Cyclic voltammetry at planar electrodes

In this section we deduce the expressions for simple electron transfer O + ne-— R, with only O initially present in solution. The initial sweep direction is therefore negative. The observed faradaic current depends on the kinetics and transport by diffusion of the electroactive species. It is thus necessary to solve the equations 

3 Cyclic voltammetry at planar electrodes The boundary conditions are 

If the species present in bulk solution is R and the initial sweep direction is in the positive direction, then [O] and [R] would be switched round in boundary conditions (9.4a) and (9.4b) and the signs in (9Ad) inverted. 

The solution of (9.2) and (9.3) is carried out by using the Laplace transform (Chapter 5 and Appendix 1). 

The final boundary condition for a reversible system is the Nernst equation 

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Cyclic voltammetry at spherical electrodes. As discussed in Chapter 1, Section 4.2.3, diffusion laws at a spherical electrode must take into account the curvature r0 of the electrode. The mathematical treatment of diffusion at a spherical electrode becomes somewhat more complicated6 with respect to the preceding one for planar diffusion and we will not dwell on it. On the basis of what we will see in Chapter 11, Section 2, it is important to consider that, under radial diffusion, the cyclic voltammogram loses its peak-shaped profile to assume a sigmoidal profile, see Figure 6. 

Fig. 7.42 Cyclic Square Wave Voltammetry. Net currents corresponding to ECE and EE mechanisms at planar electrodes calculated by using the numerical procedure described in [66,67] (ECE) and Eq. (7.65) (EE). The values of fw for the ECE mechanism are 0.01 (solid lines), 0.05 (dashed lines), 0.5 (white circles), 10 (dashed-dotted lines), and 100 (dotted lines). The curves corresponding to the EE mechanism appear with black circles. The values of Ain mV appear in the figures. sw = 50mV, AEs = 5mV, T = 298 K...

In the cyclic mode of SWV, two scans can be analyzed in an anologous way to Cyclic Voltammetry. In Fig. 7.61, the Cyclic SWV curves (7.61a) of the catalytic process given in (7.XI) for different values of A at planar electrodes have been plotted, together with the evolution of the peak currents (7.61b) and peak potentials (7.61c) of the first (1) and second (2) scans toward cathodic and anodic potentials, respectively, as a function of logA. 

In the previous chapter finite difference methods were introduced for one of the simplest situations from a theoretical point of view cyclic voltammetry of a reversible E mechanism (i.e., charge transfer without chemical complications) at planar electrodes and with equal diffusion coefficients for the electroactive species. However, electrochemical systems are typically more complex and some refinements must be introduced in the numerical methods for adequate modelling. 

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

When the electrochemical properties of some materials are analyzed, the timescale of the phenomena involved requires the use of ultrafast voltammetry. Microelectrodes play an essential role for recording voltammograms at scan rates of megavolts-per-seconds, reaching nanoseconds timescales for which the perturbation is short enough, so it propagates only over a very small zone close to the electrode and the diffusion field can be considered almost planar. In these conditions, the current and the interfacial capacitance are proportional to the electrode area, whereas the ohmic drop and the cell time constant decrease linearly with the electrode characteristic dimension. For Cyclic Voltammetry, these can be written in terms of the dimensionless parameters yu and 6 given by... 

Increasing the sean rate in cyclic voltammetry allows faster reactions to be studied. At a planar electrode, the diffusion layer grows into the solution phase during the progress of the potential cycle. The thickness of the diffusion layer at the time of the current peak. Speak, for the case of a reversible cyclic voltammetric response is given approximately by Eq. (II.6.2). 

Now, consider the reduction of solution species O at a planar electrode surface during a voltammetry experiment in which the potential is swept with time in a linear manner. This is, of course, equivalent to the first sweep of a cyclic voltammogram, and the faradaic current that we observe is ideally limited by the diffusion of O to the electrode surface. In this case the observed peak current i is typically described [1-4] by the Randles-Sevcik equation—Eq. (5). 

Eddowes and Hill found [48,49] that essentially reversible cyclic voltammetry of horse mitochondrial cytochrome c could be achieved with a Au electrode onto which was adsorbed, from the same solution, the reagent 4,4 -bipyridyl. The result is shown in Fig. 4. The criteria described by Nicholson and Shain [50] for a one-electron process controlled by linear diffusion of species to a planar electrode surface are met very closely indeed. The value of E°, given by (Ep -f- Epa)/2, was 255 mV, in good agreement with values determined by potentiometry. It could be argued that free, reduced 4,4 -bipyridyl played no part in the mechanism, since its reduction potential is much lower than that of cytochrome c. It was proposed [7] that the organic adsorbate allowed electron transfer to occur directly by providing, at the electrode surface, functionalities with which the protein could interact specifically and reversibly and thereupon donate or accept electrons rapidly. It was thus termed a promoter as opposed to a mediator, in which the latter is considered to convey electrons in bulk solution. 

In cyclic voltammetry a redox-active molecule is placed in an electroanalytical cell and the electrode potential is raised from a starting value at which there is no electroactivity. When electron transfer occurs a current is measured, and the shape of the trace depends upon, among other factors, the size and shape of the electrode. Thus, at a disk or wire of millimeter-sized dimensions (millielectrode) under conditions of linear diffusion, an initial current increase imder the control of electron-transfer kinetics meets a current decrease under diffusion control towards an effectively planar surface, and a characteristic peak shape is observed [Fig. 4(a)]. If the electron-transfer reaction produces a relatively stable species, then on reversing the scan direction a current is observed in the opposite direction. 

A conventional 3 electrode system was used for cyclic voltammetry with 1 cm square planar platinum working counter electrodes a reference electrode using the same TBAP (tetrabutyl ammonium perchlorate) electrolyte (normally at 0.1 mol dm ). In dimethyl formamide (DMF) containing solutions the Ag reference electrode was inunersed in a 0.01 mol dm Ag solution in chloromethane solutions the electrolyte was saturated with lithium chloride. An EG G Potentiostat Model 362 was coupled to a computer based data cs ture treatment system. The latter included the ability to software compensate for electrolyte resistance between reference working electrodes to semi-integrate semi-differentiate Ae current responses obtained. 

Linear scan voltammetry (LSV) and cyclic voltammetry (CV) (see Chapter 11) are among the most common electrochemical techniques employed in the laboratory. Despite their utility, however, they are not particularly well suited to careful measurements of diffusion coefficients when using electrodes of conventional size. We will briefly discuss techniques for measuring D with LSV and CV, but the reader should be cautioned that these measurements under conditions of planar diffusion (i.e., at conventional electrodes) are probably useful to only one significant digit, and then only for nemstian systems with no coupled homogeneous reactions and with no adsorption. For more reliable results with LSV and CV, UMEs should be used. 

Peak potential (in voltammetry) — It is the potential at which the maximum current appears in -> linear scan voltammetry (LSV) and several other techniques peak height). It is one of diagnostic criteria for the estimation of electrode kinetics. If the reaction is simple, fast, and - reversible the peak potential is independent of the scan rate, or frequency, or pulse duration. The condition is that the electrode reaction is not complicated by the -> adsorption, the -> amalgam formation, the precipitation of solid phase, the gas evolution, or the coupled chemical reactions. In LSV and cyclic voltammetry (CV) of a simple, reversible, semi-infinite planar diffusion-controlled reaction Oxaq h- e Redaq the cathodic and anodic peak potentials are p,c = ... 

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