Exchange Current Density, io

The exchange eurrent density can be understood as a reaction rate at either the forward or the baekward reaction of an equilibrium reaction at the reversible potential (when overpotential is zero by definition). At the reversible potential the reaction is in equilibrium, meaning fliat the forward and backward reactions progress at the same rates. 

In PEM fuel cells, the exchange current density for the electrochemical oxygen reduction reaction (ORR, 10 -10 A cm ) is much smaller than that of the hydrogen oxidation reaction (HOR, 10 -10 A cm ). Due to the larger HOR exchange current density, the HOR at the anode Pt nanoparticle/PEM interface is much faster than the ORR at the cathode interface [14]. In other words, the overpotential for the HOR is negligibly small compared with that of the ORR when the anode is adequately hydrated. The overall electrochemical kinetics of PEMFCs is therefore dominated by the relatively slow oxygen reduction reaction. 

The relationship between the net current density, the exehange current density, the overpotential, and the electron transfer coefficient is given by the Butler-Volmer equation for either cathode or anode reaction  

Equations 21.15 and 21.16 indicate that net current density varies linearly with overpotential. At high overpotential, if the forward reaction rate is mueh higher than that of the backward reaction, i.e., 4, Equation 21.14 ean be simplified 

Taking In on both sides of Equation 21.17,21.18 can then be obtained  

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The most significant parameter in the relationships given above is the equilibrium exchange current density io, which can be evaluated by extra-p>olating the linear t/ vs. log / curve to tj = 0, at which log / = log io. Alternatively, /q may be evaluated from the linear Ep vs. log / curve by extrapolating the curve to the equilibrium potential. ... 

It is now time to define some terms. The exchange current (/o) is best thought of as the rate constant of electron transfer at zero overpotential. This current is commonly expressed as a form of current density, Iq/A (cf. equation (1.1)), in which case it is called the exchange current density, io- (Incidentally, this also explains why the Butler-Volmer equation does not include an area term. This follows since both / et and /q are functions of area, thus causing the two area terms to cancel out.)... 

The exchange current density, io, and the rate constant of electron transfer, are related according to the following equation ... 

Exchange current density, io The quotient of exchange current lo and electrode area A, i.e. io = /o/A. 

Figure 4. Typical polarization curve of the electrooxidation of hydrogen and electroreduction of oxygen the exchange current density, io, determined by extrapolation of E vs, log i to the reversible potential...

Consider a zinc strip immersed in water. At equilibrium, a small number of Zn2+ ions will pass into solution per unit time, leaving twice as many electrons behind, while an equal number of Zn2+ ions already in the water will be redeposited as elemental zinc (reaction 16.1). The rate of this process, in terms of the electrons transferred per unit surface area of the metal, is the exchange current density io for equilibrium 16.1, as explained in Section 15.4 ... 

It was shown in Section III (and see also later in Section XVI) how the relative electrocatalytic activities of various cathode materials for the HER, and anode materials for the OER, had been compared on the basis of exchange current density, io, or, equivalently, standard rate constants at the reversible potential of the process concerned. However, practically, it can be more important to be able to compare activities at appreciable operating current densities, for example, 100 mA cm. The basis of such a comparison must then be not only the log ig value but, in addition, the rate of change of current density with overpotential, namely, the Tafel slope, b (131). 

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. 

Fig. 27. Current distribution relations for a case where all forms of polarization are considered. In curve (a) uniform current distribution in pore, for example, with exchange current density io = amp cm and overpotential (ij) less than 0.1 volt (b)...

The kinetics of the HER (Reactions 1 and 2) in different environments are generally characterized in terms of the exchange current density (io) and other parameters such as the transfer coefficient. The values of io for the HER can differ by orders of magnitude between metals. Table 1 lists values for various metals in sulfuric acid [5]. The noble metals such as palladium and platinum exhibit high values, whereas metals such as cadmium, lead, and mercury are distinguished by very low values. 

The exchange current density io,ox of ion migration in the oxide and the experimental field constant f summarize several constants ... 

The reaction rate in each direction can also be expressed by the transport rate of electric charges, i.e. by current or current density, called, respectively, exchange current, Iq, and (more frequently used) exchange current density, io. The net reaction rate and net current density are zero. 

Table 4.1 Exchange current densities io, cathodic Tafel constants and overvoltages at i = 1 mA/cm [4.6], (Reproduced from Uhlig HH. Corrosion and Corrosion Control. New York John Wiley and Sons, 1971.)...

Exchange current densities io and Tafel gradients be for some reduction reactions are shown in Table 4.1. 

Figure 15.4 illustrates the origin of the corrosion potential and also the principles of cathodic and anodic protection for a single oxidation reaction (M M ) and a single reduction reaction (H H2) occurring at the metal surface (the dashed lines represent the current-potential behavior of the reverse reactions and are not important to the present discussion). Because charge balance must be maintained, the potential is pinned at a value, Ecom where the cathodic current and the anodic current are equal (i.e., where the two curves intersect). This corrosion potential (Ecorr) is called a mixed potential, as it is determined by a mixture of two (sometimes more) electrochemical reactions. The anodic current (also the cathodic current, as they are equal) at this potential is the corrosion current (torr)- It is important to note that E orr and icorr are influenced by both the thermodynamics of the two reactions, manifested by the equilibrium potentials E(h+/h2) and E(m/m+)> and by the kinetics of the two reactions, manifested by the exchange current densities io(H+/h2) and o(m/m+)> and by the slopes of the two linear curves (the Tafel slopes). 

Figure 6.6 Exchange current density io and i/io for the anodic branch as a function of current density for the operating temperature of 1073 K.

The polarization behavior of the Ru02 + Ti02 electrode in 5M NaCl solutions [63] during the course of the chlorine evolution is presented in Fig. 4.5.7. The Tafel slopes of these electrodes show a value of 30-40 mV at high Ru levels and a value ca.l20mV with electrodes containing <10 at% Ru. The exchange current density, io, for the CI2... 

In electrocatalysis, the activity of different electrocatalysts is usually expressed via the exchange current and the specific activity, via the exchange current density, io (A cm ), still often computed on the basis of the superficial electrode surface area. Only when the current is normalized using the true surface area of the electrode-electrolyte interface, the comparison between different electrocatalysts is truly meaningful. The determination of the true surface area of porous electrodes is discussed in Sect. 2.3.5. 

Extrapolation of the linear (Tafel) region of the relation between log (current) and the potential to the condition 17 = 0 gives the exchange current density io- This presupposes that the potential corresponding to this condition (17 = 0) is known, i.e., that the reversible potential for the electrode reaction is known or can be determined, e.g., from appropriate thermodynamic data. For many organic electrode processes, however, the required thermodynamic data are not available so that Er cannot be calculated. 

In order to evaluate specific electrochenucal characteristics, such as exchange current density io = R- Tin F Rct -S, estimation of the particles surface area S is necessary. Note that the experimental estimation of the surface boundary between electronically and ionically conductive media in a composite material consisting of multiple particles has not been successful to date. BET surface area estimation usually tends to severely overestimate this surface area. It correlates well with irreversible capacity loss during first intercalation (lijima et al. [1995]) but not with the surface impedance of materials (Aurbach et al. [2001]), which indicates that loosely electrically connected microparticles make a major contribution to BET surface area but not to the electrochemically active area. In order to estimate only the area that is electrically accessible and also to use the same value of S for both diffusion and surface kinetics, it is common to use a summary geometric area of the particles of the active material as an estimate for surface area. See further details in the bringing it aU together section. 

Here, i is the measured current density, 4 is the kinetic current density, io is the diffusion limited current density, n is the number of electrons transferred per oxygen molecule, F is the Faraday constant (96485 C moF ), D is the diffusion coefficient of the molecular O2, Co is the concentration of molecular O2 in the electrolyte, v is the kinematic viscosity of electrolyte, and co is the angular rotation rate (rad s ). Plotting versus. yields n from the slope and 4 from the intercept on the 4 axis. The f obtained from the Koutecky-Levich plot can also be utilized to obtain the Tafel plot, logf versus E, to determine the Tafel slope and exchange current density (io). 

As described in the previous sections, the exchange current density, io, is a crucial factor in reducing the activation overvoltage. Therefore, the most important step for improving the fuel cell performance is to increase the value of io, especially at the cathode. The increase of io can be achieved in several ways summarized, as follows ... 

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