 rot min.  

The simplest and most commonly used convection apparatus consists of a disc electrode rotating with a constant angular velocity u [1-5]. The disc sucks the solution toward its surface, much in the way a propeller would as the solution approaches the disc, it is swept away radially and tangentially (see Fig. 14.1). The transport of the reacting species to the disc occurs both by convection and diffusion. Though the mathematics are complicated, the rate of transport can be calculated exactly for an infinite disc. A particularly nice feature of this setup is the fact that the transport is uniform so that the surface concentration of any reacting species is constant over the surface of the electrode. 

Right at the disc the convection current perpendicular to the surface vanishes. The transport to the surface is effected by diffusion so the particle current density jp of any species with concentration c and 

As mentioned above, on the disc this current is independent of position. It is useful to define a diffusion layer of thickness Sm through  

At a rotating disc the thickness of the diffusion layer decreases with increasing rotation rate according to  

Under steady-state conditions each molecule red transported to the surface is oxidized, and hence transformed to ox hence j/F  

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Platinum has also had its share of attention in recent years. The effect of phosphoric acid concentration on the oxygen evolution reaction kinetics at a platinum electrode using 0-7 m-17-5 m phosphoric acid at 25°C has been studied with a rotating disc electrode . The characteristics of the ORR are very dependent on phosphoric acid concentration and H2O2 is formed as an intermediate reaction. Also, platinum dissolution in concentrated phosphoric acid at 176 and 196°C at potentials up to 0-9 (SHE) has been reported . 

Polythiophene electrogeneration on a rotating disc electrode. The water content influence on polymerization and on the polymeric properties. J. Electroanal Chem., 310, 219, 1991, Fig. 9. Copyright 1991. Reprinted with permission of Elsevier Science.)... 

Beside laminar flow created by e.g. a rotating disc electrode mrbulent flow provides a means of artificially enhanced transport. A consistent mathematical description and analytical treatment of this mode of transportation is not possible. Various approximations have been proposed and tested for correctness [84Barl], an experimental setup has been described [78Ber, 83Her, 831wa]. From comparisons of measured and calculated current density vs. electrode potential relationships exchange current densities are available. (Data obtained with this method are labelled TPF.)... 

Ple Pleskov, Yu.V., Filinovskii V.Yu. The Rotating Disc Electrode, New York Consultants Bu-... 

It has been shown by employing the radioactive tracer method with C-labeled carboxylic acids [79] and with rotating disc electrode experiments [80] that carbo-xylates are adsorbed at the anode surface. 

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... 

Levich124 has given the relationships between the limiting current i) and the bulk concentration C of the metal ion for plate electrodes, conical electrodes and rotated disc electrodes (RDEs) under hydrodynamic conditions anticipating his well known equations treated in Section 3.3.2.2 on hydrodynamic electrodes, we may assume the relationships concerned using the more general equation... 

Here we have to deal with three types (see Fig. 3.68), viz. (a) the rotating disc electrode (RDE), and (b) the rotating ring electrode (RRE) and the rotating ring-disc electrode (RRDE). The construction of the latter types suits all purposes, i.e., if the disc or the ring is not included in the electric circuit, it yields an RRE or an RDE, respectively, and if not an RRDE, where either the disc forms the cathode and the ring the anode, or the reverse. 

Pleskov, Yu. V., and V. Yu. Filinovskii, The Rotating Disc Electrode, Consultants Bureau, New York, 1976. 

A simple example is the rotating disc electrode described in detail in chapter 2. The horizontal spinning disc draws liquid up and then flings it out sideways, creating a continuous but steady-state convection pattern. If the distance down from the disc is denoted by z and the distance across the disc surface by the radial distance, r, then it is not difficult to show that ... 

There arc many controllcd-convection techniques available but we will restrict our discussion to the two most commonly employed by the electrochemist the rotating disc electrode (RDE) and the rotating ring disc electrode (RRDE). 

Figure 2.89 The pattern of flow to a rotating disc electrode and across its surface, assuming...

Figure 2.91 Schematic representation of the rotating disc electrode response Tor the reduction and oxidation of a reversible couple. / = F/RT, /, is the limiting current, / is the current, E is the potential of the electrode and ° is the standard reduction potential of the couple.

Figure 14.1 Convection current at a rotating disc electrode.

In contrast to the rotating disc electrode, mass transport to the ring is nonuniform. Nevertheless, the thickness of the diffusion layer Spj, which depends on the coordinate x in the direction of flow, and the rate of mass transport can be calculated. We consider a simple redox reaction, and rewrite Eq. (14.5) in the form ... 

We note in passing that the same equation holds for the rotating disc electrode. Though the mass transport on the ring is nonuniform, the ratio ared/a0x) and hence also, turns out to be constant, so Eq. 

The rotating disc electrode is a classical method, and is covered well in a number of texts. Turbulent pipe flow, though faster, is less common. The article by Barz et al. [6] is a good review. 

Zutic, V., and W. Stumm (1984), "Effect of Organic Acids and Fluoride on the Dissolution Kinetics of Hydrous Alumina. A Model Study Using the Rotation Disc Electrode", Geochim. Cosmochim. Acta 48, 1493-1503. 

The convective diffusion theory was developed by V.G. Levich to solve specific problems in electrochemistry encountered with the rotating disc electrode. Later, he applied the classical concept of the boundary layer to a variety of practical tasks and challenges, such as particle-liquid hydrodynamics and liquid-gas interfacial problems. The conceptual transfer of the hydrodynamic boundary layer is applicable to the hydrodynamics of dissolving particles if the Peclet number (Pe) is greater than unity (Pe > 1) (9). The dimensionless Peclet number describes the relationship between convection and diffusion-driven mass transfer ... 

None of the set-ups discussed so far provides stirring of the electrolyte for bubble removal or for enhancement of the reaction rates. A standard set-up developed to study kinetic electrode processes is the rotating disc electrode [11]. The electrode is a small flat disc set in a vertical axle. The hydrodynamic flow pattern at the disc depends on rotation speed and can be calculated. An additional ring electrode set at a different potential provides information about reaction products such as, for example, hydrogen. However, because this set-up is designed to study kinetic processes and is usually equipped with a platinum disc, it becomes inconvenient if silicon samples of different geometries have to be mounted. 

To find that the limiting current at a rotated disc electrode (RDE) is directly proportional to the concentration of analyte, according to the Levich equation. 

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