Overpotential current density curves

Figure 2.3 Current density—overpotential curves of 0 + n e R reaction at three different exchange current...

Figure 2.4 Current density—overpotential curves of 0 -i- nae <- / reaction at three different electron-transfer coefficients (a = 0.25, 0.5, and 0.75, respectively), calculated according Eqn (Z28a) using the parameter values of = / =8.314 J mol, T=298 K, F=96,487 CmoP, and /=1.0x 10 Acm . (For color version of this...

The current density-overpotential curve equation (Eq. (1.20)), derived by taking the concentration dependence of io into account and the linear dependence of /q on the Cs/Cq ratio, can be rewritten in the form ... 

Figures 26.2 and 26.3 show typical current density-overpotential plots where i varies exponentially with r s, in accordance with the Butler-Volmer equation. In Figure 26.2, the effect of varying P on )-r 5 curves is shown (as P decreases, i increases at a given value of 1I5). The increase in current density at a given for increasing values of i is shown in Figure 26.3. From these two figures it can be concluded that electrochemical reactions that follow Butler-Volmer kinetics will be facile when the kinetic parameter p is small and the value of is large.

The results of such measurements are known as current density-potential curves. They represent cumulative curves given by the superimposition of the current density-potential curves of the individual reactions. For simple electrodes with defined electrode processes, these are the overpotential curves. For metals exposed to electrolytic attack, superimposition of several overpotential curves gives the actual current density-potential curves that are of significance in corrosion testing and research. Figure 20.9 shows the superimposition of the overpotential curves of a hydrogen electrode... 

FIGURE 20.9 Superimposition of the overpotential curves to form a current density-potential curve. 

Simple, purely transfer-related electrode reactions give cumulative current density-potential curves of the type shown by the unbroken Une in Figure 20.11. At the points pi and pj, it swings into the overpotential curves of the respective part reactions because beyond these points, only the anodic or cathodic reaction exists. At these points, the equilibrium potentials of the reverse reaction exceeded and superimposition no longer occurs. These pure overpotential curves thus form linear Tafel lines, which, after reflection of the cathode curve in the x-axis, can be made to intersect by extrapolation in the direction of the abscissa. The ordinate section at the point of intersection is then log that is, the log of the corrosion current density, rest potential, from which the corrosion rate can be calculated by Faraday s law. 

In the description given outlining electrochemical systems in which a current flows, key parameters include the variations of the anodic and cathodic polarisations (or overpotentials if applicable) as a function of current and time. These relationships are generally represented in the form of current-potential curves of an electrode, /= f(E), where E is the voltage between the electrode in question and a reference electrode . The experimental results can also be presented in the form of current density-potential curves. However, when the study concerns the whole electrochemical system and is not just focused on the working electrode, it is best to keep the current-potential representation I... 

Using the current density-overpotential relationships and the procedure for the determination of the ohmic potential drop, the polarization curves for electrodeposition processes can be successfully simulated [9, 20]. 

FIGURE 4.33 The model shapes of (a) the MOR rate and (b) the proton current density (solid curves) and local MOR overpotential (dashed curves) through the catalyst layer thickness, for the indicated mean cell current density. Cell temperature is 70°C. Parameters for the calculations are taken from the curve fitting in Figure 4.31. 

FIGURE 4.34 (a) The uniform (solid line) and optimal (dashed line) relative ionomer content in the cathode catalyst layer (CCL) of a PEFC. (b) The respective distributions of overpotential (two upper curves) and proton current density (lower curves) through the CCL. 

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.

Fig, 1.24 Tafel lines for a single exchange process. The following should be noted (a) linear f-log I curves are obtained only at overpotentials greater than 0-052 V (at less than 0-052 V E vs. i is linear) b) the extrapolated anodic and cathodic -log / curves intersect at tg the equilibrium exchange current density and (c) /, and the anodic and cathodic current densities... 

Polarisation Resistance slope of the linear plot of overpotential versus current density measured at potentials close to the corrosion potential, or the tangent of such a curve at the corrosion potential if the plot is not linear. If a small change in potential, A , gives rise to a change in current density. A/, then the polarisation resistance is / p(Q m ) = AE/Ai. 

Fig. 5.2 Dependence of the relative current density j/j0 on the overpotential rj according to Eq. (5.2.28). Various values of the charge transfer coefficient a are indicated at each curve. Dashed curves indicate the partial current densities (Eqs 5.2.11 and 5.2.12 for a = 0.5). (According to K. Vetter)...

Plotting the overpotential against the decadic logarithm of the absolute value of the current density yields the Tafel plot (see Fig. 5.3). Both branches of the resultant curve approach the asymptotes for r RT/F. When this condition is fulfilled, either the first or second exponential term on the right-hand side of Eq. (5.2.28) can be neglected. The electrode reaction then becomes irreversible (cf. page 257) and the polarization curve is given by the Tafel equation... 

Figure 3a is an illustration of the effect of surface overpotential on the limiting-current plateau, in the case of copper deposition from an acidified solution at a rotating-disk electrode. The solid curves are calculated limiting currents for various values of the exchange current density, expressed as ratios to the limiting-current density. Here the surface overpotential is related to the current density by the Erdey Gruz-Volmer-Butler equation (V4) ... 

It is clear from the calculated limiting-current curves in Fig. 3a that the plateau of the copper deposition reaction at a moderate limiting-current level like 50 mA cm 2 is narrowed drastically by the surface overpotential. On the other hand, the surface overpotential is small for reduction of ferri-cyanide ion at a nickel or platinum electrode (Fig. 3b). At noble-metal electrodes in well-supported solutions, the exchange current density appears to be well above 0.5 A/cm2 (Tla, S20b, D6b, A3e). At various types of carbon, the exchange current density is appreciably smaller (Tla, S17a, S17b). 

The last part of the polarization curve is dominated by mass-transfer limitations (i.e., concentration overpotential). These limitations arise from conditions wherein the necessary reactants (products) cannot reach (leave) the electrocatalytic site. Thus, for fuel cells, these limitations arise either from diffusive resistances that do not allow hydrogen and oxygen to reach the sites or from conductive resistances that do not allow protons or electrons to reach or leave the sites. For general models, a limiting current density can be used to describe the mass-transport limitations. For this review, the limiting current density is defined as the current density at which a reactant concentration becomes zero at the diffusion medium/catalyst layer interface. 

Equation 1.7 for the reduction of protons at a mercury surface in dilute sulphuric add is followed with a high degree of accuracy over the range -9 Tafel plot i.s shown in Figure 1.5. At large values of the overpotential, one reaction dominates and the polarization curve shows linear behaviour. At low values of the overpotential, both the forward and back reactions are important in determining the overall current density and the polarization curve is no longer linear. 

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