Experimental Measured Polarization Curves

In the diode the cathode is usually a W filament which can be flashed and maintained as a reference electrode at a temperature above which adsorption occurs. The anode may be of similar construction or take the form of a metal film evaporated from an adjacent filament. Experimentally, current polarization curves are obtained, first for the clean anode surface A and then for the covered anode surface A. Alternatively, resistance-voltage characteristics are measured (SO). The potential difference comprises the applied polarization and the C.P.D. between the emitter and collector. For a given anode current j,... 

Interfacial ORR kinetic parameters (i, b) employed in the fit of the model to experimental PEFC polarization curves must be in reasonable agreement with the parameters measured in studies of the ORR at model Pt/ionomer interfaces [3-6, 9]... 

Similarly to the one-dimensional chain, the borders within the framework of which function (o(k) is independent are outlined. Such borders form the three-dimensional Brillouin zone. The picture of the dispersion curves dependent on direction and from wave polarization, becomes complex and, frequently, confusing. Figure 9.18 shows an example of experimentally measured dispersion curves in an aluminum crystal for the different directions specified in the figure Figure 9.19 presents an example of the oscillation frequency distribution function gico). 

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). 

The straight lines for the partial CD t andT in Fig. 63b intersect at the equilibrium potential AE = 0. The value of CD corresponding to the point of intersection is that of the exchange CD f, according to Eq. (6.11). It follows that the exchange CD can be determined when the linear sections of the anodic or cathodic polarization curve, which have been measured experimentally and plotted as log i vs. AE, are extrapolated to the equilibrium potential. Moreover, according to Eq. (6.19) the exchange CD can be determined from the slope of the polarization curve near the equilibrium potential when the curve is plotted as i vs. AE. 

Figure 15.2 shows polarization curves for hydrogen evolution at electrodes of different metals in acidic electrolyte solutions. The results of polarization measurements are highly sensitive to the experimental conditions, in particular to the degree of solution and electrode surface purification for this reason, marked differences exist among the data reported by different workers. The curves shown still provide the correct picture of the common features. 

Often, it will be found that currents for a given reaction cannot be measured at all metals at the same value of potential. At some metals the currents would be too low for a reliable, sufficiently accurate determination at others they might be too high for a satisfactory experimental realization. A comparison will then be possible only after an extrapolation of data obtained in a different region of potentials, to the value of selected for comparison. This extrapolation may not be sufficiently reliable where the Tafel section of the polarization curve is too short or indistinct. 

Whereas is relatively easy to determine from the calculated binding energies, it is not easy to measure experimentally, since the measured potentials are always related to a specific current. Therefore, in order to compare directly with experiment, we have to calculate polarization curves, i.e., the current. The link between Gqrr and the current is the Tafel equation. 

A perfect prototype of an ideally cation-permselective interface is a cathode upon which the cations of a dissolved salt are reduced. Experimental polarization curves measured on metal electrodes fit the theory very closely. Since in dimensional units the limiting current is proportional to the bulk concentration, the polarization measurements on electrodes may serve for determining the former. This is the essence of the electrochemical analytical method named polarography. (For the theory of polarographical methods see [28]—[30].)... 

Fig. 4.7. Calculated Hanle signal curves for P, R transitions (a) linear polarized excitation (Fig. 4.2,

Fig. 4.11. Hanle effect on the degree of linear polarization V = (/y — Iff/(I + Iff) at (P, f )-excitation 1 - superpositional signal calculated at the same conditions as Fig. 4.10, dots refer to the positions a, b, c, d as in Fig. 4.10 2 - pure excited state signal at x = 0 3 - pure ground state signal at gj> = 0 4 - experimentally measured dependence for Te2 under conditions as given in Fig. 4.6, curve 1, but in the region of weaker magnetic field and at strong pumping (x 3).

Given sufficient quantitative information about the electrochemical processes occurring, mixed potential theory can be used to predict a corrosion rate. Unfortunately, in the vast majority of cases, there are few data that can be applied with any confidence. In general, experimental measurements must be made that can be interpreted in terms of mixed potential theory. The most common of these measurements in electrochemical corrosion engineering is the polarization curve. 

Figure 5.25 Comparison of the results from stress corrosion tests with those from polarization curves at fast and slow potential sweep rates for different carbonate-bicarbonate solutions, indicating the extent to which the experimentally observed cracking range can be predicted from electrochemical measurements.8...

For most cases, the experimental and simulated time-varying current densities are in good agreement. Figures 5 and 6 compare measured and simulated polarization curves under different flow conditions. Here the dimensionless plate frequency is defined as Q = col /Dci , and Pe = Vfo/VUf/ /Dcu In these figures, each point is the time-average... 

The earlier sections of this chapter discuss the mixed electrode as the interaction of anodic and cathodic reactions at respective anodic and cathodic sites on a metal surface. The mixed electrode is described in terms of the effects of the sizes and distributions of the anodic and cathodic sites on the potential measured as a function of the position of a reference electrode in the adjacent electrolyte and on the distribution of corrosion rates over the surface. For a metal with fine dispersions of anodic and cathodic reactions occurring under Tafel polarization behavior, it is shown (Fig. 4.8) that a single mixed electrode potential, Ecorr, would be measured by a reference electrode at any position in the electrolyte. The counterpart of this mixed electrode potential is the equilibrium potential, E M (or E x), associated with a single half-cell reaction such as Cu in contact with Cu2+ ions under deaerated conditions. The forms of the anodic and cathodic branches of the experimental polarization curves for a single half-cell reaction under charge-transfer control are shown in Fig. 3.11. It is emphasized that the observed experimental curves are curved near i0 and become asymptotic to E M at very low values of the external current. In this section, the experimental polarization of mixed electrodes is interpreted in terms of the polarization parameters of the individual anodic and cathodic reactions establishing the mixed electrode. The interpretation then leads to determination of the corrosion potential, Ecorr, and to determination of the corrosion current density, icorr, from which the corrosion rate can be calculated. 

The concepts associated with an analysis of Fig. 4.15 are reemphasized by examining the information derivable from experimental polarization curves (i.e., E versus log Iex curves). In general, the following are available from measurements or calculations E x, E M, the cathodic polarization curve, the anodic polarization curve, and Ecorr from asymptotic values of the polarization curves as Iex red — 0 and I x — 0. The... 

---