Reaction current versus potential curve

We again consider a transfer of redox electrons via the conduction band medi-anism as shown in Fig. 8-23. The anodic and cathodic transfer currents of redox electrons have been given in Eqns. 8-56 and 8-57, respectively. In these equations, the state density occupied by electrons in the conduction band is approximated by the concentration of conduction band electrons at the electrode interface, n, = j Dsc(E)A(E-eF(8C))dE and the state density vacant for electrons in the conduction band is approximated by the effective state density of the conduction band, Nc Nc n, j Dsd ) 1-f(e-ef ac ) de. Further, the state density of 

Under the condition of band edge level pinning, where the interfacial electron level of electrode relative to the redox electron level of redox particles is imchanged, the level differences of ej - ered and ej. - eqx remain constant irrespective of any change of the electrode potential. Consequently, the anodic transfer current of redox electrons, in(T ), in Eqn. 8—60 is independent of the overvoltage and remains equal to the exchange current ia.o as expressed in Eqn. 8-62  

On the other hand, the cathodic transfer current of redox electrons, i (ii), in Eqn. 8-61 is proportional to the concentration, n, of interfacial electrons in the electrode n. varies as an exponential fimction of overvoltage t), n. = n°exp -ej JkT) hence, j (ti) is an exponential function of overvoltage t) as shown in Eqn. 8-63  

Consequently, for the transfer reaction of redox electrons via the conduction band mechanism, the anodic current is constant and independent of the electrode potential whereas, the cathodic current increases with increasing cathodic overvoltage (decreasing electrode potential). 

Similarly, for the transfer reaction of redox holes via the valence band mechanism the anodic and cathodic currents, ip(ii) and ip(ii), are obtained, respectively, as shown in Eqns. 8-64 and 8-65  

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Figure 1 shows typical current density-potential curves of an electroorganic reaction. In this example, the thin line represents the anodic oxidation of the electrolyte without reactants at a higher potential, here at more than 0.8 V versus NHE. If the reactant 1 is present, it can be converted according to the thick compact lines at lower potentials above 0.2 V versus NHE, and this selectively can occur up to 0.5 V versus NHE. Over 0.5 V versus NHE also, an additional reactant... 

In controlled-potential coulometry, the potential of the working electrode is maintained at a constant level such that only the analyte is responsible for conducting charge across the electrode/solution interface. The charge required to convert the analyte to its reaction product is then determined by recording and integrating the current-versus-time curve during the electrolysis. 

Fig. 2.13 Current versus overpotential curves showing the effect of experimental parameters in the presence of forced convection, according to the relationship = /cL lnFc. (a) Electrode size (and shape). Ideally, in the presence of a uniform current-density distribution, Deviations may be due to edge effects, non-uniformity of flow (e.g. entrance length effects) or contributions from natural convection, (b) Concentration of electroactive species in the reactor. ii should be proportional to c. It is sometimes convenient to test this by incremental increases in c . The background curve is represented by = 0. (c) Relative velocity of the electrolyte or electrode, cc where x is a constant which depends upon the geometry and flow conditions, x may vary slightly over different ranges of Reynolds number. The limiting-current plateau may shorten and tilt as velocity increases, due to the increasing importance of electron transfer to the overall reaction kinetics. The maximum on the 1 curve may arise due to unsteady-state mass transport and is akin to a peak in linear sweep voltammetry, i.e. it may arise due to an excessive rate of potential change.

According to the literature [21], all reported electrochemical oscillations can be classified into four classes depending on the roles of the true electrode potential (or Helmholtz-layer potential, E). Electrochemical oscillations in which E plays no essential role and remains essentially constant are known as strictly potentiostatic (Class I) oscillations, which can be regarded as chemical oscillations containing electrochemical reactions. Electrochemical oscillations in which E is involved as an essential variable but not as the autocatalytic variable are known as S-NDR (Class II) oscillations, which arise from an S-shaped negative differential resistance (S-NDR) in the current density (/) versus E curve. Oscillations in which E is the autocatalytic variable are knovm as N-NDR (Class III) oscillations, which have an N-shaped NDR. Oscillations in which the N-NDR is obscured by a current increase from another process are knovm as hidden N-NDR (HN-NDR Class IV) oscillations. It is known that N-NDR oscillations are purely current oscillations, whereas HN-NDR oscillations occur in both current and potential. The HN-NDR oscillations can be further divided into three or four subcategories, depending on how the NDR is hidden. 

The type of electrode reaction employed, the cell geometry, and the manner in which the limiting-current measurement is carried out determine the shape of the current versus electrode-potential curve. Often the ideal horizontal inflection in such curves is absent, making the determination of true limiting current problematical if not impossible. Characteristics of satisfactory limiting current plateaus are as follows ... 

Figure 8-24 illustrates schematicaUy the transfer reaction currents of redox electrons and redox holes as functions of electrode potential these reaction cur rent versus electrode potential curves are obtained from the formulation of the reaction currents in Eqns. 8-62 through 8-65. 

Fig. 10-28. Polarization curves for cell reactions of photoelectrolytic decomposition of water at a photoezcited n-type anode and at a metal cathode solid curve M = cathodic polarization curve of hydrogen evolution at metal cathode solid curve n-SC = anodic polarization curve of oxygen evolution at photoezcited n-type anode (Fermi level versus current curve) dashed curve p-SC = quasi-Fermi level of interfadal holes as a ftmction of anodic reaction current at photoezcited n-type anode (anodic polarization curve r re-sented by interfacial hole level) = electrode potential of two operating electrodes in a photoelectrolytic cell p. sc = inverse overvoltage of generation and transport ofphotoezcited holes in an n-type anode.

If the product of the tip or substrate ET reaction [Eqs. (1) and (3)] participates in a homogeneous reaction within the tip-substrate gap, the feedback response is altered. In this case, the shape of the iT versus d curve depends on the rate of the homogeneous chemical reaction [84]. If the tip and the substrate are biased at extreme potentials, so that reactions (1) and (3) are rapid, the shape of the SECM current-distance curve for a relatively simple mechanism is a function of a single kinetic parameter, K = const x kc/D, where kc is the rate constant of the irreversible homogeneous reaction. 

In the simplest case E is the potential applied between two electrodes in solution and / is the current flowing in the circuit. Curve a in Fig. lA represents the dependence of current on potential when the process is controlled by the kinetics of the reaction alone. Curve b takes into account the effects of mass transport. These concepts are explained in detail in the section that follows. In actual measurement the potential E is always measured versus a fixed reference electrode and instead of the current one refers to the current density on the electrode being studied, but at this point we need not concern ourselves with these refinements. 

The slope of the plot of logarithm of current density versus potential, which characteristically is linear for an activation-controlled reaction, is defined as the Tafel slope. The Tafel slope determined in the exponential region of an i-V curve in HE solutions is about 60 mV/decade for p types and heavily doped n types of silicon samples as shown in Table 5.3. For lowly doped n-Si, since illumination is required... 

This requirement is shown graphically in Fig. 34.12, which shows the z versus t] curves for the zinc dissolution reaction and for the hydrogen evolution reaction. At the potential 0 M 5 the current densities sum to zero. At this point, z = z corr the corrosion current density. The potential of the Zn-Pt composite is a mixed potential, 0m- Since is determined by... 

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