Current-potential curves Evans diagram

Fig. 2. Current-potential curves in Evans diagram [29] format for reduction of Cu2+ ions and oxidation of H2CO. and are the equilibrium, or open circuit, potentials for the Cu2+ reduction and H2CO oxidation reactions, respectively. Assuming negligible interfering reactions, the vertical dashed lines indicate the exchange current densities for the two half reactions, and the deposition current for the complete electroless solution. Adapted from ref. 23.

Figure 8.3. Evans diagram of current-potential curves for a system with two different simultaneous electrochemical reactions. Kinetic scheme Eqs. (8.4) and (8.5).

Figure 8.4. Current-potential curves for the reduction of Cu ions and the oxidation of reducing agent Red, formaldehyde, combined into one graph (an Evans diagram). Solution for the Tafel line for the reduction of Cu ions O.IM CUSO4, 0.175M EDTA, pH 12.50, Egq (Cu/Cu ) = -0.47 V versus SCE for the oxidation of formaldehyde 0.05 M HCHO and 0.075 M EDTA, pH 12.50, (HCHO) = -1.0 V versus SCE temperature 25 0.5°C. (From Ref. 10, with permission from the American Electroplaters and Surface Finishers Society.)...

The rate of deposition and the mixed potential are determined on the basis of the mixed-potential theory using the Evans diagram. First, the current-potential curve... 

The particular form of the Evans diagram obtained depends upon the current-potential curves for the metal-dissolution and electronation reactions. Some of the common diagrams are shown in Figs. 12.18 to 12.20. They cover situations in which... 

An alternative method of presenting the current-potential curves for electroless metal deposition is the Evans diagram. In this method, the sign of the current density is suppressed. Figure 22 shows a general Evans diagram with current-potential functions i = f(E) for the individual electrode processes, Eqs (43 and 44). According to this presentation of the mixed-potential theory, the current-potential curves for individual processes, ic = iu = f(E) and ia = = f(E), intersect. The... 

Figure 3 Logarithmic presentation of current-potential curve of a mixed electrode (Evans diagram) showing the corrosion potential and the corrosion current density i. The broken lines indicate the partial current densities.

Fig. 3. Hypothetical Evans diagram and polarization curve for a metal corroding in an acidic solution, where point A represents the current density, /q, for the hydrogen electrode at equiUbrium point B, the exchange current density at the reversible or equiUbrium potential, for M + 2e and point...

The sohd line in Figure 3 represents the potential vs the measured (or the appHed) current density. Measured or appHed current is the current actually measured in an external circuit ie, the amount of external current that must be appHed to the electrode in order to move the potential to each desired point. The corrosion potential and corrosion current density can also be deterrnined from the potential vs measured current behavior, which is referred to as polarization curve rather than an Evans diagram, by extrapolation of either or both the anodic or cathodic portion of the curve. This latter procedure does not require specific knowledge of the equiHbrium potentials, exchange current densities, and Tafel slope values of the specific reactions involved. Thus Evans diagrams, constmcted from information contained in the Hterature, and polarization curves, generated by experimentation, can be used to predict and analyze uniform and other forms of corrosion. Further treatment of these subjects can be found elsewhere (1—3,6,18). 

Fig. 5. Tentative mixed potential model for the sodium-potassium pump in biological membranes the vertical lines symbolyze the surface of the ATP-ase and at the same time the ordinate of the virtual current-voltage curves on either side resulting in different Evans-diagrams. The scale of the absolute potential difference between the ATP-ase and the solution phase is indicated in the upper left comer of the figure. On each side of the enzyme a mixed potential (= circle) between Na+, K+ and also other ions (i.e. Ca2+ ) is established, resulting in a transmembrane potential of around — 60 mV. This number is not essential it is also possible that this value is established by a passive diffusion of mainly K+-ions out of the cell at a different location. This would mean that the electric field across the cell-membranes is not uniformly distributed.

Fig. 12.17. The Evans diagrams are plots of the potentials of the two reactions (a) vs. the magnitude of the two currents or (b) vs. their logarithms. The intersections of the curves define the corrosion current and corrosion potential.

The above two methods ofpreventing corrosion can be understood easily with an Evans diagram (Fig. 12.39 see Section 12.19). (These diagrams it will be recalled, result from the superposition of the potential-current curves of the electronation and... 

The data discussed in Figs. 20 through 24 represent the type of data in a polarization curve combinations of potential and applied current density. Figure 26 shows a complete polarization curve for the iron in acid systems for which the Evans diagram is shown in Fig. 25. The Evans lines are included as dotted lines in the figure. The difference between the Evans diagram and the polarization curve is that the polarization curve data display applied current densities, whereas the Evans diagram displays the reaction rates in terms of current densities. 

Consider the two materials whose polarization curves are shown in Fig. 31. Both the polarization curves and the Evans lines are shown for both materials. Material 1 is the more noble material (i.e., it has a more positive Ec0II) and has a lower circuit corrosion rate when it is uncoupled. If the surface area of the two materials is the same and the materials are coupled, then the two material-solution interfaces must come to the same potential. In a manner identical to that used for the example of iron in acid used to introduce Evans diagrams, the potential and current at which this condition is met can be found by applying the conservation of charge to the sysytem ... 

Figure 5 Schematic Evans diagram and resulting potential-controlled polarization curve for a material that undergoes an active-passive transition and is in a reducing solution. The heavy line represents the applied currents required to polarize the sample.

Figure 6 Schematic Evans diagram and resulting potential-controlled polarization curve for a material that undergoes an active-passive transition and is in an oxidizing solution. The heavy line represents the applied currents required to polarize the sample. If the sample did not undergo an active-passive transition, it would corrode at a much higher rate in this solution, as is indicated by the intersection of the dotted line and the cathodic curve.

Figure 8 Schematic Evans diagram and potential-controlled polarization curve for a material/environment combination that exhibits a cathodic loop. Note that the direction of the applied current changes three times in traversing the curve.

These equations are straight lines in a plot of E versus log i, such as that in Fig. 2. This plot of versus log i is called an Evans diagram. Actually, the Butler-Volmer equation is described better by the curve in Fig. 5. The net current at the reversible potential is zero because the forward and reverse current, each equal to the exchange current density, balance each other. The log of the current density approaches negative infinity at the reversible potential at which the net current density goes to zero, and the polarization curve points down at the reversible potential when plotted on semilogarithmic axes. 

Some books also call these curves polarisation curves, especially those which choose to represent the potential as a function of the current. The Evans diagrams, depicting the use of currents in corrosion, provide an example of such a type of representation. In this document, we will only choose to use the current-potential representation which is quite a natural choice if the data are recorded using potentiostatic techniques. 

---