Cyclic Nernstian systems

FIGURE 1.3. Cyclic voltammetry of a Nernstian system involving the reduction of free-moving molecules. Concentration profiles of A ( ) and B (—) alongside the potential scan. 

Cyclic Voltammetry of Two-Electron Nernstian Systems. Disproportionation... 

Cyclic ac voltammograms for completely nernstian systems are easy to predict on the basis of results from the previous section. The mean surface concentrations, Co(0, Om Cr(0, Om adhere to (10.5.3) and (10.5.4) unconditionally hence at any potential they are the same for both the forward and reverse scans. The cyclic ac voltammogram should therefore show superimposed forward and reverse traces of ac current amplitude dc-We expect a peak-shaped voltammogram that adheres in every way to the conclusions reached in Section 10.5.1 about the general ac voltammetric response to a reversible system at a planar electrode. 

The cyclic voltammetric currents were normally not the main source of attention but rather the semi-integral Ij of the current was calculated from this the semi-differential or square root of time deconvolution dlj/dt. This dlj/dE were used for the clearest displays of results. The main difference in application of the latter pair depends on whether a potential ramp linear with time is applied at die working electrode surface i.e. hardware compensated at tte potentiostat if necessary for resistance between working counter electrodes. In this case using the linearly varying potential as an axis dlj/dt dl/dE are similar in shape either provides a suitable display. If uncompensated resistance remains then in Nernstian systems I is a function of the appropriate E (E ) suitable compensation via -i.R can be sqiplied post csqiture... 

Obviously, therefore there must be an intermediate case in which the kinetics of both the forward and reverse electron-transfer processes have to be taken account of. Such systems are described as being quasi-reversible and as would be expected, the scan rate can have a considerable effect on the nature of the cyclic voltammetry. At sufficiently slow scan rates, quasi-reversible processes appear to be fully reversible. However, as the scan rate is increased, the kinetics of the electron transfer are not fast enough to maintain (Nernstian) equilibrium. In the scan-rate region when the process is quasi-reversible, the following observations are made. 

It can be seen that cyclic voltammograms at low scan rate have peak-to-peak separations close to the value theoretically expected for a reversible process of A p = 2.218 X 7 r/ = 57 mV at 298 K [47] and the peak current increases with the square root of the scan rate. Under these conditions, the process is diffusion controlled and termed electrochemically reversible or Nernstian within the timescale applicable to the experiment under consideration. Hence, as with all reversible systems operating under thermodynamic rather than kinetic control, no information concerning the rate of electron transfer at the electrode surface or the mechanism of the process can be obtained from data obtained at slow scan rate. The increase of A p at faster scan rate may be indicative of the introduction of kinetic control on the shorter timescale now being applied (hence the rate constant could be calculated) or it may arise because of a small amount of uncompensated resistance. Considerable care is required to distinguish between these two possible origins of enhancement of A p. For example, repetition of the experiments in Table II.l.l at... 

In acetonitrile solutions, the cyclic voltammograms for PVF in LiC104 electrolyte are nearly Nernstian in character. Epeak (anodic) is approximately equal to Epeak (cathodic), and the peaks are almost symmetrical. Thinner films approach the ideal behaviour most closely. As film thickness is increased (at a fixed scan rate), a larger ohmic drop in the film causes separation of the anodic and cathodic peaks (AEpgak) and the peaks become asymmetric. Figure 2.4 shows a typical cyclic voltammogram for the PVF/LiC104/acetonitrile system. 

In the case of the reversible system discussed above, the electron transfer rates at all potentials are significantly greater than the rate of mass transport, and therefore Nernstian equilibrium is always maintained at the electrode surface. When the rate of electron transfer is insufficient to maintain this surface equilh brium then the shape of the cyclic voltammogram changes. Fig. 6.6 shows an example of such a system. At lov/ potential sweep rates the rate of electron transfer is greater than that of mass transfer, and a reversible cyclic voltanuno-gram is recorded. As the sweep rate is increased, however, the rate of mass... 

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