Current-potential curves characteristics

The reduction wave of peroxydisulphate at dme starts at the potential of the anodic dissolution of mercury. The current-potential curve exhibits certain anomalous characteristics under various conditions. At potentials more negative than the electrocapillary maximum, a current minimum can be observed this is due to the electrostatic repulsion of the peroxydisulphate ion by the negatively charged electrode surface. The current minimum depends on the concentration and nature of the supporting electrolyte, and can be eliminated by the adsorption of capillary active cations of the type NR4. ... 

In cyclic voltammetry, simple relationships similar to equations (1.15) may also be derived from the current-potential curves thanks to convolutive manipulations of the raw data using the function 1 /s/nt, which is characteristic of transient linear and semi-infinite diffusion.24,25 Indeed, as... 

In cyclic voltammetry, the current-potential curves are completely irreversible whatever the scan rate, since the electron transfer/bond-breaking reaction is itself totally irreversible. In most cases, dissociative electron transfers are followed by immediate reduction of R, as discussed in Section 2.6, giving rise to a two-electron stoichiometry. The rate-determining step remains the first dissociative electron transfer, which allows one to derive its kinetic characteristics from the cyclic voltammetric response, ignoring the second transfer step aside from the doubling of the current. 

In the case of cyclic voltammetry, too, amplification of the current upon addition of the substrate may be exploited to determine the kinetic characteristics of the electrode electron transfer. Replacing Nemst s law by a kinetic law and assuming, as already discussed, that dr /dt is negligible, the dimensionless current-potential curves are given by... 

Thin-film ideal or Nemstian behavior is the starting point to explain the voltammetric behavior of polyelectrolyte-modified electrodes. This condition is fulfilled when (i) the timescale of the experiment is slower than the characteristic timescale for charge transport (fjD pp, with Ithe film thickness) in the film, that is all redox within the film are in electrochemical equibbrium at any time, (ii) the activity of redox sites is equal to their concentration and (iii) all couples have the same redox potential. For these conditions, anodic and cathodic current-potential waves are mirror images (zero peak splitting) and current is proportional to the scan rate [121]. Under this regime, there exists an analytical expression for the current-potential curve ... 

Figure 9 shows a cyclic voltammogram (CV) of hexacyanoferrate(III) (Fe(III)) in water observed at a gold microelectrode (8 fim wide x 33 fim long x 0.2 fim thick). A cathodic current at 200 mV corresponds to reduction of Fe(III) to Fe(II). At a micrometer-sized electrode, mass transfer of a solute in water to the electrode proceeds very efficiently owing to hemispherical diffusion of the solute. This is proved by a characteristic sigmoidal current-potential curve in the CV, different from a peak current observed at a millimeter-size electrode (linear diffusion) [32,64]. Using... 

Note that the reversible l(E, t) response is expressed as a product of a potential-dependent function ((c 0 - c Rt l)/( + ye 1)) and a time-dependent function (FA sjDo/(nt)). This behavior is characteristic of reversible electrode processes. In the next sections the current-time curves at fixed potential (Chronoamperograms) and current-potential curves at a fixed time (Voltammograms) will be analyzed. 

The characteristics of the current-potential curves (polarograms) are similar to that discussed in Sect. 3.2.1.2.2 for planar electrodes. 

In single step voltammetry, the existence of chemical reactions coupled to the charge transfer can affect the half-wave potential Ey2 and the limiting current l. For an in-depth characterization of these processes, we will study them more extensively under planar diffusion and, then, under spherical diffusion and so their characteristic steady state current potential curves. These are applicable to any electrochemical technique as previously discussed (see Sect. 2.7). In order to distinguish the different behavior of catalytic, CE, and EC mechanisms (the ECE process will be analyzed later), the boundary conditions of the three processes will be given first in a comparative way to facilitate the understanding of their similarities and differences, and then they will be analyzed and solved one by one. The first-order catalytic mechanism will be described first, because its particular reaction scheme makes it easier to study. 

Eq. (42) gives rise to a negative feedback loop if the current potential curve is S-shaped, but not for Z-shaped characteristics. Thus, in S-NDR systems DL may stabilize the middle branch of the S, or it may induce oscillations. This is not possible in Z-shaped systems, where an incorporation of DL in the dynamic description only increases the width of the bistable region but never results in qualitatively different behavior. For this reason, DL is not an essential variable in the latter type of systems. Thus, they have to be classified as systems with chemical instabilities only and will not be further treated here. 

We first discuss current-potential curves in supporting electrolyte solutions [38, 39] as a base characteristic of diamond electrodes. It is these curves that are the background against which the kinetic, impedance, photoelectrochemical, electro-analytical properties of diamond electrodes manifest themselves. 

To conclude with the primary electrode characteristics, we describe briefly the DLC electrodes. The data are scarce and partly contradictory, probably due to the differences in film preparation methods. According to Howe [60], even films as thin as 50 nm are quite stable against corrosion. However, in later works [61, 62] such thin films turned permeable for electrolytes. The penetration of the electrolyte to a substrate metal resulted in its corrosion and, ultimately, in film peeling. Thicker films (0.1 to 1 pm) were less subjected to damage. The current-potential curves in supporting electrolytes resemble those for crystalline diamond electrodes (see Figs. 7, 8) the potential window is narrower, however [63], Fluorination of a-C H enhances corrosion resistance of the films significantly [64],... 

Similar results were obtained by Clerbois et a1 (45). These authors compared the current-potential curves of two 18 /B stainless steels tempered for two hours at 650°C one of the steels was Ti-stabilized and the other contained no Ti. The Ti-free-steel (A. LS. I. 302) shows a characteristic peak in 20% H2SO4 at a potential of - 50 mV. This peak corresponds to cfee corrosion sensitization of the grain boundaries. The Ti-stabilized steel (A, l. S. L 347) is not sensitized by the same tempering and does not show any peak at - 0.50 mV (Fig, 20). Similar observations have been presented more recently by Serge and Jacquet (4c). 

Fig. 6. The anodic portion of the potentiodynamic current-potential curve for El 11/A (400 rpm) [186, 187], exhibiting a characteristic current density maximum.

It is easily seen from this simple representation that as soon as the rate of the chemical removal of P is larger than that of the back electron transfer, the rate-determining step of the overall process is the forward electron transfer. Thus, independently of the intrinsic value of k°, the Butler-Volmer law in Eq. (109) simplifies to that in Eq. (117), because (P)x=o is made negligible. As a result, the R/P electron transfer presents all the kinetic characteristics of a slow electron transfer [85]. However, since this behavior is not related to the intrinsic value of k°, the current-potential curve may be observed in the close vicinity of E° or even positive to E° for a reduction (negative to E° for an oxidation) [81]... 

Figure 23. Cyclic voltammetry, (a) Imposed potential versus time variations, (b) Resulting transient current-potential curve for a simple electron transfer. The concentration profiles of the reactant R and product P are indicated at various characteristic potentials of the voltammogram. Epc and Epa, cathodic and anodic peak potentials, (c) Schematic change of the cyclic voltammogram as a function of the chemical stability of the product.

The photoeletrochemical behavior has been extensively studied by Hodes [35, 36]. Surprisingly, the corresponding current-potential curve measured with such an electrode (CdSe) in contact with an electrolyte containing, for example, /Sp as a redox system, showed a typical diode characteristic (Fig. 9.34). On the other hand, when a gold layer was deposited on the CdSe nanocrystalline film instead of making a contact... 

Figure 3 shows current - potential curves (b-f) for 5 solutions with 2 mM KAu(CN)2 + 1 M KOH with different concentrations of KCN, hence, with different equilibrium potentials for the Au(CN)2 / Au redox couple. The scan rate was 10 mV s 1 in all cases. The KCN concentration was varied from 2 M (curve b), corresponding to a redox potential of -1.01 V, to 0.02 M (curve e) which corresponds to a redox potential of -0.78 V. Curve a corresponds to the current - potential characteristics in 0.04 M KCN at pH 14. It can be seen that the gold deposition peak shifts to more negative potential with... 

In this work, the main aim has been to determine the steady-state behaviour behaviour by measuring the current-potential curve. In general, the steady state is the most important characteristic of an electrode reaction. Fortunately, most known electrochemical reactions have a steady state and are variations of the redox type of reaction. As shown above, the steady current-potential curve can be exactly interpreted for redox reactions. In order carry out a complete analysis, it is essential to measure the components of the steady state by impedance-potential measurements. In addition, impedance delivers information about the charging processes as they appear in the high-frequency double layer capacity-potential curve. This last parameter is the parameter which should connect electrochemistry and surface science. The unfortunate fact is that it is still not very well understood. 

Fig. 14. Rotating (45 Hz) ruthenium dioxide/titanium dioxide electrode (35% w/w ruthenium dioxide) in 0.1 M NaCl solution, (a) Standard rate constant-potential curve for the chloride oxidation reaction [reaction (1)] assuming a constant Tafel slope of 70mV, Da — 5 x 10 6cm s 1, Z)cl2 = 7 x 10 6cm s 1, E[ = 1050mV SCE, and R = 2.2ohm cm2. The characteristics of the oxygen evolution reaction [reaction (2)] with a Tafel slope of 200 mV were chosen to be fej, = 1 x 10 8 cm s, EH = 1257 mV SCE and Dq2 = 1 x 10 5 cm2 s 1, (b) Common experimental and calculated current-potential curve using parameters of Fig. 14(a). The broken curve refers to the calculated "reversible curve.

Fig. 20. Typical result of measuring the characteristics of dissolution of a dental amalgam (Dispersalloy, electrode 37 HD) in 2/3 strength Ringer s solution. The measurements are almost in the steady state at 60 s per potential point, (a) Charge transfer-potential curve (b) Current-potential curve, also showing the return potential sweep and (c) double layer capacity-potential curve.

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