Current-potential curves transient

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... 

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.

Cyclic voltammetry is a widely used electrochemical technique, which allows the investigation of the transient reactions occurring on the electrode surface when the potential applied to the electrode is varied linearly and repetitively at a constant sweep rate between two given suitable limits. The steady-state current-potential curves or voltammograms provide direct information as to the adsorption-desorption processes and allow estimating the catalytic properties of the electrode surface. 

A great deal of effort has been spent in studying the mechanisms of complex electrode reactions. One general approach is based on steady-state current-potential curves. Theoretical responses are derived on the basis of mechanistic alternatives, then one compares predicted behavior, such as the variation of exchange current with reactant concentration, with the behavior found experimentally. A number of excellent expositions of this approach are available in the literature (8-14, 25, 26, 35). We will not delve into specific cases in this chapter, except in Problems 3.7 and 3.10. More commonly, complex behavior is elucidated by studies of transient responses, such as cyclic voltammetry at different scan rates. The experimental study of multistep reactions by such techniques is covered in Chapter 12. 

This particular characteristic of current-potential curves is linked to the steady character, which is chosen for this description. In transient experiments such as voltammetry, using a copper electrode with no CcF ions in the solution, one would see a reduction current during the reverse scan of the... 

The dissolution inhibition is easily seen if, at selected times, one generates the current-potential curves from the current transients shown in Figure 4. These selected cunent voltammograms are shown in Figure 5(a) for times of 1 to 5 seconds. The dissolution inhibition is clearly seen as is tiie fact that shorter times are required to inhibit tiie dissolution when larger potential steps ate imposed. It is also apparent that when the potential of the niobium wire is stepped to values above 1.4V, inhibition is avoided altogether. It is not clear whether tiiis is due to the oxidation of niobium to a higher, more soluble oxidation state or by some interaction with Cl which may be present on tiie niobium surface due to the oxidation of AlCV. 

Oscillatory behavior observed as periodic potential transients at constant current or periodic current transients at constant potential is found frequently when more than two parallel electrode reactions are coupled. Usually, an upper and a lower current-potential curve limit the oscillation region. These two curves represent stable states [139] according to the theory of stability of electrode states [140]. Oscillatory phenomena occurring during the oxidation of certain fuels on solid electrodes are discussed in this section. The discussion is not extended to porous electrodes because the theory of the diffusion electrode has not been developed to the point to allow an adequate description of the complex coupling of parallel electrode reactions and mass transport processes in the liquid and gaseous phase. 

The variation of the diffusion layer thicknesses at planar, cylindrical, and spherical electrodes of any size was quantified from explicit equations for the cases of normal pulse voltammetry, staircase voltammetry, and linear sweep voltammetry by Molina and coworkers (Molina et al., 2010a). Important limiting behaviours for the linear sweep voltammetry current-potential curves were reported in all the geometries considered. These results are of special physical relevance in the case of disk and band electrodes which possess non-uniform current densities since general analytical solutions were derived for the above-mentioned geometries for the first time. Explicit analytical expressions for diffusion layer thickness of disk and band electrodes of any size under transient conditions... 

Bioanalytical Systems BAS 100 and BAS lOOA Electrochemical Analyzers, a PAR 174 polarograph and a pulse generator-transient recorder combination were used for performing cyclic voltammetry, linear-sweep voltammetry, and chronocoulometry. Rotating-disc current-potential curves were recorded with a Tacussel model EDI electrode operating at rates of 100 to 2500 rpm. All measurements were made at ambient temperature (21 2 C) in a single-compartment cell employing saturated calomel (SCE) or saturated sodium chloride calomel (SSCE) reference electrodes and platinum discs as counter electrodes. 

Potential Sweep Method, In the transient techniques described above, a set of measurements of the potential for a given current or the current for a given potential is measured in order to construct the current-potential function, i = f(E). For example, the Tafel lines shown in Figure 6.20 were constructed from a set of galvanostatic transients of the type shown in Figure 6.18. In the potential sweep technique, i = f(E), curves are recorded directly in a single experiment. This is achieved by sweeping the potential with time. In linear sweep voltammetry, the potential of the test electrode is varied linearly with time (Fig. 6.23a). If the sweep rate is... 

The SG/TC mode of SECM was also applied by Martin et al. [86] to study the oxidation of DMPPD. The generator was a 2-mm2 substrate electrode, and the collector was a 25-pm diameter Pt disk electrode. The substrate potential was stepped from 0 V versus Ag quasi reference electrode, where no Faradic process took place, to +500 mV, where the oxidation of DMPPD was diffusion controlled. The tip potential was held at 0 V, at which the oxidized form of DMPPD could be reduced at a diffusion controlled rate. After the tip-substrate separation was found from the positive feedback current-distance curve, the rate constant was obtained from the current transient at the tip. The feedback and SG/TC modes were also used to study the reduction of... 

In practice there are several limitations to such measurement. Obviously it implies that both members of the half-reaction are sufficiently stable for a cell to be realized. This is a serious difficulty in organic chemistry owing to usual great reactivities of the species formed upon electron transfers. For the most frequent cases it is then impossible to rely on reversible thermodynamic transformations to determine experimental values of standard reduction potentials. However, these important figures, or at least very precisely approximated values, can be obtained from current intensity potential curves or transient electrochemical methods as is discussed in a later section. 

Figure 5.12 (a) Logarithmic cathodic current transients experimentally obtained from the Liq -hs[Ti5/3LiT/3]O4 electrode at the potential drops from 1.700V (versus Li/Li ) to various lithium injection potentials below the plateau potential (b) Cumulative charge versus time plots reproduced from panel (a), along with electrode potential curve of Liq 5 7ri5y3Liqy3]O4. (Reproduced with permission from (a) Ref. [11] (b) Ref. [96].)... 

Both of these results are in good agreement with the digital simulation (22) a typical disk transient is shown in Figure 9.5.1. At short times, when the diffusion layer thickness is much thinner than Sq, the potential step transient follows that for a stationary electrode [equation 5.2.11]. The time required for the current to attain its steady-state value can be obtained from the curve in Figure 9.5.1. The current is within 1% of ii(ss) at a time T when... 

Chronoamperograms and chronopotenti-ograms More information with respect to the processes that are responsible for the low-current potential regime of the partial anodic polarization curves may be derived from current-time transients. As shown by Fig. 13, there is a continuous decay of the dissolution rate of Cu from a Cu—20 at.% Pd alloy in acidified 1 N Na2S04 (Ec 0.72 V) as long as < Ec-Similar transients have been reported in the hterature for other aUoy/electrolyte systems. Usually, they follow a power law of the form /(/) where m... 

Figure. 7. (a) Logariiiiniic cathodic current transients obtained experimentally with a LUV Oj electrode at potential drops frotn 3.43 V vs. Li/Li to various lithiutn injection potentials below the plateau potential, (b) Cunuilalive charge vs. r plots obtained from Figure 7(a), along with the electrode potential curve of LUV.2OS. Reprinted from with permission from Elsevier Science. 

Voltammetry under transient (e.g., cyclic voltammetry) or steady-state (e.g., rotated disk or microelectrode) conditions which requires the interpretation of current-potential-time (I-E-i) curves. 

Fig. 3.6 Current (upper curve) and potential (lower curve) transients due to potential step of 6 mV applied to electrical equivalent circuit R(C(R(CR))) current scale is 7 mA and potential scale is 2 mV per major division. The time scale is 50 ns per major horizontal division (From Ref [90] reproduced by permission of Electrochemical Society)...

It does have an effect, i.e., a drop in "current" transiently as the tip enters the cell, and only if there is a flat plateau in the current-voltage curve do we consider it an absolute measurer of p02 It is especially troublesome in the beating heart where the action potential (intracellular) varies with the applied voltage. 

---