Steady polarization curve

Figure 3 Steady polarization curves for H2 oxidation on pure Pt and Pt-Fe alloy electrodes at 2000 rpm in 0.1 M HCIO4 saturated with H2 or 100 ppm CO/H2 balance.

In contrast to selective dissolution, evenly dissolving alloys can be dealt with, up to a sophisticated level including non-steady-state responses, by macroscopic, i.e., kinetic descriptions. As shown in Figure 23, Olivier [1851] pointed out that the steady polarization curves of Fe-Cr alloys in a 0.5 M sulfuric solution display the decay of active and passive currents with increasing Cr content and the emergence of the transpassive dissolution of Cr to the hexavalent state. 

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... 

FIGURE 12.7 Polarization curves (1) steady state, (2) without concentration polarization,... 

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). 

This equation describes the cathodic current-potential curve (polarization curve or voltammogram) at steady state when the rate of the process is simultaneously controlled by the rate of the transport and of the electrode reaction. This equation leads to the following conclusions ... 

This equation is analogous to Eq. (5.4.18) or (5.4.19) for the steady-state current density, although the instantaneous current depends on time. Thus, the results for a stationary polarization curve (Eqs (5.4.18) to (5.4.32)) can also be used as a satisfactory approximation even for electrolysis with the dropping mercury electrode, where the mean current must be considered... 

Fig. 12. Steady-state anodic polarization curves (a), and potentiostatic transient curves (b), of a mild steel hemisphere in neutral Na2S04 solution. From [15].

Figure 22. Steady-state polarization curves of aluminum in pure and mixed NaOH -f NaCl solutions , 4Af NaOH A, 4 M NaOH + 2 M NaCl O, 1 M NaOH + 2 M NaCl , 2 M NaCl (pH 1 to 13). Labels on the lines denote measured capacitances of the interface.

Steady-State Kinetics, There are two electrochemical methods for determination of the steady-state rate of an electrochemical reaction at the mixed potential. In the first method (the intercept method) the rate is determined as the current coordinate of the intersection of the high overpotential polarization curves for the partial cathodic and anodic processes, measured from the rest potential. In the second method (the low-overpotential method) the rate is determined from the low-overpotential polarization data for partial cathodic and anodic processes, measured from the mixed potential. The first method was illustrated in Figures 8.3 and 8.4. The second method is discussed briefly here. Typical current—potential curves in the vicinity of the mixed potential for the electroless copper deposition (average of six trials) are shown in Figure 8.13. The rate of deposition may be calculated from these curves using the Le Roy equation (29,30) ... 

B) Steady-state polarization curves of carbon paste electrodes in the presence of 33.3 pM glucose. (C) Variation of the steady-state current of carbon paste electrodes with glucose concentration (at +350 mV vs. SCE). 

Fig. 7 Experimental steady state polarization curves of Zn(ll) electroreduction for various electrolytes (SI) additive-free bath (1.6 M ZnCh -E5.3 M KCl) (S2) industrial bath (1.6 M ZnCh -E 5.3 M KCl + long-chain polymer + pH buffer of pH 4.7) solution (S3) (1.6 M ZnCh -f 5.3 M KCl + long-chain polymer with the same additive at the concentration of 10 M in volume) [218] ...

Figure 3. Steady state polarization curves in KF-2HF at 90 C O layer plane of pyrolytic graphite, edge plane of pyrolytic graphite...

Current-potential curves obtained under steady state conditions are called polarization curves. If two or more faradaic processes occur at the electrode, the fraction of current (ir) driving the rth process is the instantaneous current efficiency. Over a period of operating time the fraction of the total number of coulombs used in the rth process ( r) is related to the overall current efficiency of that process (OCE), i.e. 

The polarization curve is obtained step by step, at every potential until obtention of a steady-state value. The polarization curve must be identical during forward or backward potential scan. If not, either the steady state has not been obtained, or, more frequently, the surface of the electrode has been modified by the electrochemical reaction. Covering the platinum electrode by a Nafion film reduces the limiting current 71( by the addition of a supplementary diffusion resistance, depending on the thickness of the Nafion film (Figures 1.13 and 1.14). 

This parameter specifies the potential upon which the AC signal is imposed. Oftentimes, to maintain the steady state of the system, the DC potential is selected as 0 mV vs. open circuit. However, the response of a system can be evaluated over a potential range by running successive experiments with different DC potentials. Thus the impedance response of a system could be mapped to a potentio-dynamic polarization curve by specifying various DC potentials defined by the polarization curve. In all experiments performed in this laboratory, the DC potential was set to 0 mV versus open circuit. 

An -> ideal nonpolarizable electrode is one whose potential does not change as current flows in the cell. Much more useful in electrochemistry are the electrodes that change their potential in a wide potential window (in the absence of a - depolarizer) without the passage of significant current. They are called -> ideally polarized electrodes. Current-potential curves, particularly those obtained under steady-state conditions (see -> Tafel plot) are often called polarization curves. In the -> corrosion measurements the ratio of AE/AI in the polarization curve is called the polarization resistance. If during the -> electrode processes the overpotential is related to the -> diffusional transport of the depolarizer we talk about the concentration polarization. If the electrode process requires an -> activation energy, the appropriate overpotential and activation polarization appear. 

Assuming negligible anode polarization, the steady-state polarization curves can be described by a semi-empirical equation ... 

Fig. 12. Polarization curves of various metal oxides on Ti substrate electrodes in 02-saturated 4 M KOH obtained by pseudo-steady-state galvanostatic method (3 min./point). Curves recorded from low to high currents T = 22°C [243]. a, Fe A, Pr , Pd , Rh , Ir O, Ru.

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