Polarization curve

The real situation can be estimated by digital simulation.7,24 It will be performed for example for one-electron transfer process and P = 0.5 and y = O.5.7 In all cases, the apparent current density is standardized to the apparent surface of modified electrode. 

As told earlier, the shape of polarization curves does not depend strongly on Sw at large jo/jh ratios. At lower ones, the important effect arises. 

It can be seen from Fig. 5 that the approximation of (43) by (44) is acceptable at all overpotentials and ratios jo//l, being completely 

Equation (7) is valid for the complete active electrode surface. On the other hand, if the inert substrate is partially covered with the same active material, the polarization curve equation is given by (44).7 

Using the recently derived equation (44), it was possible to elucidate the Ohmic-controlled electrodeposition of metals by the consideration of silver electrodeposition on the graphite electrode, where each microelectrode was independent relative to the other ones. 

CutTEfit (density) for which the over errtiai is defined -  

FIGURE 2.1 (a) Examples of polarization characteristics of a fuel cell cathode and anode outlining the definition of the overpotential as deviation from the equilibrium (theoretical) potential at a given current density (reaction rate), (b) Overall cell polarization as a sum of anode and cathode polarization and the power of a fuel cell as an integral of the voltage by the current. Usual figures of merit are indicated on both polarization and power curves. 

Obtaining electrode polarization as a function of the current (and even better, of the current density) is the main method of analysis of the fuel cell performance. The closer the data are collected to a steady-state operation mode, the more adequate is the performance represented. In an ideal case, hydrodynamic polarization is the preferred method that eliminates all hydrodynamic and transport effects and is 

Among the various parameters that may affect the reactivity of an electrochemical reaction (the current density), one of the most important is the potential e at the electrode, which is ultimately the difference at the equilibrium. 

We will be informed about an electrochemical reaction by studying the influence of the potential. To do this, we draw the curves e(i) that are the polarization curves corresponding to the reaction being considered. Curves ri(/) are also called polarization curves. They differ from the previous ones by a translation, and pass through the origin (if i = 0, the overpotential is zero because the electrode potential is equal to the thermodynamic potential e ). 

It is always difficult to obtain a polarization curve because we must avoid potential parasites that can appear in different parts of the circuit, particularly in the vicinity of the electrode. 

The electrode potential is measured relative to a reference electrode (REF) using an electronic voltmeter with very high impedance, which is working with a current close to zero. Measurement of the potential in the vicinity of the electrode is performed by a capillary tube extending from a siphon of the reference electrode. 

Polarization of the electrode can be achieved using three different set-ups  

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Corrosion protection of metals can take many fonns, one of which is passivation. As mentioned above, passivation is the fonnation of a thin protective film (most commonly oxide or hydrated oxide) on a metallic surface. Certain metals that are prone to passivation will fonn a thin oxide film that displaces the electrode potential of the metal by +0.5-2.0 V. The film severely hinders the difflision rate of metal ions from the electrode to tire solid-gas or solid-liquid interface, thus providing corrosion resistance. This decreased corrosion rate is best illustrated by anodic polarization curves, which are constructed by measuring the net current from an electrode into solution (the corrosion current) under an applied voltage. For passivable metals, the current will increase steadily with increasing voltage in the so-called active region until the passivating film fonns, at which point the current will rapidly decrease. This behaviour is characteristic of metals that are susceptible to passivation. 

Figure C2.8.2. (a) Schematic polarization curves for tire anodic and catliodic reaction of an Fe/Fe electrode. The anodic and catliodic branches of tire curve correspond to equations (C2.8.12 ) and (C2.8.13 ) respectively. The equilibrium potential of tliis electrode will adjust so tliat j = j tire corresponding potential is of Fe. (b)...

Schematic polarization curves for a mixed electrode (Fe in an aqueous solution in tire presence of hydrogen ions),...

Figure C2.8.3. A tliree-electrode electrochemical set-up used for the measurement of polarization curves. A potentiostat is used to control the potential between the working electrode and a standard reference electrode. The current is measured and adjusted between an inert counter-electrode (typically Pt) and the working electrode.

In tlie polarization curve of figure C2.8.4 (solid line), tlie two regimes, activation control and diffusion control, are schematically shown. The anodic and catliodic plateau regions at high anodic and catliodic voltages, respectively, indicate diffusion control tlie current is independent of tlie applied voltage and7 is reached. 

Figure C2.8.4. The solid line shows a typical semilogaritlimic polarization curve (logy against U) for an active electrode. Different stages of reaction control are shown in tlie anodic and catliodic regimes tlie linear slope according to an exponential law indicates activation control at high anodic and catliodic potentials tlie current becomes independent of applied voltage, indicating diffusion control.

Passivation is manifested in a polarization curve (figure C2.8.4) dashed line) by a dramatic decrease in current at a particular onset potential (the passivation potential, density, is lowered by several orders of magnitude. 

From polarization curves the protectiveness of a passive film in a certain environment can be estimated from the passive current density in figure C2.8.4 which reflects the layer s resistance to ion transport tlirough the film, and chemical dissolution of the film. It is clear that a variety of factors can influence ion transport tlirough the film, such as the film s chemical composition, stmcture, number of grain boundaries and the extent of flaws and pores. The protectiveness and stability of passive films has, for instance, been based on percolation arguments [67, 681, stmctural arguments [69], ion/defect mobility [56, 57] and charge distribution [70, 71]. 

In the potential range catliodic to one frequently observes so-called metastable pitting. A number of pit growtli events are initiated, but tire pits immediately repassivate (an oxide film is fonned in tire pit) because the conditions witliin tire pit are such that no stable pit growtli can be maintained. This results in a polarization curve witli strong current oscillations iU [Pg.2728]

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. 

Hi) Surface blockers. Type 1 tlie inliibiting molecules set up a geometrical barrier on tlie surface (mostly by adsorjDtion) such as a variety of ionic organic molecules. The effectiveness is directly related to tlie surface coverage. The effect is a lowering of tlie anodic part of tlie polarization curve witliout changing tlie Tafel slope. 

Type 2 tlie inliibiting species takes part in tlie redox reaction, i.e. it is able to react at eitlier catliodic or anodic surface sites to electroplate, precipitate or electropolymerize. Depending on its activation potential, tlie inliibitor affects tlie polarization curve by lowering tlie anodic or catliodic Tafel slope. 

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). 

Graphs of operating potential versus current density are called polarization curves, which reflect the degree of perfection that any particular fuel cell technology has attained. High cell operating potentials are the result of many years of materials optimization. Actual polarization curves will be shown below for several types of fuel cell. 

Typical polarization curves for alkaline fuel cells are shown in Fig, 27-63, It is apparent that the all aline fuel cell can operate at about 0,9 and 5()() rnA/cnr current density. This corresponds to an energy conversion efficiency of about 60 percent IIII, The space shuttle orbiter powder module consists of three separate units, each measuring 0,35 by 0,38 by I rn (14 by 15 by 40 in), weighing 119 kg (262 lb), and generating 15 kW of powder. The powder density is about 100 W/L and the specific powder, 100 W/kg,... 

Being acidic, fluorocarbon ionomers can tolerate carbon dioxide in the mel and air streams PEFCs, therefore, are compatible with hydrocarbon fuels. However, the platinum catalysts on the fuel and air elec trodes are extremely sensitive to carbon monoxide only a few parts per million are acceptable. Catalysts that are tolerant to carbon monoxide are being explored. Typical polarization curves for PEFCs are shown in Fig. 27-64. 

Typical polarization curves for SOFds are shown in Fig. 27-67. As discussed earlier, the open-circuit potential of SOFds is less than 1 because of the high temperature, but the reaction overpotentials are... 

FIG. 28-8 The potentiostat apparatus and circuitry associated with controlled potential measurements of polarization curves. 

FIG. 28-9 Typical electrochemical polarization curve for an active/passive alloy (with cathodic trace) showing active, passive, and transpassive regions and other important features. (NOTE Epp = primary passive potential, Ecaa- — freely corroding potential). 

FIG. 28-14 Logic sequence Diagram 3 used to qualitatively evaluate the degree of corrosion for systems that cannot be evaluated by extrapolation of the cathodic polarization Curve 2 from a CBD. 

The validity of Eq. (3-15) further follows from the results given in Fig. 3-4. It represents the current-potential curve for a buried storage tank. The difference f/ n - I/off is proportional to the current /. The quotient R is equal to the grounding resistance of the tank. The (/) curve corresponds to the true polarization curve. 

It is worth emphasising too, that the position of those lines representing equilibria with the dissolved species, M, depend critically on the solubility of the ion, which is a continuous function of pH. For example, iron in moderately alkaline solution is expected to be very passive and so it is in borate solutions (in the absence of aggressive ions). However, the anodic polarization curve still shows a small active loop at low potential. 

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 . 

Figure 5. Polarization curves for bifunctional air electrode in 1.5Ah Zn/air cell with 12 KOH at 27 °C. From Ross 1351.

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.)...

Figure 10.9. Stationary polarization curve obtained with 10 mol % V205 - 90 mol % K2S207 catalyst at 440°C. 2 Reproduced by permission of the Electrochemical Society.

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. 

Mishra et al. [198] discussed in an exemplary way the dark and photocorrosion behavior of their SnS-electrodeposited polycrystalline films on the basis of Pourbaix diagrams, by performing photoelectrochemical studies in aqueous electrolytes with various redox couples. Polarization curves for the SnS samples in a Fe(CN) redox electrolyte revealed partial rectification for cathodic current flow in the dark, establishing the SnS as p-type. The incomplete rectification was... 

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