Open-Circuit-Decay Transients

Whereas the charge-injection method is a small-amplitude perturbation method, in which measurement is conducted during open-circuit decay, we now discuss a 

Assuming that Cdi is independent of potential in the range of interest, we can write 

the Tafel slope can be determined from the slope of the open-circuit decay curve, once the parameter t is known. The latter is found by trial and error, as the number that yields the best straight line on a semi-logarithmic plot of Tj vs. In(t-i-T). This line must merge with the plot of t] versus Int at long times, when t X. 

If the current-potential relationship can be determined experimentally and compared to the open-circuit-decay behavior, the validity of the assumption that the capacitance is independent of potential can be tested. Indeed, under these conditions the capacitance can readily be found from the open-circuit-decay curve, with the use of Eq. (14.14), by determination of the slope dq/dt, as a function of q, and employing the value of j corresponding to each overpotential. 

We might ask ourselves why is it that the results in the two cases of open-circuit decay are so different For small transients we found that In q is proportional to t 

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Fig. 7K Charge injection followed by open-circuit decay (the coulostatic method). Diffusion limitation (low values of /x ) slows down the decay transient, as expected from the equivalent circuit shown in Fig. 2K.

Fig. 3 Absorbance-time transients for the carbonium ion generated in a potential step followed by an open-circuit decay period. Full lines curves computed for the DISPl and ECE mechanisms. Dashed line the experimental transient obtained for pentamethylbenzene at 467 nm. (Reprinted from Electrochim. Acta. 1980, 25, 931. Copyright 1980, with permission from Elsevier Science.)...

The field of cathode activation, as well as that of anode activation, requires the use of complementary physical techniques to evaluate systems otherwise difficult to understand. Electrochemical techniques are sufficient to evaluate the kinetic parameters and the state of intermediates, especially if digital acquisition of open-circuit potential-decay transients, coupled with computer processing of the data, is used [104-106]. But the chemical and physical characterization of the surface remains essential. The literature shows that such an approach is becoming more accepted, so that there are hopes that the real situation of a number of systems will become clarified in the near future. 

Under such conditions no faradaic reaction takes place during the charging pulse. Once on open circuit, the capacitor will be discharged through the faradaic resistor, R. It is easy to derive the form of the decay transient. On the one hand, the current is given by ... 

Remember that this is an internal current, since the the decay transient is followed at open circuit. It is interesting to note, in this... 

In the earliest treatment of open-circuit potential-decay transients (729), C was identified with the double-layer capacitance, C, but it was recognized (cf. Refs. 105, 129) that this formulation did not account for changes in the coverage fractions by any electroactive intermediates involved. Conway and co-workers (126-128) were the first to treat the problem with allowance for changes in coverage of the adsorbed intermediate. However, C was interpreted as the sum of Cj, and C, and the potential-decay behavior for several... 

As described, the alternative method for the deduction of radical kinetics is the use of ESR transient signals [65, 66]. Transient signals are obtained by open-circuiting an electrode which was previously at a potential corresponding to the diffusion-limited current. The electrode is open circuited by opening a switch, rather than stepping the potential between two defined values since the latter method may produce contributions to the radical decay from, e.g. re-oxidation of a radical anion, if the latter is generated by... 

Fig. 19. ESR decay transient for the 2-nitropropane radical anion produced by open-circuiting the working electrode.

Attention is now turned to the use of EPR signal transients in the deduction of radical decay kinetics. The transient signals may be experimentally observed (at constant magnetic field induction) by either open-circuiting an electrode that had been previously held at a potential at which Faradaic processes occur, or... 

Recombination is either characterized using steady state measurements, for instance in the dark or under open-circuit conditions, or transient methods where the decay of the concentration of charges is used to analyze the strength and type of recombination. To determine the recombination rate itself is not useful because the continuity equations are solved in terms of the charge densities of electrons and holes on which the recombination rate is strongly dependent. Therefore, we need to measure directly a recombination lifetime r or an effective recombination prefactor k, which is usually defined as k = R/rP, where n is the average excess electron and hole concentration. Typically, these measurements are done by transient photovoltage measurements [31, 42, 148-152], by transient absorption measurements [148, 153] or by impedance measurements [154—156]. 

Usually, for a potential-decay experiment, the system is at steady state just before the circuit is opened. Therefore the value of K(0) to be used to define the initial conditions for solution of the differential equations is the potential at which the system was held prior to the transient. The initial value of 6 is the corresponding steady-state value, obtained by inserting K(0) into Eq. (54), setting Eq. (54), equal to zero, and solving for 6. It is this 6 that is required for evaluation of the adsorption behavior of the electroactive intermediate. The required differential kinetic equations can be solved numerically for various mechanisms and forms of transients t) t) or V t) derived. 

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