Levich rotating disc electrode

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 ... 

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. 

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. 

In many respects, similar to the diffusion layer concept, there is that of the hydrodynamic boundary layer, <5H. The concept was due originally to Prandtl [16] and is defined as the region within which all velocity gradients occur. In practice, there has to be a compromise since all flow functions tend to asymptotic limits at infinite distance this is, to some extent, subjective. Thus for the rotating disc electrode, Levich [3] defines 5H as the distance where the radial and tangential velocity components are within 5% of their bulk values, whereas Riddiford [7] takes a figure of 10% (see below). It has been shown that... 

The development of convective-diffusion theories is due principally to Prandtl9 and Schlichting10, and their application in electrochemistry to Levich11. Levich was the first to solve the equations for the rotating disc electrode. 

Miller and Bruckenstein [27,28] introduced the hydrodynamically modulated rotating disc electrode (HMRDE) in 1974. The steady-state current density at a rotating disc electrode is well-defined, given by the Levich equation (equation (10.15)) ... 

The elimination of transport effects is not so readily achieved. One relatively simple procedure is to measure currents (/m) as a function of electrode angular velocity (co) using a rotating disc electrode. Currents free of diffusive transport effects (/k) can then be obtained by application of the Koutecky-Levich equation,... 

As already mentioned before, the diffusion of the redox species can be enhanced by disturbing the solution. The most well-defined mass transport is obtained by using a rotating disc electrode as described in Section 4.2.3). As derived at first by Levich, the... 

The limiting current, iL, of the rotating disc electrode is given by the Levich equation [1]... 

The contribution of diffusion overpotential to the total overpotential can be achieved by an increase of convection near the electrode surface. In a very controlled manner this is possible with the rotating disc electrode. In the Koutecky—Levich equation the separation of diffusion contributions and charge transfer contributions to the overpotential was achieved. A general charge transfer reaction with exchange of n electrons was chosen. The Koutecky-Levich equation is... 

The rotating disc electrode can be used for kinetic studies. A deviation of a plot j vs uh from a straight line that intersects the origin suggests a slow kinetic step. In this casecan be plotted against and is known as the Koutecky—Levich plot. This plot should be linear and can be extrapolated to t r -> = 0 ... 

The theoretical description of electrocatalysis that takes into account electron and ion transfer and the transport process, the permeations of the substrates, and their combined involvement in the control over the overall kinetics has been elaborated by Albeiy and Hillman [312,313,373] and by Andrieux and Saveant [315], and a good summary can be found in [314]. Practically all of the possible cases have been considered, including Michaelis-Menten kinetics for enzyme catalysis. Inhibition, saturation, complex mediation, etc., have also been treated. The different situations have also been represented in diagrams. Based on the theoretical models, the respective forms of the Koutecky-Levich eqrration have been obtained, which make analyzing the resirlts of voltarrrmetry on stationary artd rotating disc electrodes a straightforward task. 

Mass transport towards a rotating disc electrode wherein the electrode with radius r is embedded in insulating material in the front of a rotating cylinder has been mathematically described first by Levich [7] (see also [8, 9]) (Fig. 1). 

Fig. 5. Current voltage curves for the reduction of N2O on a silver rotating disc electrode. The limiting currents obey the Levich equation.

The Levich equation for the transport-limited current, Fiim, at a rotating disc electrode is given by... 

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. 

Disc electrodes are commonly used in voltammetry as stationary and as rotating electrodes. The diffusion of electroactive species towards the surface of these electrodes is linear, as shown in Fig. 1.6a. The advantage of the second configuration is that rotation of the electrode causes convection in solution that compensates for the increase of the diffusion layer thickness with time after a period of about 200 ms. This results in a limiting current instead of a peak-shaped current (see also section 3.2) according to the Levich equation3 ... 

Up until the mid-1940s, most physical electrochemistry was based around the dropping mercury electrode. However, in 1942, Levich showed that rotating a disc-shaped electrode in a liquid renders it uniformly accessible to diffusion, yet the hydrodynamics of the liquid flow are soluble and the kinetic equations relatively simple. In addition, in contrast to the case of a stationary planar electrode, the current at an RDE rapidly attains a steady-state value. 

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