Current-potential relation

Fig. 2-15 Current-potential relation for passivatable metals (explanation in the text), = passivating current, = activation current.

In general, the effects of the process variables on electrocodeposition are often interdependent and therefore, are ill understood. Often a slight change of one variable can sometimes lead to a dramatic change in the amount of particle incorporation. For specific systems, the current density at which maximum incorporation occurs seems to be related to a change in the slope of the current-potential relation-... 

The complete current-potential relation is shown in Fig. 6.3. For small overpotentials we observe Butler-Volmer behavior, for large overpotentials a limiting current. 

In Figure 16 is shown the photo-current / potential relation for an n-type GaP anode and a p-type GaP cathode. The current at zero applied potential is larger in this case, but this is because the anodic reaction is dissolution of the GaP and not oxygen evolution. 

Boltzmann term, 1078 computer simulation. 1161 current density, 1078, 1081 current potential relation, 1082 doping, 1073 effect of light on, 785 -/junction, 1081 electrode kinetics of, 170 electrodeposition on, 1344... 

Fig. 7.24. The current-potential relation at a p-n semiconductor junction differs from that of an electrode/solution interface by being totally asymmetrical.

The Current-Potential Relation at a Semiconductor/Electrolyte Interface (Negligible Surface States)21... 

Equation (7.7), in which cR is the concentration of an intermediate, may give an erroneous impression that the current-potential relation is completely determined by the exponential term in d< ). However, species R was the result of a series of charge-transfer mechanisms, and thus its concentration, as shown below, is also potential dependent. To unravel this dependence, it will be recalled that all steps preceding and following the rds can often be assumed to be at equilibrium. Then, one can equate their forward and backward rates, e.g., for the first step A + e B,... 

R. Parsons, Trans. Faraday Soc. 147 1332(1951). General scheme for current-potential relations and mechanism determination. 

By eliminating 0 between Eqs. (7.220b) and (7.207) one obtains the required current-potential relation ... 

The Steady-State Current-Potential Relation under Conditions of Transport Control... 

In order to convert a current-potential relation from one based on the assumption that transport is plentiful to one that takes into account both transport and the interfacial reactions, it is first necessary to relate ce, the concentration of the reactant ion (or... 

Fig. 8.14. Current-potential relation for two-electron transfer for E, > E The scan rate is 0.1 mV s-1. (Reprinted from D. Gosser, Cyclic Voltammetry, pp. 74, 77, 84, copyright 1993, VCH-Wiley. Reprinted by permission of John Wiley Sons, Inc.)...

Why did we introduce this purely experimental material into a chapter that emphasizes theoretical considerations It is because the ability to replicate Tafel s law is the first requirement of any theory in electrode kinetics. It represents a filter that may be used to discard models of electron transfer which predict current-potential relations that are not observed, i.e., do not predict Tafel s law as the behavior of the current overpotential reaction free of control by transport in solution. 

Fundamentals of Electrode Reactions and Current-Potential Relations... 

In many electrochemical techniques, we measure current-potential curves for electrode reactions and obtain useful information by analyzing them. In other techniques, although we do not actually measure current-potential curves, the current-potential relations at the electrodes are the basis of the techniques. Thus, in this section, we briefly discuss current-potential relations at the electrode. 

The current-potential relation for process (2) and that for the whole process [(1) to (3)] are discussed in the following sections. 

Current-Potential Relation for Electron Transfer at the Electrode... 

Figure 5.3 shows the current-potential relations for a=0.25 and 0.50.2) At E=Eeq, the net current (i) is equal to zero but currents of the same magnitudes (i0) flow in opposite directions. i0 is called the exchange current. The net current is an oxidation current (anodic current) at E>Eeq and a reduction current (cathodic current) at E[Pg.113]

Fig. 5.3 Current-potential relations for electrode reactions with a= 0.25 (left) and 0.50 (right).

From the current-potential relation, we can determine the current at a given potential and, inversely, the potential at a given current. 

Fig. 5.4 Current-potential relations for electrode reactions with (a) a large exchange current (small overpotential) and (b) a small exchange current (large overpotential).

The current-potential relation in Eq. (5.9) is shown by curves 1 to 3 in Fig. 5.6. Curve 2 is for CRed=0 and curve 3 is for COx=0. The curves are S-shaped and the currents at potentials negative enough and positive enough are potential-indepen-dent, being equal to ig and igi, respectively. These currents are called limiting currents and are proportional to the bulk concentrations of Ox and Red, respectively [Eqs (5.7) and (5.8)]. The potential at i = (ig + ibi)/2 is equal to E1/2 in Eq. (5.10) and is called the half-wave potential. Apparently from Eq. (5.10), the half-wave potential is independent of the concentrations of Ox and Red and is almost equal to the standard redox potential E°, which is specific to each redox system. From the facts that the limiting current is proportional to the concentration of the electroactive species and that the half-wave potential is specific to the redox system under study, the current-potential relation can be used both in quantitative and qualitative analyses. 

Curves 4 and 4 in Fig. 5.6 show an example of the current-potential relation obtained for an irreversible electrode process. For a reversible electrode process, the reduction wave appears at the same potential as the oxidation wave, giving an oxidation-reduction wave if both Ox and Red exist in the solution (curves 1, 2 and 3 in Fig. 5.6). For an irreversible process, however, the reduction wave (curve 4) is clearly separated from the oxidation wave (curve 4 ), although the limiting currents for the two waves are the same as those in the reversible process. The cur-rent-potential relation for the irreversible reduction process can be expressed by... 

Fig. 5.7 Current-potential relations for an irreversible electrode reaction.

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