The Polarization Curve

In Fig. 3.5, the experimental polarization curve for a PEM stack of 500 W is reported together with the output power supplied by the stack in the experimental conditions indicated in the caption. This stack is constituted by 32 individual fuel 

The parameter R reported in the legend of Fig. 3.5 (stoichiometric ratio) is defined as R — Rett/Rstoich, where Agff is the ratio between the air and hydrogen mass flow rates, while Astoich is the same ratio as required by the stoichiometric equation of H oxidation (see Sects. 4.3 and 6.2). 

The theoretical interpretation of the first voltage drop at low current is based on the Butler-Volmer equation, which is derived by an analysis of electrode kinetics and provides a general description of the relationship between current density and surface overpotential for an electrochemical converter [46]  

Equation 3.26, derived by electrode kinetics, has the same form of an empirical equation proposed by Tafel [48, 49], which gives the relationship between 

The plot of overpotential versus current density in log scale gives the parameters a, b, and io (h is called the Tafel slope). Equation 3.28, which is only valid for i io, suggests that the exchange current density io can be also regarded as the current density value at which the overpotential begins to exert its function to make possible the electrochemical reaction, becoming different from zero. 

---

Based on the polarization curves of figure C2.8.4 tliere are several possibilities for reducing or suppressing tire corrosion reaction. The main idea behind every case is to shift tire corroding anode potential away from E. This can be done in tire following ways. 

Duncan and Frankenthal report on the effect of pH on the corrosion rate of gold in sulphate solutions in terms of the polarization curves. It was found that the rate of anodic dissolution is independent of pH in such solutions and that the rate controlling mechanism for anodic film formation and oxygen evolution are the same. For the open circuit behaviour of ferric oxide films on a gold substrate in sodium chloride solutions containing low iron concentration it is found that the film oxide is readily transformed to a lower oxidation state with a Fe /Fe ratio corresponding to that of magnetite . 

In the polarization curve for anodic dissolution of iron in a phosphoric acid solution without CP ions, as shown in Fig. 3, we can see three different states of metal dissolution. The first is the active state at the potential region of the less noble metal where the metal dissolves actively, and the second is the passive state at the more noble region where metal dissolution barely proceeds. In the passive state, an extremely thin oxide film called a passive film is formed on the metal surface, so that metal dissolution is restricted. In the active state, on the contrary, the absence of the passive film leads to the dissolution from the bare metal surface. The difference of the dissolution current between the active and passive states is quite large for a system of an iron electrode in 1 mol m"3 sulfuric acid, the latter value is about 1/10,000 of the former value.6... 

Figure 11. Schematic diagram of anodic polarization curve of passive-metal electrode when sweeping electrode potential in the noble direction. The dotted line indicates the polarization curve in the absence of Cl-ions, whereas the solid line is the polarization curve in the presence of Cl ions.7 Ep, passivation potential Eb, breakdown potential Epit> the critical pitting potential ETP, transpassive potential. (From N. Sato, J, Electrochem. Soc. 129, 255, 1982, Fig. 1. Reproduced by permission of The Electrochemical Society, Inc.)...

Cu9ln4 and Cu2Se. They performed electrodeposition potentiostatically at room temperature on Ti or Ni rotating disk electrodes from acidic, citrate-buffered solutions. It was shown that the formation of crystalline definite compounds is correlated with a slow surface process, which induced a plateau on the polarization curves. The use of citrate ions was found to shift the copper deposition potential in the negative direction, lower the plateau current, and slow down the interfacial reactions. 

Indicator electrodes are used both for analytical purposes (in determining the concentrations of different substances from values of the open-circuit potential or from characteristic features of the polarization curves) and for the detection and quantitative characterization of various phenomena and processes (as electrochemical sensors or signal transducers). One variety of indicator electrode are the reference electrodes, which have stable and reproducible values of potential and thus can be used to measure the potentials of other electrodes. 

Polarization equations are convenient when (1) the measurements are made in solutions of a particular constant composition, and (2) the equilibrium potential is established at the electrode, and the polarization curve can be measured both at high and low values of polarization. The kinetic equations are more appropriate in other cases, when the equilibrium potential is not established (e.g., for noninvertible reactions, or when the concentration of one of the components is zero), and also when the influence of component concentrations on reaction kinetics is of interest. 

An analysis of Eq. (6.13) show that for n = 1 and P = 0.5 and for current densities less than 4% of t the polarization is very low (less than 1 mV) and can practically be neglected. The linear section of the polarization curve extends up to current densities which are 40% of f. At current densities higher than 4f, the semilogarith-mic polarization relation is observed. 

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. 

Fig. 6.4a, curve 2), and the polarization curve is of unusual shape in the region of high anodic CD where i 5S> (the oxidizing agent is the anodic reaction product, hence this relation is possible). In this region... 

Figure 6.7 shows a typical special feature of the polarization curves. In the case of reversible reactions (curve 1), the anodic and cathodic branches of the curve form a single step or wave. In the case of irreversible reactions, independent, anodic and cathodic, waves develop, each having its own inflection or half-wave point. The differences between the half-wave potentials of the anodic and cathodic waves will be larger the lower the ratio fH. ... 

It is basically irrelevant in steady-state measurements in which direction the polarization curves are recorded that is, whether the potential is moved in the direction of more positive (anodic scan) or more negative (cathodic scan) values. But sometimes the shape of the curves is seen to depend on scan direction that is, the curve recorded in the anodic direction does not coincide with that recorded in the cathodic direction (Eig. 12.3). This is due to changes occurring during the measurements in the properties of the electrode surface (e.g., surface oxidation at anodic potentials) and producing changes in the kinetic parameters. 

The current is recorded as a function of time. Since the potential also varies with time, the results are usually reported as the potential dependence of current, or plots of i vs. E (Fig.12.7), hence the name voltammetry. Curve 1 in Fig. 12.7 shows schematically the polarization curve recorded for an electrochemical reaction under steady-state conditions, and curve 2 shows the corresponding kinetic current 4 (the current in the absence of concentration changes). Unless the potential scan rate v is very low, there is no time for attainment of the steady state, and the reactant surface concentration will be higher than it would be in the steady state. For this reason the... 

Thus, in the region of very high anodic or cathodic polarization, the RDS is always the first step in the reaction path. The transfer coefficient of the full reaction which is equal to that of this step is always smaller than unity (for a one-electron RDS), while slope i in the Tafel equation is always larger than 0.06 V. When the potential is outside the region of low polarization, a section will appear in the polarization curve at intermediate values of anodic or cathodic polarization where the transfer coefficient is larger than unity and b is smaller than 0.06 V. This indicates that in this region the step that is second in the reaction path is rate determining. 

A break in the polarization curve will not be observed when the kinetic parameters of the two steps and E. 2 t ) are drastically different, and hence,... 

For an analysis of the polarization curves at low values of polarization (low overpotentials), we shall use the general polarization equation... 

It follows that from the slope of the linear section in the polarization curve close to the equilibrium potential, we can determine the exchange CD of the overall reaction. 

Thus, in the case of two-step reactions, different methods of determining the exchange CD generally yield different results (in contrast to the case of simple reactions discussed earlier) Extrapolation of the limiting anodic and cathodic sections of the semilogarithmic plots yields values and if, respectively, while the slope of the linear section in an ordinary plot of the polarization curve yields the value of ig. It is typical for multistep reactions that the exchange CD determined by these methods differ. 

The exchange CD determined by different methods will coincide only in the case of quasi-one-step reactions mentioned above. Thus, when the value of if is so much higher than if that the extreme anodic section cannot be measured and there is no break in the polarization curve, all three methods of determination lead to the same value of if. This implies that step 1 has no effect at all on the kinetics of the overall reaction and that its (high) exchange CD cannot be determined. The same conclusion holds in the opposite case of if [Pg.227]

FIGURE 13.2 Polarization curves for the partial current densities of reactions involving the metal and hydrogen, and the polarization curves for the overall current density. 

The electrode s open-circuit potential (steady potential) , depends on the relative values of the exchange CD of both reactions and also on the slopes of the polarization curves. When the exchange CD and slopes are similar, the open-circuit potential will have a value, the mixed (or compromise ) potential, which is intermediate between the two equilibrium potentials (Fig. 13.2a). However, when the exchange CD for one of the reactions is much higher than that for the other, the open-circuit potential will practically coincide with the equilibrium potential of this reaction (Fig. 13.2b). 

FIGURE 14.6 Influence of surface-active ions [N(C4H9)4]+ (curve 2) and I (curve 3) on the polarization curve for hydrogen evolution at a mercury electrode in acidic solutions (curve 1 is for the base electrolyte). 

The form of the kinetic equation depends on the way in which the surface potential X varies with electrode potential E. When the surface potential is practically constant, the first factor in Eq. (14.24) will also be constant, and the potential dependence of the reaction rate is governed by the second factor alone. The slope b of the polarization curve will be RT/ F (i.e., has the same value as that found when the same reaction occurs at a metal electrode). When in another case a change in electrode potential E produces an equally large change in surface potential (i.e., E = x + const), while there is practically no change in interfacial potential. Then Eq. (14.24) changes into... 

It can be seen from Fig. 14.7 that the polarization curve for this reaction involving p-type germanium in 0.1 M HCl is the usual Tafel straight-line plot with a slope of about 0.12 V. For -type germanium, where the hole concentration is low, the curve looks the same at low current densities. However, at current densities of about 50 AJvcF we see a strong shift of potential in the positive direction, and a distinct limiting current is attained. Thus, here the first reaction step is inhibited by slow supply of holes to the reaction zone. 

The polarization curves for the oxygen evolution reaction are more complex than those for hydrogen evolution. Usually, several Tafel sections with different slopes are present. At intermediate CD their slope b is very close to 0.12 V, but at low CD it sometimes falls to 0.06 V. At high CD higher slopes are found at potentials above 2.2 V (RHE) new phenomena and processes are possible, which are considered in Section 15.6. 

The shape of polarization curves for metals with low polarizability depends primarily on concentration polarization. In the case of highly polarizable metals, where activation polarization can be measured sufficiently accurately, the polarization curve can usually be described by an equation of the type (6.3) (i.e., by a Tafel equation). For metals forming polyvalent ions, slope b in this equation often has values between 30 and 60 mV. 

When the polarization curve is recorded in the opposite (cathodic) direction, the electrode will regain its active state at a certain potential The activation potential is sometimes called the Flade potential (Flade, 1911). The potentials of activation and passivation as a rule are slightly different. 

FIGURE 18.6 Schematic of the polarization curves for smooth (1) and porous (2) electrodes. 

The surface of the base metal is anodically polarized under the effect of local cells. For a graphical analysis of the phenomena, one must construct the polarization curves for the partial currents at the base metal as well as the overall anodic 4 vs. E curve reflecting the effective rate of dissolution of this metal under anodic polarization. The rate of the cathodic process, 4, at the inclusions is described by the corresponding cathodic polarization curve (since the surface areas of anodic and cathodic segments differ substantially, currents rather than current densities must be employed here). At open circuit the two rates are identical. 

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. 

Applying the Tafel equation with Uq, we obtain the polarization curves for Pt and PtsNi (Fig. 3.10). The experimental polarization curves fall off at the transport limiting current since the model only deals with the surface catalysis, this part of the polarization curve is not included in the theoretical curves. Looking at the low current limit, the model actually predicts the relative activity semiquantitatively. We call it semiquantitative since the absolute value for the prefactor on Pt is really a fitting parameter. 

In order to prove the S-shaped character of the polarization curve, the system was studied galvanostatically. The model predicts that the sandwiched branch of the polarization curve should be stable, and therefore measurable under galvanostatic conditions. Figure 6.10 shows the results of the experiment depending on the scan rate, an S-shaped curve can be observed in the back scan, i.e., from high to low current. At low... 

---