Voltammetry reversible electrode reaction

Fig. 9.10. EC mechanism in cyclic voltammetry (reversible electrode reaction and irreversible homogeneous reaction), (a) Plot of the ratio /p,a//p,cl with lg r) where vt = EV2 - Ex (from Ref. 6 with permission), (b) Variation of cathodic peak potential, EPjC9 as a function of lg (k Jo).

Table 2.1 Square-wave voltammetry of fast and reversible electrode reaction (1.1). The dimensionless net peak current, the ratio of peak currents of the forward and backward components, the peak potentials of the components and the half-peak width as functions of SW amplitude ...

The best way to gauge the influence of convective stirring on prospective elec-troanalytical experiments such as chronoamperometry or cyclic voltammetry is to conduct preliminary experiments with a well-behaved, reversible electrode reaction employing the same experimental setup to be used for examination of the system of interest. Increases in the expected constant values of it1/2 with increasing t or ip/v1/2 with decreasing v, respectively, signal the point at which convective transport becomes important. 

In the preceding chapter, single pulse voltammetry and chronoamperometry were applied to the study of reversible electrode reactions of species in solution. Under these conditions, the surface concentrations fulfill Nemst equation and are independent of the duration of the experiment, regardless of the diffusion field... 

In linear scan voltammetry (LSV) the peak current of fast and reversible electrode reactions controlled by semi-infinite planar diffusion is given by the following equation [i] ... 

Reversible square-wave voltammogram — Figure. Theoretical dimensionless square-wave voltammogram of a reversible electrode reaction (see - reversible redox reaction) of a dissolved redox couple at a planar electrode assuming a semi-infinite diffusion model simulated with nEsw = 50 mV and a scan increment of the staircase ramp of 5 mV (see - square-wave voltammetry)... 

SAMPLED-CURRENT VOLTAMMETRY FOR REVERSIBLE ELECTRODE REACTIONS... 

Sampled-Current Voltammetry for Reversible Electrode Reactions 177... 

Cyclic voltammetry is a method frequently used to measure 7s,i ni. Mediated bioelectrocatalysis yields cyclic voltammograms (CVs) of different shapes as illustrated in Fig. 2, depending on the measuring conditions [11]. Curve (a) is the wave for a reversible electrode reaction of an Mox/Mred redox couple. Bioelectrocatalysis mediated with the Mqx/ Mred redox couple produces a sigmoidal catalytic wave as curve (c) under the conditions [Mred] - M and [S] Ks. When [Mred] is increased to higher concentrations, an anodic peak of the diffusion current of Mred rnay be overlapped on the catalytic current as depicted by curve (d) the current, however, becomes steady state after appropriate periods... 

The relationship between electrode potential and current is determined by the electrochemical reaction taking place at the working electrode. Measurements are done usually in a three-electrode arrangement with a reference electrode to control the potential of the working electrode (typically no current is in practice allowed to flow through the reference electrode and its potential is constant) and a counter (auxiliary) electrode where a counterbalancing but not rate-deterrnmirig electrode process takes place. In cyclic voltammetry for a reversible electrode reaction, the cathodic, pc and anodic, pa peak potentials depend on the formal potential, E ... 

This equation is often used to determine the formal potential of a given redox system with the help of cyclic voltammetry. However, the assumption that mid-peak potential is equal to formal potential holds only for a reversible electrode reaction. The diagnostic criteria and characteristics of cyclic voltammetric responses for solution systems undergoing reversible, quasi-reversible, or irreversible heterogeneous electron-transfer process are discussed, for example in Ref [9c]. An electro-chemically reversible process implies that the anodic to cathodic peak current ratio, lpa/- pc equal to 1 and fipc — pa is 2.218RT/nF, which at 298 K is equal to 57/n mV and is independent of the scan rate. For a diffusion-controlled reduction process, Ip should be proportional to the square root of the scan rate v, according to the Randles-Sevcik equation [10] ... 

Yeh and Kuwana " were the first to report on the electrochemistry of cytochrome c at doped metal oxide semiconductor electrodes. A nearly reversible electrode reaction was indicated by the cyclic voltammetry and differential pulse voltammetry of cytochrome c at tin-doped indium oxide electrodes. Except for the calculated diffusion coefficient, all of the characteristics of the electrochemistry of cytochrome c at this electrode indicated that the electrode reaction was well-behaved. A value of 0.5 x 10" cmVs was determined for the diffusion coefficient which, like previously determined values at mercury, is lower than the value obtained by nonelectrochemical methods (i.e., 1.1 X 10 cm /s " " ). The electrochemical response of cytochrome c at tin oxide semiconductor electrodes was reported to be quasi-reversible, although no details were given. " ... 

Fig. 6.1. Cyclic voltammetry of the second-order catalytic mechanism (black lines) under linear diffusion conditions and for a fully reversible electrode reaction (grey line).

Very promising is the use of microelectrodes in pulse voltammetry. The theory describing the reversible electrode reaction in RPV at a disc microelectrode was derived and verified in [77]. Due to the steady-state... 

The peak current is also proportional to the amplitude of the AC potential V. This is, however, limited to small amplitudes—that is, to quasilinear conditions. In principle, AC voltammetry can be carried out at considerably larger values in order to increase the sensitivity and signal-to-noise ratio of the method. Although under these conditions the peak current is not proportional to the AC amplitude any longer, it could be demonstrated that the area imder the peak is proportional to the perturbaHon amplitude and the analyte concentration. Since the rules for semi-infinite diffusion apply, a phase angle of -45° for the impedance vs. frequency co dependence can be observed for any reversible electrode reaction. 

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... 

After tq is passed, the second step starts by scanning the potential from Ed to a potential when all the deposited metals are re-oxidized (the reverse of reaction 25). The oxidation current recorded as a function of potential is the anodic stripping voltammogram (ASV). A typical ASY of three metals (Cd, Pb, and Cu) deposited on a mercury film electrode is shown in Fig. 18b.12b. The sensitivity of ASY can be improved by increasing the deposition time and by using the pulse technique to record the oxidation current. ASV in Fig. 18b. 12b was obtained by using the square wave voltammetry. In most cases a simple linear or step ramp is sufficient to measure sub-ppm level of metals in aqueous solution. The peak current of a linear scan ASV performed on a thin mercury film electrode is given by... 

Determination of the kinetic parameters by using cyclic voltammetry is conceptually very similar to this t = 0 is taken to be the time at the formation of the intermediate (here Br2), i.e. at the forward current peak Ipa, and the time when it is monitored at t = t, i.e. at the current peak for the reverse electrode process, pc. The time-scale of the reaction, r, is given by the following equation ... 

---