Current-potential curves response

Fig. 32. Cyclic current-potential curve for Au(l 11), covered with an octadecanethiol SAM, in 0.1 M H2SO4 + 1 mM CUSO4. Scan rate 10 mV s-1. The C18-SAM blocks Cu deposition up to very high overpotentials. Inset Current response of a bare Au(lll) electrode for the same potential cycle [98],...

FIGURE 1.17. Cyclic voltammetry of slow electron transfer involving immobilized reactants and obeying a Butler Volmer law. Normalized current-potential curves as a function of the kinetic parameter (the number on each curve is the value of log A ) for a. — 0.5. Insert irreversible dimensionless response (applies whatever the value of a). 

The normalized current-potential curves are thus a function of the two parameters A and oc. An example corresponding to a = 0.5 is shown in Figure 1.19. Decreasing the parameter A as a result of a decrease in the rate constant and/or an increase in scan rate triggers a shift of the cathodic potential toward negative values and of the anodic potential in the reverse direction, thus increasing the irreversibility of the cyclic voltammetric response. When complete irreversibility is reached (i.e., when there is no anodic current underneath the cathodic current, and vice versa), a limiting situation is reached, characterized by... 

There are two mains aspects of the role of dimerization of intermediates on the electrochemical responses that are worth investigating in some detail. One concerns the effect of dimerization on the primary intermediate on the current-potential curves that corresponds to the first electron transfer step, the one along which the first intermediate is generated. Analysis of this effect allows the determination of the dimerization mechanism (radical-radical vs. radical-substrate). It is the object of the remainder of this section. 

In cyclic voltammetry, the current-potential curves are completely irreversible whatever the scan rate, since the electron transfer/bond-breaking reaction is itself totally irreversible. In most cases, dissociative electron transfers are followed by immediate reduction of R, as discussed in Section 2.6, giving rise to a two-electron stoichiometry. The rate-determining step remains the first dissociative electron transfer, which allows one to derive its kinetic characteristics from the cyclic voltammetric response, ignoring the second transfer step aside from the doubling of the current. 

Thus, the dimensionless current-potential curves depend on the dimensionless parameters 1, A, A , oq, and a2. Simulating the dimensionless cyclic voltammograms then consists of finite difference resolutions of equations (6.57) and (6.58), taking into account all initial and boundary conditions. Examples of such responses are given in Section 2.5.2 (Figure 2.35). 

A preliminary electrochemical overview of the redox aptitude of a species can easily be obtained by varying with time the potential applied to an electrode immersed in a solution of the species under study and recording the relevant current-potential curves. These curves first reveal the potential at which redox processes occur. In addition, the size of the currents generated by the relative faradaic processes is normally proportional to the concentration of the active species. Finally, the shape of the response as a function of the potential scan rate allows one to determine whether there are chemical complications (adsorption or homogeneous reactions) which accompany the electron transfer processes. 

SWV experiments are usually performed on stationary solid electrodes or static merciuy drop electrodes. The response consists of discrete current-potential points separated by the potential increment AE [1,20-23]. Hence, AE determines the apparent scan rate, which is defined as AE/t, and the density of information in the response, which is a number of current-potential points within a certain potential range. The currents increase proportionally to the apparent scan rate. For better graphical presentation, the points can be interconnected, but the fine between two points has no physical significance, as there is no theoretical reason to interpolate any mathematical function between two experimentally determined current-potential points. The currents measured with smaller A are smaller than the values predicted by the interpolation between two points measured with bigger AE [3]. Frequently, the response is distorted by electronic noise and a smoothing procedure is necessary for its correct interpretation. In this case, it is better if AE is as small as possible. By smoothing, the set of discrete points is transformed into a continuous current-potential curve. Care should be taken that the smoothing procedttre does not distort the square-wave response. 

A complete comprehension of Single Pulse electrochemical techniques is fundamental for the study of more complex techniques that will be analyzed in the following chapters. Hence, the concept of half-wave potential, for example, will be defined here and then characterized in all electrochemical techniques [1, 3, 8]. Moreover, when very small electrodes are used, a stationary current-potential response is reached. This is independent of the conditions of the system prior to each potential step and even of the way the current-potential was obtained (i.e., by means of a controlled potential technique or a controlled current one) [9, 10]. So, the stationary solutions deduced in this chapter for the current-potential curves for single potential step techniques are applicable to any multipotential step or sweep technique such as Staircase Voltammetry or Cyclic Voltammetry. Moreover, many of the functional dependences shown in this chapter for different diffusion fields are maintained in the following chapters when multipulse techniques are described if the superposition principle can be applied. 

Note that the reversible l(E, t) response is expressed as a product of a potential-dependent function ((c 0 - c Rt l)/( + ye 1)) and a time-dependent function (FA sjDo/(nt)). This behavior is characteristic of reversible electrode processes. In the next sections the current-time curves at fixed potential (Chronoamperograms) and current-potential curves at a fixed time (Voltammograms) will be analyzed. 

The NPP current-potential curves calculated from Eq. (2.124) for i Is and different values of t2 have been plotted in Fig. 2.10. As can be seen from these curves, the decrease of the potential pulse time t2 leads to an increase of the response (and therefore of its sensitivity), whereas it does not affect the location of the current-potential curve. 

Even in the simplest situation for which a = a2 = 0.5, the global behavior of the response depends upon three parameters, the difference between the formal potentials AEf, and the rate constants of both steps k(j and k. Thus, the observed current-potential curves are the result of the interaction of thermodynamic and kinetic effects so the appearance of two or one waves would not be due solely to thermodynamic stability or instability of the intermediate species but also to a kinetic stabilization or destabilization of the same [4, 31]. This can be seen in Fig. 3.19 in which the current-potential curves of an EE process with AE = 0 mV taking place at a planar electrode with a reversible first step... 

It is of interest at this point to compare the study of Multipulse Chronoamperometry and Staircase Voltammetry with those corresponding to Single Pulse Chronoamperometry and Normal Pulse Voltammetry (NPV) developed in Chaps. 2 and 3 in order to understand how the same perturbation (i.e., a staircase potential) leads to a sigmoidal or a peak-shaped current-potential response as the equilibrium between two consecutive potential pulses is restored, or not. This different behavior is due to the fact that in SCV the current corresponding to a given potential pulse depends on the previous potential pulses, i.e., its history. In contrast, in NPV, since the equilibrium is restored, for a reversible process the current-potential curve is similar to a stationary one, because in this last technique the current corresponding to any potential pulse is independent of its history [8]. 

As discussed in Sect. 3.4.7, a stationary current-potential response of these reaction mechanisms can only be obtained when microelectrodes are used. In this case, the expression of the current-potential curves corresponding to CE and EC mechanisms for a microsphere of radius rs is (see also Eqs. (3.239) and (3.240)) ... 

The location of the response is not affected by the ratio between pulse times in the case of DNMPV. This effect can be seen in Fig. 7.4 in which the current potential curves calculated for different values of (t -zt) and planar electrodes have been plotted. This ratio only affects the magnitude of the current and not the peak potential, which coincides with the formal potential in all the cases. For nonplanar electrodes, this behavior also holds when the diffusion coefficients of oxidized and reduced species are equal [9]. 

Although the usual way of analyzing the influence of the kinetics of the electron transfer on the SWV response is based on the variation of the frequency at fixed values of the staircase and square wave amplitude, a new approach for carrying out this analysis has been proposed based on the study of the influence of the square wave amplitude sw on the current potential curves at a fixed value of the frequency (or the time pulse) [19, 33, 34], The square wave amplitude has been used rarely as a tool in mechanistic and kinetic studies. One of the main reason is that, as stated in Sect. 7.1, in SWV the current is plotted versus an index potential which is an average potential between the forward and reverse potentials (see Eq. (7.7)) and leads to a discrepancy between the plotted and actual potentials at which the current is sampled. Therefore, the role played by Esw in the process is complex. 

The DSCVC response has a peak-shaped feature similar to that obtained in Cyclic Voltammetry. Indeed, the most appropriate way of analyzing the DSCVC response is to divide Qdscvc by the pulse amplitude AE in order to obtain the (Qdscvc/AE) — E response, since the following relationship between the continuous current-potential curve corresponding to CV and the (QdscvcM-E) — curve obtained from a discrete staircase potential sequence can be established for AE < RT/F ... 

Figure 10.9 Calculated steady-state and impedance response for coupled reactions dependent on potential and surface coverage, a) Simulated current-potential curve following equation (10.66) with the kinetic parameters = 4F A/cm, — 36 V, Kx = 10 F A/cm, bx = 10 V r = 2 X 10 mol/cm, and Cji = 20jiF/cm. The points A, B and C correspond to the simulated impedance, b) impedance diagram simulated at the point A (V = —0.65 V) c) impedance diagram simulated at the point B (V = —0.585 V) and d) impedance diagram simulated at the point C V — —0.50 V).

Analytical applications of electrochemistry, where the objectives are well defined, have fared better. There is a long list of papers going back twenty years on the applications of computers and then microprocessors. Reviews of this subject appear in the Fundamental Reviews sction of Analytical Chemistry (see refs. 8 and 9). In general, the aim in electroanalytical methods is to avoid interfering effects, such as the ohmic loss and the double layer capacity charging, and to use the Faradaic response peak current-potential curve as an analytical tool. Identification of the electroactive species is achieved by the position of the response peak on the potential axis and "pattern recognition , and quantitative analysis by peak shape and height. A recent development is squarewave voltammetry [10]. 

A great deal of effort has been spent in studying the mechanisms of complex electrode reactions. One general approach is based on steady-state current-potential curves. Theoretical responses are derived on the basis of mechanistic alternatives, then one compares predicted behavior, such as the variation of exchange current with reactant concentration, with the behavior found experimentally. A number of excellent expositions of this approach are available in the literature (8-14, 25, 26, 35). We will not delve into specific cases in this chapter, except in Problems 3.7 and 3.10. More commonly, complex behavior is elucidated by studies of transient responses, such as cyclic voltammetry at different scan rates. The experimental study of multistep reactions by such techniques is covered in Chapter 12. 

With only a qualitative understanding of the experiments described in Section 5.1.1, we saw that we could predict the general shapes of the responses. However, we are ultimately interested in obtaining quantitative information about electrode processes from these current-time or current-potential curves, and doing so requires the creation of a theory that can predict, quantitatively, the response functions in terms of the experimental parameters of time, potential, concentration, mass-transfer coefficients, kinetic parameters, and so on. In general, a controlled-potential experiment carried out for the electrode reaction... 

So far, it has been most convenient to think of (5.2.24) as describing the current-time response following a potential step however it also describes the current-potential curve in sampled-current voltammetry, just as we understood (5.4.17) to do for reversible systems. At a fixed sampling time r, A becomes f 0), which is a function... 

A typical LSV response curve for the anthracene system considered in Section 5.1 is shown in Figure 6,1.2b. If the scan is begun at a potential well positive of for the reduction, only nonfaradaic currents flow for a while. When the electrode potential reaches the vicinity of the reduction begins and current starts to flow. As the potential continues to grow more negative, the surface concentration of anthracene must drop hence the flux to the surface (and the current) increases. As the potential moves past E the surface concentration drops nearly to zero, mass transfer of anthracene to the surface reaches a maximum rate, and then it declines as the depletion effect sets in. The observation is therefore a peaked current-potential curve like that depicted. 

Selection of scan parameters. As mentioned earher, the scan rate significantly influences the shape and quantitative features of voltammograms. Usually, a variation of v gives important information. There are, however, other scan-related parameters that may affect the current/potential curves. In computer controlled instruments, the ideal linear variation of E is often simulated using a staircase function (Fig. 7). The response from such an excitation function... 

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