Cyclic mass transport

The great advantage of the RDE over other teclmiques, such as cyclic voltannnetry or potential-step, is the possibility of varying the rate of mass transport to the electrode surface over a large range and in a controlled way, without the need for rapid changes in electrode potential, which lead to double-layer charging current contributions. 

For quasi-reversible systems (with 10 1 > k" > 10 5 cm s1) the current is controlled by both the charge transfer and mass transport. The shape of the cyclic voltammogram is a function of k°/ JnaD (where a = nFv/RT). As k"/s/naD increases, the process approaches the reversible case. For small values of k°/+JnaD (i.e., at very fast i>) the system exhibits an irreversible behavior. Overall, the voltaimnograms of a quasi-reversible system are more drawn-out and exhibit a larger separation in peak potentials compared to those of a reversible system (Figure 2-5, curve B). 

Appropriate electroanalytical procedures to verify the one or other case have been given in the references of this section. The main techniques are cyclic voltammetry, chronoamperometry, chronocoulometry, and rotating disk voltammetry. The last one appears to be best suited since constant mass transport in the film is a very important feature as outlined aixive Table 2 gives examples for... 

Having defined our near electrode region, we turn now to consider the various techniques that can be employed in the in situ investigation of the reactions that occur within it. The various methods that can be employed will each provide different types of information on the processes occurring there. As has already been discussed, cyclic voltammetry is the most common technique first employed in the investigation of a new electrochemical system. However, in contrast to the LSV and CV of adsorbed species, the voltammetry of electroactivc species in solution is complicated by the presence of an additional factor in the rate, the mass transport of species to the electrode. Thus, it may be more useful to consider first the conceptually more simple chronoamperometry and chronocoulometry techniques, in order to gain an initial picture of the role of mass transport. 

If the electrochemical kinetics of the process are facile then the overall process will be dominated entirely by mass transport. Kinetic parameters such as the exchange current cannot, therefore, be obtained from such a system by analysis of the cyclic voltammetric response. Systems which satisfy this condition are normally referred to as reversible . This is slightly unfortunate... 

Figure 3.98 Comparison of a reversible conventional cyclic voltammogram (linear diffusion) and reversible steady-state voltammogram obtained at a single microelectrode disc where mass transport is solely by radial diffusion. Current axis not drawn to scale. From A.M. Bond and H.A.O. Hill, Metal Inns in Biological Systems, 27 (1991) 431. Reprinted by courtesy of Marcel...

For the investigation of charge tranfer processes, one has the whole arsenal of techniques commonly used at one s disposal. As long as transport limitations do not play a role, cyclic voltammetry or potentiodynamic sweeps can be used. Otherwise, impedance techniques or pulse measurements can be employed. For a mass transport limitation of the reacting species from the electrolyte, the diffusion is usually not uniform and does not follow the common assumptions made in the analysis of current or potential transients. Experimental results referring to charge distribution and charge transfer reactions at the electrode-electrolyte interface will be discussed later. 

The ability of varying the rate of the mass transport by agitating the solution (or the working electrode) constitutes the basis of hydrodynamic methods (hydrodynamics = liquids in motion), which are a further support to the study of electrode kinetics. Nevertheless we wish to cite them here simply to cover a drawback of cyclic voltammetry. In fact, cyclic voltammetry is unable to discriminate between oxidation and reduction processes, and vice-versa. 

Figure 5.12 Typical cyclic voltammogram at 0.3mV/s of a hydrogenase film adsorbed at a pyrolytic graphite edge electrode immersed in a pH 9.00 hydrogen saturated solution at 45°C (active-inactive interconversion is too slow to be reasonably studied at lower temperatures) and rotating at ISOOrpm. Under these conditions mass transport of hydrogen is not rate limiting.

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. 

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 . 

Double-potential-step chronoamperometry does not require precise control of potential. It is only necessary that the potential during each step be at a value for which the desired reaction occurs at the mass-transport-limited rate. Thus, it was not necessary to correct for solution iR drop in these experiments as it would have been if cyclic voltammetry had been selected as the method for quantitative evaluation of the rate constant. 

Figures 5.4 and 5.5 summarize results of a recent study of P. versicolor laccase electrochemistry based on cyclic and rotating disk voltammetry [60]. Figure 5.4 shows unequivocally that this laccase is voltammetrically active and gives a kinetically controlled, unpromoted four-electron peak at edge-plane pyrolytic graphite. Electrochemical reduction of 02 catalyzed by an immobilized laccase monolayer is close to reversible, and unrestricted by mass transport. The electrocatalysis follows, moreover, a Michaelis-Menten pattern (Fig. 5.5). Finally, there is a characteristic bell-shaped functional pH-profile with a pronounced maximum at pH 3.1.

Cyclic load frequency is the most important factor that influences corrosion fatigue for most material environment and stress intensity conditions. The dominance of frequency is related directly to the time dependence of the mass transport and chemical reaction steps involved for brittle cracking. 

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