Double current step

In the last section the capacitive contribution was neglected. However, for some galvanostatic experiments this procedure is not possible. Various theoretical treatments have been developed to analyse chrono-potentiograms, but always with approximations that are difficult to justify, such as, for example, Ic constant  

A better alternative is to modify the experiment. The use of a double current step10, as demonstrated in Fig. 10.7, can reduce the problem. The first step has sufficient length to charge the double layer the current is then reduced to a lower value at which there is not capacitive component. 

---

Figure 4.1 General excitation signals for controlled-current techniques. (A) Current step. (B) Double current step.

Fig. 10.7. The double current step. The first pulse is to charge the double layer.

Double current steps, where the second step reverts to the initial value of the applied current, have been used in mechanistic studies11. 

A related technique is the current-step method The current is zero for t < 0, and then a constant current density j is applied for a certain time, and the transient of the overpotential 77(f) is recorded. The correction for the IRq drop is trivial, since I is constant, but the charging of the double layer takes longer than in the potential step method, and is never complete because 77 increases continuously. The superposition of the charge-transfer reaction and double-layer charging creates rather complex boundary conditions for the diffusion equation only for the case of a simple redox reaction and the range of small overpotentials 77 [Pg.177]

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. 

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

For times t> t, where the reoxidation of the previously generated species Red takes place, the diagram represents the double potential step response. Under these conditions, the anodic current follows the equation ... 

Figure 49 The variation of the current ratio in a double potential step experiment for a simple reduction process (t > t)...

In the second experimental approach, the Cgo molecules are deposited on top of an insulating self-assembled monolayer, thus creating a double barrier tunnel junction coimected in series and sharing an electrode [66, 67]. Under these conditions current steps in the I-V graph are observed, because when a potential is applied the capacitances of each junction has to be charged to a threshold potential before an electron can tunnel through the junction and when it is favorable for an electron to sit in the middle electrode the amount of current that flows through the junctions increases [68],... 

Double potential step experiments have provided useful information on some details of the electrochemiluminescence phenomenon. As expected, they have shown that emission is not generated on potential reversal when the initially generated ion is not sufficiently stable to be detected with cyclic voltammetry. Furthermore, current reversal with... 

Feldberg68,69 has made a valuable analysis of the relationship of the light produced in a double potential step electrochemiluminescence experiment to the current, time, and kinetic parameters involved. The analysis presumes that the reaction which produces excited states is cation-anion radical annihilation which occurs when the radical ions, separately produced, diffuse together in the solution near the electrode. The processes that Feldberg initially considered were eqs. (7)—(13). The assumptions involved are that decay of the excited state... 

Double potential step Chronocoulometry with current reversal... 

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. 

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]... 

The simulation of the ECE mechanism may also employ the double-potential-step technique, but a working curve can be constructed from single-potential-step data also. This is because some of the current that passes, as A is converted to B, is due to the electrolysis of C, the decomposition product of B. The greater the decomposition rate of B, the more current flows, approaching the rate of... 

Figure 21.9 (Left) Anodic-cathodic current-time curve for 2,2,5,7,8-pentamethyl-6-hydroxychroman (lb) showing the method of current and time measurements for the double-potential-step chronoamperometric method. The xr/xf ratio shown here is 0.3. (Right) Plot of kxf vs. xf for the ring opening of lib in 75 vol% water-25 vol% acetonitrile pH 3.99 0.5 M chloroacetic acid, 0.5 M sodium chloroacetate. (From Ref. 6, reprinted with permission.]...

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

A current step applied to an electrode provokes a change in its potential. The flux of electrons is used first to charge the double layer, and then for the faradaic reactions. The study of the variation of the potential with... 

---