Potential step chronoamperometry

Step and pulse techniques 10.2 Potential step chronoamperometry 

The study of the variation of the current response with time under potentiostatic control is chronoamperometry. In Section 5.4 the current resulting from a potential step from a value of the potential where there is no electrode reaction to one corresponding to the mass-transport-limited current was calculated for the simple system O + ne-— R, where only O or only R is initially present. This current is the faradaic current, If, since it is due only to a faradaic electrode process (only electron transfer). For a planar electrode it is expressed by the Cottrell equation4 

When a rapid electrode process is being studied and 50 jus is too long a timescale, the use of a microelectrode is recommended for the following reason. For a step in potential, AEy applied to an RC series element we obtain 

In an electrochemical cell, R is the solution resistance, RQ, independent of electrode area, and C is the double layer capacity, Cd, directly 

For this reason, in the rest of this section we consider only the faradaic current. 

---

FIG. 2 Principal methods for inducing and monitoring interfacial processes with SECM (a) feedback mode, (b) induced transfer, and (c) double potential step chronoamperometry. 

These expressions are designed for cyclic voltammetry. The expressions appropriate for potential step chronoamperometry or impedance measurements, for example, are obtained by replacing IZT/Fv by the measurement time, tm, and the inverse of the pulsation, 1/co, respectively. Thus, fast and slow become Af and Ah I and -C 1, respectively. The outcome of the kinetic competition between electron transfer and diffusion is treated in detail in Section 1.4.3 for the case of cyclic voltammetry, including its convolutive version and a brief comparison with other electrochemical techniques. 

If the nonlinear character of the kinetic law is more pronounced, and/or if more data points than merely the peak are to be used, the following approach, illustrated in Figure 1.18, may be used. The current-time curves are first integrated so as to obtain the surface concentrations of the two reactants. The current and the surface concentrations are then combined to derive the forward and backward rate constants as functions of the electrode potential. Following this strategy, the form of the dependence of the rate constants on the potential need not be known a priori. It is rather an outcome of the cyclic voltammetric experiments and of their treatment. There is therefore no compulsory need, as often believed, to use for this purpose electrochemical techniques in which the electrode potential is independent of time, or nearly independent of time, as in potential step chronoamperometry and impedance measurements. This is another illustration of the equivalence of the various electrochemical techniques, provided that they are used in comparable time windows. 

ESTABLISHING THE MECHANISM AND MEASURING THE RATE CONSTANTS FOR HOMOGENEOUS REACTIONS BY MEANS OF CYCLIC VOLTAMMETRY AND POTENTIAL STEP CHRONOAMPEROMETRY... 

This is a case where another electrochemical technique, double potential step chronoamperometry, is more convenient than cyclic voltammetry in the sense that conditions may be defined in which the anodic response is only a function of the rate of the follow-up reaction, with no interference from the electron transfer step. The procedure to be followed is summarized in Figure 2.7. The inversion potential is chosen (Figure 2.7a) well beyond the cyclic voltammetric reduction peak so as to ensure that the condition (Ca) c=0 = 0 is fulfilled whatever the slowness of the electron transfer step. Similarly, the final potential (which is the same as the initial potential) is selected so as to ensure that Cb)x=0 = 0 at the end of the second potential step whatever the rate of electron transfer. The chronoamperometric response is recorded (Figure 2.7b). Figure 2.7c shows the variation of the ratio of the anodic-to-cathodic current for 2tR and tR, recast as Rdps, with the dimensionless parameter, 2, measuring the competition between diffusion and follow-up reaction (see Section 6.2.3) ... 

FIGURE 2.7. Double potential step chronoamperometry for an EC mechanism with an irreversible follow-up reaction, a Potential program with a cyclic voltammogram showing the location of the starting and inversion potentials to avoid interference of the charge transfer kinetics, b Example of chronoamperometric response, c Variation of the normalized anodic-to-cathodic current ratio, R, with the dimensionless kinetic parameter X. 

FIGURE 2.12. Double potential step chronoamperometry for an ECE (dashed line) and a DISP (solid line) mechanism. Variation of the normalized anodic-to-cathodic current ratio, RDps = [—ia(2tR)/ic(tR)]/(l — l/y/2), with the dimesionless kinetic parameter X — ktR. 

Calculation stability implies that At/Ay2 <0.5. The fulfillment of this condition may become a problem when fast reactions, or more precisely, large values of the kinetic parameter, are involved since most of the variation of C then occurs within a reaction layer much thinner than the diffusion layer. Making Ay sufficiently small for having enough points inside this layer thus implies diminishing At, and thus increasing the number of calculation lines, to an extent that may rapidly become prohibitive. This is, however, not much of a difficulty in a number of cases since the pure kinetic conditions are reached before the problem arises. This is, for example, the case with the calculation alluded to in Section 2.2.5, where application of double potential step chronoamperometry to various dimerizations mechanisms was depicted. In this case the current ratio becomes nil when the pure kinetic conditions are reached. 

Potential Step and Double Potential Step Chronoamperometry of Nernstian Systems... 

Overlapping of Double-Layer Charging and Faradaic Currents in Potential Step and Double Potential Step Chronoamperometry. Oscillating and Nonoscillating Behavior... 

TABLE 6.3. Double-Layer Charging and Ohmic Drop in Potential Step Chronoamperometry Characteristic Function f(s) and /(f) in the Laplace and Original Spaces0... 

The simplest chronoamperometric technique is that defined as single potential step chronoamperometry. It consists of applying an appropriate potential to an electrode (under stationary conditions similar to those of cyclic voltammetry), which allows the electron transfer process under study (for instance Ox + ne — Red) to run instantaneously to completion (i.e. COx(0,0 —1 0). At the same time the decay of the generated current is monitored.20... 

The simplest and most useful case that one can study by single potential step chronoamperometry is that in which " /2> 0/i (z.e. AEor = E2 - E 5 180 mV). This means that the primarily electrogenerated species Red converts to a new species Ox, which is more easily reducible than the initial species Ox. As seen in Section 1.4.3, in cyclic voltammetry such a system exhibits a single reversible process in the forward scan. 

The hydrogenase film on the electrode was very stable, and this allows the study of active/inactive interconversion under strict potential control. By comparing cyclic voltammetry and potential step chronoamperometry, we were able to integrate energetics, kinetics and H e stoichiometry of the reaction. The effects of pH on these processes could also be conveniently observed. 

The catalytic rate of hydrogenase adsorbed on the graphite electrode was measured by potential step chronoamperometry, in which cnrrent is monitored throughout a fixed sequence of potentials. This allows for direct observation of hydrogen oxidation activity at a particular potential over a period of time. Figures 5.14 and 5.15 show how chronoamperometry can be used to study the kinetics of reductive activation and oxidative inactivation respectively. A series of oxidative inactivation curves from several experiments like that shown in Fig. 5.14, showing the effect of pFl on oxidative inactivation, are shown in Fig. 5.15. The kinetics of the reactivation process can be... 

Figure 9. Dependence of Dapp of compound 6 (O, right axis) and compound 7 (, left axis) on the weight fraction of the cross-linker. Obtained by cyclic voltammetry and potential-step chronoamperometry on a 3-mm-diameter glassy carbon electrode under argon 0.1 M NaCl, 20 mM phosphate buffer, pH 7, 37 °C, 20 mV/s. Reprinted with permission from ref 126. Copyright 2003 American Chemical Society.

Both cyclic voltammetry and double potential step chronoamperometry have been... 

Such electrochemical experiments have been used to generate and study the reactivity of anionic species [(R4)- = NCCH2 ]112. In another application, electrogenerated extra radical anions or dianions were used in the determination of pKA values for common phosphonium ions, via double potential step chronoamperometry at a platinum cathode180. 

The motivation behind the considerable effort that was exerted in the development of DCV [42, 49, 50, 69] was based on the need to make CV and LSV quantitative tools for the study of electrode kinetics. At that time, there were three major problems that had to be overcome. These were (a) the precision in the measurement of Ep and AEp, (b) the problem with accurately defining the baseline for the reverse sweep and (c) the problem as to how to handle Rn in a practical manner. The development of DCV did indeed provide suitable solutions to all three of these problems, although the methods developed to handle the Ru problem [41, 42] only involve the derivative of the response in terms of precision necessary for the measurements. More recent work [55, 57] is indicative that the precision in Ep/2, Ep) and AEP measurements can be as high as that observed during DCV (see Sect. 3.4). Also, a recent study in which rate constants were evaluated using CV, DCV, and double potential step chronoamperometry for a particular electrode reaction showed that the precision to be expected frcm the three techniques are comparable when the CV baseline, after subtracting out the charging... 

The excitation signal in chronoamperometry is a square-wave voltage signal, as shown in Figure 3.3A, which steps the potential of the working electrode from a value at which no faradaic current occurs, E , to a potential, Es, at which the surface concentration of the electroactive species is effectively zero. The potential can either be maintained at Es until the end of the experiment or be stepped to a final potential Ef after some interval of time t has passed. The latter experiment is termed double-potential-step chronoamperometry. The reader is referred to Section II. A for a detailed description of the resulting physical phenomena that occur in the vicinity of the electrode. 

Double-potential-step chronoamperometry is particularly suited for studying systems that follow EC [11] or dimerization [12] mechanisms. 

Here, the electrode reaction is followed by a first-order irreversible chemical reaction in solution that consumes the primary product B and forms the final product C. The rate of this chemical reaction can be measured conveniently with cyclic voltammetry, double-potential-step chronoamperometry, reverse pulse voltammetry, etc. However, this is only true if the half-life of B is greater than or equal to the shortest attainable time scale of the experiment. 

---