Linear-sweep and Cyclic Voltammetry

Variation of fhe interfacial potential difference, p, allows one to change the charge accumulated in the electric double layer and thus to control reactions which involve charge transfer. For example, for the rate of a reduction process, r, this dependence is given explicitly by (Furtak 1994) 

The potential of the working electrode can be ramped at a fixed scan rate v. The resulting current density measured as a function of the applied potential is called a voUammogram. In linear-sweep voltammetry, the potential of the 

A typical CV contains peaks which provide information about reactions taking place at the electrode during the scan (Fig. 2.23). These peaks are of similar shape in both forward and reverse scan directions and, in the case of fully reversible reactions, they have identical magnitudes (Monk 2001). 

With reference to reversible electrode reactions, we have tackled the question of how slow the rate of change in potential has to be for the resulting voltammogram to be indistinguishable from that under true steady-state conditions [67]. It was concluded that, in order to obtain both the correct half-wave potential (to within 1 mV) and Tafel slope, the scan rate, va, must be such that 

Equation (63) was confirmed experimentally, as shown in Fig. 12, by measurements on the well-characterized one-electron reversible reduction of the dye fluorescein in the presence of 0.1 M aqueous NaOH. 

Aoki et al. [62] have recently extended the analysis of this problem, at the level of the Levich approximation, to include both the half-wave (or halfpeak) potential and peak (or maximum) current (in terms of Iv/Ium) dependences on t for t 1.0. The variations of these two quantities with j are shown in Fig. 13 and 14. Good agreement between the analysis of Compton and Unwin [67] and Aoki et al. [62] is displayed (Fig. 13) for a 1.0. 

Singh and Dutt, using the approximation described in Sect. 2.3, have theoretically predicted, and experimentally verified, the behaviour when very fast scans are applied in both the linear sweep and cyclic voltammetric modes, for reversible [22, 23], quasi-reversible [25], and irreversible [24] electrode kinetics. Very attractive agreement with experiment is typically found, of which Fig. 15 is representative. 

2 HETEROGENEOUS ELECTRON TRANSFER TRANSIENT METHODS 15.2.1 Linear sweep and cyclic voltammetry 

The mass transfer coefficient in linear sweep voltammetry and cyclic voltammetry is directly proportional to the square root of the potential scan rate Accordingly, the apparent reversibility of an ET reaction under voltanunetric conditions is determined by the value of the dimensionless parameter A = k° jRT/FDv (4), and the kinetic zones can be specified as follows  

It is relatively easy to extract the kinetic parameters of a one-step irreversible ET reaction from a linear sweep voltammogram obtained at a large, e.g., mm-sized electrode (see Chapter 6 for discussion of the differences between macro- and microelectrode behaviors). The transfer coefficient a can be found from the slope of the linear dependence of the peak current vs. square root of the potential scan rate (i vs. 

The same parameter can also be found from the difference between the peak potential 

The task to measure quasi-reversible kinetic parameters is more common than the analysis of completely irreversible voltammograms. The method developed by Nicholson (5) for extraction of standard rate constants from quasi-reversible cyclic voltammograms (CVs) has been most frequently used (and misused) during the last four decades. The method of Nicholson became so popular because of its extreme simplicity. The only required experimental parameter is the difference of two peak potentials, Afip = F — 1, where F and F are the potentials of the anodic and cathodic peaks, respectively. Nicholson showed that A is a function of the single dimensionless kinetic parameter. 

TABLE 3.1 Comparison of Polarographic Methods for Determination of Metal Ions 

Phase-sensitive AC with natural time 5 x 10 7 1 x 10 6 AE = 10 mV frequency = 100 Hz recommended far superior to nonphase-sensitive AC polarography 

Square-wave 5 x 1(T9 5 x 10 8 Sensitive method, but requires complicated differential pulse 

Derivative pulse 5 x 1(T7 Poor reproducibility at low concentrations not recommended for trace analysis 

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The redox characteristics, using linear sweep and cyclic voltammetry, of a series of (Z)-6-arylidene-2-phenyl-2,3-dihydrothiazolo[2,3-r][l,2,4]triazol-5(6//)-ones 155 (Figure 24) have been investigated in different dry solvents (acetonitrile, 1,2-dichloroethane, tetrahydrofuran (THF), dimethyl sulfoxide (DMSO)) at platinum and gold electrodes. It was concluded that these compounds lose one electron forming the radical cation, which loses a proton to form the radical. The radical dimerizes to yield the bis-compound which is still electroactive and undergoes further oxidation in one irreversible two-electron process to form the diradical dication on the newly formed C-C bond <2001MI3>. 

Parker, V. D. Precision in Linear Sweep and Cyclic Voltammetry, in Electronalytical Chemistry, Bard, A. J., Ed., Marcel Dekker New York, 1985, Vol. 14. 

Linear sweep and cyclic voltammetry (LSV and CV) are probably the most widely used techniques to investigate electrode reaction mechanisms. They are easy to apply experimentally, readily available in... 

Fig. 5 Linear sweep and cyclic voltammetry (a) dotted lines five profiles respectively at various typical excitation signal (b) current response times, increasing time shown by arrows] for a and concentration profiles [(c) forward scan cyclic voltammetric experiment.

Linear-Sweep and Cyclic Voltammetry at Solid Electrodes... 

Fig. 8.11. A cyclic voltammogram for a reversible charge-transfer reaction. (Reprinted from V. D. Parker, Linear Sweep and Cyclic Voltammetry, in Comprehensive Chemical Kinetics, Electrode Kinetics, Principles and Methodology, C. H. Bamford and R. C. Compton, eds., copyright 1986, p. 148, with permission from Elsevier Science.)...

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 . 

Potential control or potential measurements are fundamental to electroanalytical studies, so the cells used are usually of the three-electrode type. A typical cell for electroanalytical work, such as linear sweep and cyclic voltammetry, is shown in Fig. 6.2. 

Electron transfer reactions are classified as reversible, quasi-reversible or irreversible depending on the ability of the reaction to respond to changes in E, which, of course, is related to the magnitude of k°. The distinction is important, in particular, for the (correct) application of linear sweep and cyclic voltammetry, and for that reason further discussion of this classification will be postponed until after the introduction of these techniques in Section 6.7.2. 

The task now at hand is to find solutions to these second-order differential equations under theboundary conditions defined by the electroanalytical method in question. Nowadays, this is most often accomplished by numerical integration, known in electroanalytical chemistry as digital simulation. It is beyond the scope of this chapter to go into the mathematical details, and the interested reader is referred to the specialist literature [33]. Commercial user-friendly software for linear sweep and cyclic voltammetry is available (DigiSim ) software for other methods has been developed and is available through the Internet. 

The term voltammetry refers to measurements of the current as a function of the potential. In linear sweep and cyclic voltammetry, the potential steps used in CA and DPSCA are replaced by linear potential sweeps between the potential values. A triangular potentialtime waveform with equal positive and negative slopes is most often used (Fig. 6.8). If only the first half-cycle of the potential-time program is used, the method is referred to as linear sweep voltammetry (LSV) when both half-cycles are used, it is cyclic voltammetry (CV). The rate by which the potential varies with time is called the voltage sweep (or scan) rate, v, and the potential at which the direction of the voltage sweep is reversed is usually referred to... 

In the case of an irreversible reaction of the type 0 + we - R, linear sweep and cyclic voltammetry lead to the same voltammetric profile, since no inverse peak appears on inversing the scan direction. 

This chapter is meant to serve both as a guide for the beginner and as an overview for the nonelectrochemist with a need to know the methods available. Approximately half of the chapter is concerned with various aspects of linear sweep and cyclic voltammetry in view of the importance and widespread use of these techniques. Some general aspects of the heterogeneous electron transfer process, and the chemical reactions associated with it, are introduced in this part. Electrochemical reactions in which the electroactive substrate is formed in a chemical reaction in solution prior to the electron transfer [1-5] and catalysis of chemical reactions by electron transfer [6] are not included in this chapter. The reader interested in the details of such reactions should consult the presentations referred to. The reader is encouraged also to consult Chapter 1, where a number of basic electrochemical concepts are discussed in detail. 

Figure 2. Experimental setup for linear sweep and cyclic voltammetry. W, working electrode R, reference electrode C, counterelectrode.

Part IV is devoted to electrochemical methods. After an introduction to electrochemistry in Chapter 18, Chapter 19 describes the many uses of electrode potentials. Oxidation/reduction titrations are the subject of Chapter 20, while Chapter 21 presents the use of potentiometric methods to obtain concentrations of molecular and ionic species. Chapter 22 considers the bulk electrolytic methods of electrogravimetry and coulometry, while Chapter 23 discusses voltammetric methods including linear sweep and cyclic voltammetry, anodic stripping voltammetry, and polarography. 

Table 6.1 Linear sweep and cyclic voltammetry characteristics associated with the four categories (see text), where 5 is the size of the diffusion zone, Rb is the microdisc radius, d is the center-to-center separation, /p is the peak current, lum is the limiting current, and V is the scan rate [35].

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