Reversible waves, potential-time curves

Here, A is the electrode area, C and D are the concentration and the diffusion coefficient of the electroactive species, AE and co(=2nfj are the amplitude and the angular frequency of the AC applied voltage, t is the time, and j=nF (Edc-Ei/2) / RT. For reversible processes, the AC polarographic wave has a symmetrical bell shape and corresponds to the derivative curve of the DC polarographic wave (Fig. 5.14(b)). The peak current ip, expressed by Eq. (5.24), is proportional to the concentration of electroactive species and the peak potential is almost equal to the half-wave potential in DC polarography ... 

When dehydration occurs as a consecutive reaction, its effect on polarographic curves can be observed only, if the electrode process is reversible. In such cases, the consecutive reaction affects neither the wave-height nor the wave-shape, but causes a shift in the half-wave potentials. Such systems, apart from the oxidation of -aminophenol mentioned above, probably play a role in the oxidation of enediols, e.g. of ascorbic acid. It is assumed that the oxidation of ascorbic acid gives in a reversible step an unstable electroactive product, which is then transformed to electroinactive dehydroascorbic acid in a fast chemical reaction. Theoretical treatment predicted a dependence of the half-wave potential on drop-time, and this was confirmed, but the rate constant of the deactivation reaction cannot be determined from the shift of the half-wave potential, because the value of the true standard potential (at t — 0) is not accessible to measurement. 

An important point on the curve is that at which the diflfiision current is equal to one-half of the total diffusion current the voltage at which this current is reached is the half-wave potential Ei. The half-wave potential is used to characterize the current waveforms of particular reactants. Whether a process is termed reversible or not depends on whether equilibrium is reached at the surface of the electrode in the time frame of the measurements. In other words, a process is reversible when the electron transfer reactions are sufficiently fast so that the equilibrium... 

In cyclic voltammetry, the forms of the curves will be different from that for the first sweep since the concentration gradients will not be the same at various times during the first and subsequent sweeps. Each cycle gives a cathodic and an anodic branch and the comparison of these cycles can serve as an indication of the reversibility of the electrode process. The following relation between the half-wave potential E1/2, obtained from conventional polarography, and the peak potential Ep has been derived by Delahay " for a reversible electrode process assuming linear diffusion to the electrode ... 

There are well-defined criteria for this "reversible" system in terms of peak separation, wave shape, etc. and the maximum current scales inversely with the square root of the scan rate. The half-wave potential of a "reversible" redox process may readily be obtained from the voltammogram. If, however, the electron transfer produces a species that is chemically reactive on the experimental time scale, then the return wave is missing and the peak potential shifts as a function of the kinetics of the follow-up processes. The peak is not as well defined, and without a proper return wave it is now not straightforward to obtain thermodynamic half-wave potentials from the trace of such an irreversible system. Furthermore, if a disk electrode is used of micrometer-dimensions, then hemispherical diffusion now takes place and a sigmoidal current-potential curve is obtained [Fig. 4(b)]. 

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 kind of voltammetry described in Sect. 4.2. is of the single-sweep type, ie., only one current-potential sweep is recorded, normally at a fairly low scan rate (0.1-0.5 V/min), or by taking points manually. Cyclic voltammetry is a very useful extension of the voltammetric technique. In this method, the potential is varied in a cyclic fashion, in most cases by a linear increase in electrode potential with time in either direction, followed by a reversal of the scan direction and a linear decrease of potential with time at the same scan rate (triangular wave voltammetry). The resulting current-voltage curve is recorded on an XY-recorder,... 

Since the forward reaction for a potential step to the limiting current region is unperturbed by the irreversible following reaction, no kinetic information can be obtained from the po-larographic diffusion current or the limiting chronoamperometric i-t curve. Some kinetic information is contained in the rising portion of the i-E wave and the shift of 1/2 with Wx- Since this behavior is similar to that found in linear potential sweep methods, these results will not be described separately. The reaction rate constant k can be obtained by reversal techniques (see Section 5.7) (32, 33). A convenient approach is the potential step method, where at = 0 the potential is stepped to a potential where Cq(x = 0) = 0, and at t = T it is stepped to a potential where Cr(x = 0) = 0. The equation for the ratio of (measured at time j.) to (measured at time Figure 5.7.3) is... 

Because of the different dependency of the current on time for t < and t > the i-t curve at potentials of the adsorption prewave can have an unusual appearance for Wx m- The current increases until t then falls off with a dependence. For a nemstian reaction, both the prewave and the main wave will have the usual reversible shapes (33). Note also, from the dependence of m and t on the corrected mercury column height, /zcorr [i- - Kon and t oc (see Section 7.1.4)] that is directly proportional to /icon- [see (14.3.32)], compared to the dependence for... 

At the end of the waiting time the potential is stepped to values at which the product is oxidized B-> A + no,e. If the oxidation and the reduction are reversible processes (A = A and n d = Uo,), a single wave appears in the RPP mode (curve 1 in Fig. 27). It may be compared with the NPP wave recorded under the same conditions (curve 2 in Fig. 27). If the pulse potentials in RPP mode are still in the region of the DCP plateau, the current response, Irp (represented by the lower part of the curve 1) is identical with the limiting DCP current. If the pulse potentials in the RPP mode grow to sufficiently positive potentials so that the total oxidation of the product B proceeds, the limiting current I, Rp is obtained (see curve 1, the upper part). The relation between these... 

The relationship between the stripping peak current of a fast and reversible mixed reaction and the square-wave frequency is a curve defined by Aip = 0, for /= 0, and an asymptote Aip = fc/+ z [90]. The intercept z depends on the delay time and apparently vanishes when t eiay > s. Consequently, the ratio Aip// may not be constant for all frequencies. This effect is caused by the additional adsorption during the first period of the stripping scan. The stripping peak potential of a reversible mixed reaction depends linearly on the logarithm of frequency [89] ... 

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