Convection Hydrodynamic electrodes

The fundamentals of the electrochemical response at electrodes operating in a regime of forced convection, hydrodynamic electrodes, and the information that can be obtained have been reviewed [23, 24]. Some of these electrodes are good candidates for direct introduction into flow systems, in particular tube/channel electrodes and impinging jet (wall-jet and wall-tube) electrodes. Particular practical advantages of these flow-past hydrodynamic electrodes are that there is no reagent depletion while the sample plug passes the electrodes, and there is no build-up of unwanted intermediates or products. Recent advances in instrumentation also mean... 

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. 

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. 

Lionbashevski et al. (2007) proposed a quantitative model that accounts for the magnetic held effect on electrochemical reactions at planar electrode surfaces, with the uniform or nonuniform held being perpendicular to the surface. The model couples the thickness of the diffusion boundary layer, resulting from the electrochemical process, with the convective hydrodynamic flow of the solution at the electrode interface induced by the magnetic held as a result of the magnetic force action. The model can serve as a background for future development of the problem. 

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. 

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. 

Hydrodynamic modulation has been performed almost exclusively at the rotating disc electrode. It has found use for analytical purposes at rotating and tubular electrodes owing to the fact that non-convectively dependent electrode processes are unaffected by the modulation [236]. 

Chapter 1 serves as an introduction to both volumes and is a survey of the fundamental principles of electrode kinetics. Chapter 2 deals with mass transport — how material gets to and from an electrode. Chapter 3 provides a review of linear sweep and cyclic voltammetry which constitutes an extensively used experimental technique in the field. Chapter 4 discusses a.c. and pulse methods which are a rich source of electrochemical information. Finally, Chapter 5 discusses the use of electrodes in which there is forced convection, the so-called hydrodynamic electrodes . 

On one hand, mercury-film electrodes give increased resolution when compared to the hanging mercury drop electrode (HMDE). On the other hand, BCFMEs have the inherent characteristics of an ERD. Hence, it would be extremely desirable to combine all properties. Furthermore, this combination may provide additional advantages such as easy handling, low cost, and other well-known analytical advantages associated with the use of UMEs itself, for example, the elimination of convective hydrodynamics along the accumulation step in stripping voltammetric techniques. 

The second part of the book discusses ways in which information concerning electrode processes can be obtained experimentally, and the analysis of these results. Chapter 7 presents some of the important requirements in setting up electrochemical experiments. In Chapters 8—11, the theory and practice of different types of technique are presented hydrodynamic electrodes, using forced convection to increase mass transport and increase reproducibility linear sweep, step and pulse, and impedance methods respectively. Finally in Chapter 12, we give an idea of the vast range of surface analysis techniques that can be employed to aid in investigating electrode processes, some of which can be used in situ, together with photochemical effects on electrode reactions— photoelectrochemistry. 

As described in Chapter 5, forced convection leads to a thin layer of solution next to the electrode, within which it is assumed that only diffusion occurs (i.e. it is assumed that all concentration gradients occur within this layer)—the diffusion layer of thickness <5. At a particular point on a hydrodynamic electrode and for constant convection, 6 is constant. If the value of <5 is constant over the whole electrode surface then the electrode is uniformly accessible to electroactive species that arrive from bulk solution. 

Advantages of using hydrodynamic electrodes in linear sweep voltammetry are weak dependence on the physical properties of the electrolyte, suppression of natural convection, and the possibility of obtaining values of /p and /L in only one experiment. 

At a hydrodynamic electrode forced convection increases the transport of species to the electrode. However, the fraction of species converted is low. For example, for a ImM aqueous solution of volume 100 cm3 and a rotating disc of area 0.5 cm2 rotating at W = 4 Hz, the quantity electrolysed in 15 minutes is approximately 1 per cent. 

Electrochemical systems can be studied with methods based on impedance measurements. These methods involve the application of a small perturbation, whereas in the methods based on linear sweep or potential step the system is perturbed far from equilibrium. This small imposed perturbation can be of applied potential, of applied current or, with hydrodynamic electrodes, of convection rate. The fact that the perturbation is small brings advantages in terms of the solution of the relevant mathematical equations, since it is possible to use limiting forms of these equations, which are normally linear (e.g. the first term in the expansion of exponentials). 

Hydrodynamic electrodes permit the control of the diffusion layer thickness by imposing convection. This thickess can also be modulated. Implicit functions link the current, potential and convection modulation. For the rotating disc electrode... 

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. 

The theoretical solution to the equations for electrode processes nearly always has to involve approximations, not only for numerical but also for analytical solutions—such as, for example, the assumption that there is no convection within the diffusion layer of hydrodynamic electrodes. In other cases, of complex mechanism, it is not even possible to resolve the equations algebraically. There is another possibility for theoretical analysis, which is to simulate the electrode process digitally. 

See also -> convection, -> Grashof number, - Hagen-Poiseuille, -> hydrodynamic electrodes, -> laminar flow, - turbulent flow, -> Navier-Stokes equation, -> Nusselt number, -> Peclet number, -> Prandtl boundary layer, - Reynolds number, -> Stokes-Einstein equation, -> wall jet electrode. 

Hydrodynamic electrodes — are electrodes where a forced convection ensures a -> steady state -> mass transport to the electrode surface, and a -> finite diffusion (subentry of -> diffusion) regime applies. The most frequently used hydrodynamic electrodes are the -> rotating disk electrode, -> rotating ring disk electrode, -> wall-jet electrode, wall-tube electrode, channel electrode, etc. See also - flow-cells, -> hydrodynamic voltammetry, -> detectors. 

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). 

A reversible one-electron transfer process (19) is initially examined. For all forms of hydrodynamic electrode, material reaches the electrode via diffusion and convection. In the cases of the RDE and ChE under steady-state conditions, solutions to the mass transport equations are combined with the Nernst equation to obtain the reversible response shown in Fig. 26. A sigmoidal-shaped voltammogram is obtained, in contrast to the peak-shaped voltammetric response obtained in cyclic voltammetry. 

For hydrodynamic electrodes, in order to solve the convective-diffusion equation analytically for the steady-state limiting current, it is necessary to use a first-order approximation of the convection function(s) (such as the Leveque approximation for the channel). These approximate expressions for the steady-state mass transport limited currents were introduced in Section 4 (see Table 5). 

A characteristic of the primary distribution, in general, is that it is less uniform than the secondary distribution for a given electrode geometry and the electrochemical cell device. There is only one exception that arises from the concentric cylindrical electrode system depicted in Figure 13.2a, where both the primary and the secondary current distributions are uniform in the case of the forced convective hydrodynamics (rotating electrodes). 

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