Chronoamperometry, double potential

Amperometry Chronoamperometry Double Potential Step Chronoamperometry ... 

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

As with the other reaction schemes involving the coupling of electron transfer with a follow-up homogeneous reaction, the kinetics of electron transfer may interfere in the rate control of the overall process, similar to what was described earlier for the EC mechanism. Under these conditions a convenient way of obtaining the rate constant for the follow-up reaction with no interference from the electron transfer kinetics is to use double potential chronoamperometry in place of cyclic voltammetry. The variations of normalized anodic-to-cathodic current ratio with the dimensionless rate parameter are summarized in Figure 2.15 for all four electrodimerization mechanisms. 

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... 

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. 

Figure 3.3 Chronoamperometry. (A) Potential excitation signal for double potential step. (B) Current-time response signal (chronoamperogram).

Current as a function of time is the system response as well as the monitored response in chronoamperometry. A typical double-potential-step chronoamperogram is shown by the solid line in Figure 3.3B. (The dashed line shows the background response to the excitation signal for a solution containing supporting electrolyte only. This current decays rapidly when the electrode has been charged to the applied potential.) The potential step initiates an instantaneous current as a result of the reduction of O to R. The current then drops as the electrolysis proceeds. 

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. 

Double-potential-step chronoamperometry does not require precise control of potential. It is only necessary that the potential during each step be at a value for which the desired reaction occurs at the mass-transport-limited rate. Thus, it was not necessary to correct for solution iR drop in these experiments as it would have been if cyclic voltammetry had been selected as the method for quantitative evaluation of the rate constant. 

Figure 16.2 Double-potential-step chronoamperometry of 4.6 mM [Fe(CO)2(r)5-Cp)]2 in 0.1 M Bu4NPF6/propionitrile at -43°C. Step time Texp = 0.1 s. (A) Current transients for potential step from -0.8 to -1.9 V in blank electrolyte solution (thin line) and with added [Fe(CO)2(rj5-Cp)]2 (dark line). (B) Ratio of experimental currents -i(t + texp)/i(t) for 0 < t < Texp versus normalized time (t/texp) compared to theory (solid line) for kobs = 10.5 s 1. Electrode area = 0.0032 cm2. [Reprinted with permission from E.F. Dalton, S. Ching, and R.W. Murray, Inorg. Chem. 30 2642 (1991). Copyright 1991 American Chemical Society.]...

A more elaborate version of the chronoamperometry experiment is the symmetrical double-potential-step chronoamperometry technique. Here the applied potential is returned to its initial value after a period of time, t, following the application of the forward potential step. The current-time response that is observed during such an experiment is shown in Figure 3.3(B). If the product produced during a reduction reaction is stable and if the initial potential to which the working electrode is returned after t is sufficient to cause the diffusion-controlled oxidation of the reduced species, then the current obtained on application of the reverse step, ir, is given by [63]... 

C. The kinetics of the hydrolysis reaction were studied by double-potential-step chronoamperometry. The potential is stepped from here, where I is electroinactive,. . . ... 

Double potential-step chronoamperometry (lU), AG9, > AH06, AM59, A007... 

Potential step experiments (chronoamperometry and double potential step chronoamperometry)... 

Fig. 6.5 Potential-time program (top) and current-time response curves (bottom) for chronoamperometry (f < ff) and double potential step chronoamperometry (f < 2ff).

Fig. 6.6 Relative concentration profiles for O (solid line) and R(dots) near a planar working electrode (a) at f = 0.5, 2 and 7 seconds, corresponding to a chronoamperometry experiment, and (b) at f = 10.5,12 and 17 seconds, corresponding to the second half of a double potential step chronoamperometry experiment.

Fig. 6.7 The double potential step chronoamperometry working curve for the eCei, mechanism (full line) and experimental data for the protonation of the anthracene radical anion by phenol (points). The scale at the top corresponds to the working curve and the scale at the bottom to the experimental data. (The parameter 6 in the figure corresponds to ff in the text.) Note that the data for the variation of ff and [PhOH] have been plotted on the same working curve. Reprinted with permission [35].

They are applicable to electrodes of any shape and size and are extensively employed in electroanalysis due to their high sensitivity, good definition of signals, and minimization of double layer and background currents. In these techniques, both the theoretical treatments and the interpretation of the experimental results are easier than those corresponding to the multipulse techniques treated in the following chapters. Four double potential pulse techniques are analyzed in this chapter Double Pulse Chronoamperometry (DPC), Reverse Pulse Voltammetry (RPV), Differential Double Pulse Voltammetry (DDPV), and a variant of this called Additive Differential Double Pulse Voltammetry (ADDPV). A brief introduction to two triple pulse techniques (Reverse Differential Pulse Voltammetry, RDPV, and Double Differential Triple Pulse Voltammetry, DDTPV) is also given in Sect. 4.6. 

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