Electrodes hydrodynamic

7 Hydrodynamic electrodes in the investigation of coupled homogeneous reactions 

Hydrodynamic electrodes1 are electrodes which function in a regime of forced convection. The advantage of these electrodes is increased transport of electroactive species to the electrode, leading to higher currents and thence a greater sensitivity and reproducibility. Most of the applications of these electrodes are in steady-state conditions, i.e. constant forced convection and constant applied potential or current. In this case dc/dt = 0, which simplifies the solution of the convective diffusion equation (Section 5.6) 

Even when dc/dt= 0, i.e. in applications of these electrodes in combination with transient techniques, forced convection is useful at the very least for improving the reproducibility of the results, owing to the weak dependence of the electrode response on the physical properties of the solution, such as viscosity (Section 8.8). 

The method of resolution of (8.1) was indicated in Sections 5.7-5.9, showing as an example the calculation of the limiting current at the rotating disc electrode. In this chapter we discuss this and other hydrodynamic electrodes used in the study of electrode processes. The rotating disc electrode has probably been the hydrodynamic electrode 

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Similarly to the response at hydrodynamic electrodes, linear and cyclic potential sweeps for simple electrode reactions will yield steady-state voltammograms with forward and reverse scans retracing one another, provided the scan rate is slow enough to maintain the steady state [28, 35, 36, 37 and 38]. The limiting current will be detemiined by the slowest step in the overall process, but if the kinetics are fast, then the current will be under diffusion control and hence obey the above equation for a disc. The slope of the wave in the absence of IR drop will, once again, depend on the degree of reversibility of the electrode process. 

In an alternative design, the actual tip of the ultrasonic hom may be used as the working electrode after insertion of an isolated metal disc [77, 78 and 79]. With this electrode, known as the sonotrode, very high limiting currents are obtained at comparatively low ultrasound intensities, and diflflision layers of less than 1 pm have been reported. Furdiemiore, the magniPide of the limiting currents has been found to be proportional to D, enabling a parallel to be drawn with hydrodynamic electrodes. 

At the beginning of Section 3.3 a distinction was made between voltammetric techniques with non-stationary and stationary electrodes the first group consists of voltammetry at the dme or polarography, already treated, and voltammetry at hydrodynamic electrodes, a later subject in this section however, we shall now first consider voltammetry at stationary electrodes, where it is of significance to state whether and when the analyte is stirred. 

If during measurement in the stripping step the electrode is rotated, in principle we have to deal with a hydrodynamic electrode (see Section 3.3.2.2), but in practice it is useful to treat their application in SV in this section. 

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... 

Voltammetry at other hydrodynamic electrodes The particular features of this technique are (a) plate, conical and tubular electrodes in contact with the flowing solutions and (b) vibrating dme and streaming mercury electrodes. 

Finally, hydrodynamic electrodes remain of much interest especially in continuous analysis the equations concerned, although complex, show that the ix values are linearly proportional to the analyte concentration. 

Substrate orientation should be examined to determine if some planes are preferentially etched. If there is preferential etching taking place, what is its dependence on the etching cycle conditions The hardware being used for these studies should also be investigated. Very little has been done to optimize the flow cell. It is anticipated that a hydrodynamic electrode system such as a rotating disk or wall jet should work as well. 

We will note how the shadow is in a state of continual movement. The patterns are caused by eddy currents around the heater as the air warms and then rises. After just a quick glance, it s clear that the movement of the warmed air is essentially random. By extension, we see that, as an electroanalytical tool, electrode heating is not a good form of convection, because of this randomness. Conversely, a hydrodynamic electrode gives a more precisely controlled flow of solution. In consequence, the rate of mass transport is both reproducible and predictable. 

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. 

Why are hydrodynamic electrodes employed at all if there are possible problems with the maximum current densities ... 

Levich, V. G., Physicochemical Hydrodynamics, Prentice Hall, Englewood Cliffs, NJ, USA 1962. Levich s book is the text on hydrodynamic electrodes. Although not at all up-to-date, most of the principles described are timeless. The text is quite mathematical, and somewhat fearsome-looking for the uninitiated, but is nevertheless an excellent and reliable reference source. 

Brett, C. M. A. and Brett A. M. C. F. O., Hydrodynamic Electrodes , in Comprehensive Chemical Kinetics, Vol. 27, Bamford, C. H. and Compton R. G. (Eds), Elsevier, Amsterdam, 1986, pp. 355-441. This monograph provides a thorough and useful introduction to the topics of mass transport and convection-based electrodes. It also contains one of the better discussions on flow systems, in part because it can be read quite easily despite the overall treatment being so overtly mathematical. 

Solid electrodes, including metals and semiconductors, have attracted attention since the 1950s and extensive research has been done by Vetter, Gerischer, Bockris, Conway, Parsons, Yeager, etc. The development of hydrodynamic electrodes other than the DME in the late fifties and sixties... 

As is thoroughly discussed in Chap. 2 of this volume, the convective diffusion conditions can be controlled under steady state conditions by use of hydrodynamic electrodes such as the rotating disc electrode (RDE), the wall-jet electrode, etc. In these cases, steady state convective diffusion is attained, becomes independent of time, and solution of the convective-diffusion differential equation for the particular electrochemical problem permits separation of transport and kinetics from the experimental data. 

Since kd can be computed for a particular hydrodynamic electrode, the standard rate coefficient, k°, can be obtained. 

In electrode kinetics, however, the charge transfer rate coefficient can be externally varied over many orders of magnitude through the electrode potential and kd can be controlled by means of hydrodynamic electrodes so separation of /eapp and kd can be achieved. Experiments under high mass transport rate at electrodes are the analogous to relaxation methods such as the stop flow method for the study of reactions in solution. 

The first hydrodynamic electrode to be invented was the dropping mercury electrode [1]. It has a cyclic operation and can thus be considered only as quasi-steady-state its hydrodynamic character derives from drop growth. The principal advantage of a dropping electrode is that a fresh electrode surface is constantly exposed to the solution however, there are few electrode materials available and mathematical solution of the mass transport to the drop surface is complicated by the fact that the surface is expanding. 

The development of solid hydrodynamic electrodes, which have the advantage of fixed area and a wide range of available electrode materials, occurred rather later. This was due mainly to the lack of a theoretical description of the mass transport. Levich s work on mass transfer to electrodes, which was largely unknown to the non-Russian-speaking world except for the occasional indication, e.g. ref. 2, only became widely available with the publication in 1962 of the English translation of Physicochemical Hydrodynamics [3]. This dealt with many... 

The goal of this chapter is to describe the application of hydrodynamic electrodes to the study of electrode kinetics and the kinetics of electrode and coupled homogeneous reactions. In order to do this, it is important to describe first the mass transport and how to fulfil experimentally the conditions described by the mass transport equations, i.e. electrode construction and operation. 

Combination of hydrodynamic electrodes and non-steady-state techniques, though more complex to analyse theoretically, is very powerful in its application with increased sensitivity. These more recent developments and their applications to electrochemical kinetics will be discussed. 

Table 1 shows the particular forms of the convective diffusion equation for different geometries. It is fortunate that, due to the symmetrical nature of hydrodynamic electrodes, some of these terms may be neglected. Also, the major part of investigations conducted are under conditions of steady-state flow where dc/dt = 0. The exception to this is, of course, the cyclic operation of the DME. 

There are other equivalent ways of solving eqn. (17) for example, by double integration [3]. However, as will be shown in following sections, the approach outlined above is particularly valuable as it may be applied directly to other hydrodynamic electrodes. 

Although it was the first hydrodynamic electrode to be invented, the mathematical solution of mass transport at the DME is complex owing to the fact that no genuine steady-state can be attained such that dc/dt =h 0... 

Diffusion-limited currents at hydrodynamic electrodes under laminar flow conditions3... 

A summary of limiting current expressions at many hydrodynamic electrodes is given in Table 3. 

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