Exchange current density determination

Figure 2.30 shows current-voltage curves for the ion transfer reaction as a function of a with constant N, and at the interface. The exchange current density determines the slope of the current-voltage curves at i) = 0 and constant Ng... 

It is evident from these expressions that since in the Tafel region / (the current density actually determined) must be greater than /(, (the equilibrium exchange current density), the signs of the overpotentials will conform to equations 1.60 and 1.61, i.e. will be negative and will be positive. 

The slope of the Tafel curve drj/d log / is only one of the criteria that are required to determine the mechanism of the h.e.r., since different mechanisms, involving different r.d.s. often have the same Tafel slope. Parameters that are diagnostic of mechanism are the transfer coefficient, the reaction order, the stoichiometric number, the hydrogen coverage, the exchange current density, the heat adsorption, etc. 

The potential of the electrode surface is determined by the Nernst equation introduced in Sec. 1.3.3. In an equilibrium, the currents in anodic and cathodic directions are equal. If they are related to an electrode area, they are called exchange-current densities, j0 ... 

Little work has been done on bare lithium metal that is well defined and free of surface film [15-24], Odziemkowski and Irish [15] showed that for carefully purified LiAsF6 tetrahydrofuran (THF) and 2-methyltetrahydrofuran 2Me-THF electrolytes the exchange-current density and corrosion potential on the lithium surface immediately after cutting in situ, are primarily determined by two reactions anodic dissolution of lithium, and cathodic reduc-... 

Again the extent to which such parallel reactions contribute to the measured current is not very easy to quantify. However, fortunately, such a quantification is not necessary for the description of NEMCA. What is needed is only a measure of the overall electrocatalytic activity of the metal-solid electrolyte interface or, equivalently, of the tpb, and this can be obtained by determining the value of a single electrochemical parameter, the exchange current I0, which is related to the exchange current density i0 via ... 

If no concentration of the educt is given the standard exchange current density y oo is stated. Values of)t are printed in italics values of the apparent rate constant k pp are printed in parentheses in italics. For electrode potentials where the latter rate constant was actually determined the reader is referred to the original literature. 

Fach of these reactions has its own exchange current density and its own equilibrium potential. The condition of overall balance at this electrode is determined not by Fq. (2.7) but by the equation... 

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

As a rule, because of the high temperatures, electrochemical reactions in melts are fast and involve little polarization. For such reactions the exchange current densities are as high as 10 to KFmA/cm. Therefore, reactivities in melts (and also in high-temperature systems with solid electrolytes) are usually determined not by kinetic but by thermodynamic features of the system. 

The method permits the simultaneous determination of reaction order, m, and reaction rate constant, k, from the slope and the intercept of the straight line. The procedure can be repeated for various potential values below the limiting current plateau to yield k as a function of electrode potential. The exchange current density and the Tafel slope of the electrode reaction can be then evaluated from the k vs. potential curves. 

Figure 5. Measurement and analysis of steady-state i— V characteristics, (a) Following subtraction of ohmic losses (determined from impedance or current-interrupt measurements), the electrode overpotential rj is plotted vs ln(i). For systems governed by classic electrochemical kinetics, the slope at high overpotential yields anodic and cathodic transfer coefficients (Ua and aj while the intercept yields the exchange current density (i o). These parameters can be used in an empirical rate expression for the kinetics (Butler—Volmer equation) or related to more specific parameters associated with individual reaction steps.(b) Example of Mn(IV) reduction to Mn(III) at a Pt electrode in 7.5 M H2SO4 solution at 25 Below limiting current the system obeys Tafel kinetics with Ua 1/4. Data are from ref 363. (Reprinted with permission from ref 362. Copyright 2001 John Wiley Sons.)...

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...

As in Eq. (3.22), F is the Faraday constant, n is the number of electrons taking part in the reaction, but iq is a new quantity called the exchange current density. These rates have units of mol/cm s, so the exchange current density has units of A/cm. Typical values of io for some common oxidation and reduction reactions of various metals are shown in Table 3.4. Like reversible potentials, exchange current densities are influenced by temperature, surface roughness, and such factors as the ratio of oxidized and reduced species present in the system. Therefore, they must be determined experimentally. 

The slowest step, or rate-determining step, can be either (a) electron transfer at the electrode-solution interface or (b) formation of atoms at the electrode surface. The activation polarization component of the overpotential, r)a, is related to the actual rate of oxidation or reduction, i, and the exchange current density ... 

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-... 

Thus, the exchange current density, i0, is a useful arbiter of the dynamic nature of the electrode reaction. The larger the i0, the faster the exchange of ions and charge takes place, although because it is equilibrium, there is no net electronation or deelectronation current. We will see shortly that i0 determines the rate of electrode reactions at any potential A —and indeed leads to the study of electrodes acting as catalysts. 

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