Overpotentials half-cells

It is clear that for a half-cell the sum of the overpotentials should be as low as possible. Depending on their origin, a distinction has to be made between few different types ... 

Polarization. The net current flow produced in a cell results in a deviation of each half-cell potential from the equilibrium value listed in Table 3.3. This deviation from equilibrium is termed polarization, the magnitude of which is given the lowercase greek symbol eta, q and is called the overpotential, E-E°. There are two primary types of polarization activation polarization and concentration polarization. 

Given that the rates of oxidation and reduction of the half-reactions are controlled by activation polarization only, that = 4-0.07 and = —0.08, and that the exchange current densities for both the oxidation of Fe and reduction of hydrogen in acidic solution are identical, use the data in Tables 3.3 and 3.4 to determine the following quantities. Recall that the potential for each half-cell is the sum of the equilibrium potential and the corresponding overpotential, in this case, r]a-... 

Quantitative treatment of overpotential and related phenomena goes back to 1905, when Tafel showed empirically that, for an electrochemical half-cell from which a net electrical current I is being drawn, an excess potential AE away from the equilibrium potential will inevitably exist, and AE will be a linear function of the logarithm of the current density i (i = I/area of interface) ... 

Consider two half-cell reactions, one for an anodic and the other for a cathodic reaction. The exchange current densities for the anodic and the cathodic reactions are lO-6 A/cm2 and 1(T2 A/cm2, respectively, with transfer coefficients of 0.4 and 1, respectively. The equilibrium potential difference between the two reactions is 1.5 V. (a) Calculate the cell potential when the current density of 1CT5 A/cm2 flows through the self-driving cell, neglecting the concentration overpotentials. The solution resistance is 1000 Q cm2, (b) What is the cell potential when the current density is 10-4 A/cm2 (Kim)... 

This implies that the latent image has the potential of the silver half-cell and so the overpotential AE is the difference between the potentials of the silver and developer half-cells (Eq. (78)). 

Historically, Faraday observed that single-electrode half-cell potentials shifted from their equilibrium values when current passed through electrochemical cells. This deviation is referred to as overpotential or overvoltage. It is generally designated as q and is defined by the relationship ... 

In the derivations of Eq 3.14 and 3.19 for the metal oxidation current density, iox M, and the metal-ion reduction current density, ired M, it was not necessary to restrict the half-cell potential to its equilibrium value. Deviation from E M will occur if the potential of either the metal or the solution is changed, resulting in an overpotential defined in general by Eq 3.1. More specifically, small deviations are associated with charge-transfer polarization, and the overpotential is designated as ... 

Oxidation overpotential is said to occur if the potential of the metal is increased, relative to E M, as would be accomplished by attaching the positive terminal of a battery to the metal, thus raising the potential by removal of electrons. (This also induces metal ions to pass into solution.) A somewhat more descriptive statement is that for oxidation overpotential the metal is attached to an electron sink, such as a more noble half cell or the positive terminal of a battery, the negative terminal of which is attached to an inert electrode such as platinum,... 

It should be noted that Eq 3.41 and 3.42 have the relatively simple form of an exponential term involving the overpotential, r CT, multiplying the exchange current density to give the current densities of the oxidation and reduction components of the polarized half-cell reaction. When an overpotential exists, the oxidation and reduction current densities are no longer equal When r CT > 0, then iox M > ired M, and when r CT < 0, then ired M > i0X M-... 

By combining the Nernst equation with the expressions for charge-transfer overpotential (r CT) and diffusion overpotential (r D), equations can be written for the total experimental polarization behavior, E(iex ox) and E(iex red), of a single half-cell reaction ... 

It is shown in Chapter 3 that a simple kinetic model of half-cell reactions leads to Tafel equations in which the overpotentials (r ) or polarizations of the oxidation and reduction components of a half-cell reaction are linearly dependent on the logarithm of the oxidation and reduction currents (Iox and Ired), respectively, or... 

With the ion concentration so determined the current-voltage characteristic can be obtained by integrating the equation for the potential distribution. Again, as in the case of the electrolytic cell, some care must be exercised with respect to the boundary conditions. In particular, the total potential drop must equal that in the dialysate half-channel, plus that in the concentrate halfchannel, plus the Donnan potential drop across the membrane. The Donnan potential drop arises from the discontinuities in concentration at the boundaries of the membranes (in this case, the cation exchange membrane for the half-cell as considered). The origin and expression for the Donnan potential are the same as for the electrode concentration overpotential. For the cation exchange membrane the Donnan potential drop is... 

L The potential of an iron electrode when polarized as cathode at 0.001 A/cm is -0.916 V versus 1N calomel half-cell. Tlie pH of the electrolyte is 4.0. What is the value of the hydrogen overpotential ... 

The corrosion potential of mild steel in a deaerated solution of pH = 2 is -0.64 V versus saturated CU-CUSO4 half-cell. The hydrogen overpotential (volts) for the same steel follows the relation 0.7 + 0.1 log/, where i = A/cml Assuming that approximately all the steel surface acts as cathode, calculate the corrosion rate in mm/y. 

The intercept voltage, Vq, is principally the aggregate of the anode and cathode half-cell reversible potentials, the anode and cathode overpotentials, and the liquid-junction potential at the membrane (usually small). For a typical new cell with activated cathodes, Vq is about 2.4 V. With uncoated cathodes, this increases to about 2.7 V. 

Fig. 9.8 Half-cell investigated ORR overpotential at a current density of 0.5 mA cm plotted versus mesopore surface areas of catalyst synthesized frran different transition metal oxalate structure-forming agents (reprinted from [59], with permission from Elsevier)...

Jome J, Kim JT, Kralik D (1979) The zinc-chlorine battery half-cell overpotential measurements. J Appl Electrochem 9 573-579. doi 10.1007/BF00610944... 

Figure 1.3 Schematic for the calculation of voltage loss in a fuel cell (for discussion see text). ACL and CCL are the abbreviations for the anode and cathode catalyst layers, respectively. Yellow shaded areas indicate the local polarization voltage r]. For simplicity, the proton conductivity of catalyst layers is taken to be equal to the proton conductivity of the bulk membrane (otherwise the curve loses smoothness at the membrane interfaces). Note that the half-cell voltage loss is given by the value of the overpotential at the catalyst layer/membrane interface.

In fuel cell modelling, it is convenient to use the picture of potential distribution across the cell sketched in Figure 1.3 (Kulikovsky et al., 2000). In this picture, the physical potentials of the anode carbon phase and of the membrane phase are shifted as a whole along the y-axis. This shift, however, does not change the anode and cathode half-cell overpotentials, which are of primary interest in modelling. 

Suppose that the catalyst layer ageing occurs due to a certain electrochemical process, characterized by the Tafel rate Q(T, r ). Typically, the electrochemical ageing process can be considered as secondary, i.e. this process is controlled by the distribution of overpotential rj, which is determined by the useful half-cell reaction. 

Equation (5.190) contains local current densities and half-cell overpotentials in the ME As n and n + 1. These values are calculated using the equations from Section 5.5. 

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