I0, exchange current

In the latter case one would like to know the length Apb of the metal-solid electrolyte-gas three-phase-boundaries (tpb) (in m or in metal mols, for which we use the symbol Ntpb throughout this book) and the value of the exchange current I0, where (W2F) expresses the value of the (equal and opposite under open-circuit conditions) forward and reverse rates of the charge-transfer reaction 4.1. 

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 ... 

The exchange current I0 is an important parameter for the quantitative description of NEMCA. As subsequently analyzed in this chapter it has been found both theoretically and experimentally1,4 19 that the order of magnitude of the absolute value A of the NEMCA enhancement factor A defined from ... 

The break in the plot log I vs coincides with the observed inflection in rH2 and r0, and corresponds to the onset of Pt oxide formation.6 As shown in Fig. 10.3 the, predominantly catalytic, rates rH2 and r0 depend exponentially on catalyst potential Uriie, as in studies with solid electrolytes with slopes comparable with the Tafel slopes seen here. This explains why the observed magnitude of the faradaic efficiency A (-2-20) is in good agreement with 2F rc° /I0 (rc° is the open-circuit catalytic rate and I0 is the exchange current) which is known to predict the expected magnitude of A in solid-electrolyte studies. 

In fact, it means that there exists a so-called exchange current, i0 = ic = ja, which, in accordance with Faraday s law, can be written as... 

For most of the reactions frequently employed in limiting-current studies, the surface overpotential is not negligible. A criterion for assessing its magnitude is the exchange-current density i0, which is a measure of the reaction rate at the equilibrium potential of the electrode (i.e., when anodic and cathodic rates are equal). 

Here ir is a local polarization characteristic, referred to as a unit of electrode volume. Sr,i0 are the specific surface and the exchange current density,... 

At equilibrium, AG = 0 and AGa = AGc, but more importantly, inet = 0. Although there is no net current density at equilibrium, the anodic and cathodic reaction rates are non-zero. The reaction rates, and therefore the current densities, are equal. The current density at equilibrium is called the exchange current density, and is denoted i0. 

As will now be discussed, the exchange current is proportional to the standard rate constant, thus resulting in the common practice of using i0 instead of k° in kinetic equations. 

In the treatment of the kinetics of the electron transfer illustrated in Section 4.1, it has been assumed that the propulsive force for the electron transfer was the electrochemical potential E i.e. a quantity directly related to 4>M — < >s). However, since the solvated ions cannot enter the inner layer of the double layer (IHP), the true propulsive force should be < )M — standard rate constant, k°, and the exchange current, i0, should become respectively ... 

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. 

For a given reaction and temperature, i0, the exchange current density (Section 7.2.1) is constant so that for a given reaction and constant temperature ... 

The real case, a partly polarizable (and hence partly nonpolarizable) electrode, can be described in terms of the exchange current density i0. From the linearized Butler-Volmer equation [Eq. (7.25)], then ... 

It follows that the exchange current density, i0, previously written in a rudimentary form, needs modifying to account for the structure at the interface (implied in Fig. 7.17). Thus [cf. Eq. (7.21)], the corrected i0 becomes... 

Since there is no net diffusion under equilibrium conditions, then- p hole current is equal to the p —> n hole current. These equilibrium currents are analogous to the equilibrium exchange currents at an electrode/solution interface. They represent the exchange of holes across the junction between the n- and p-types of material and will be designated by the symbol i0fl. This i0 will now be examined more carefully. 

The value of the gradient of In i0 versus 1 IT is clearly measurable one determines the exchange current density at a number of temperatures. But Eq. (7.92) shows that the result is not the heat of activation of the electrode reaction at the reversible potential (that s what one would like to have), but that quantity diminished by the heat of reaction of the reaction (e.g., 02 + 4H+ + 4e —> 2HzO) being examined. 

The conductivity oof any step is determined largely by its equilibrium exchange-current density i0j. The smaller the i0 j is for the step, the lower is its conductivity. Thus one can say that the step with the smallest i0j generally determines the overall current.63... 

Figure 5.3 shows the current-potential relations for a=0.25 and 0.50.2) At E=Eeq, the net current (i) is equal to zero but currents of the same magnitudes (i0) flow in opposite directions. i0 is called the exchange current. The net current is an oxidation current (anodic current) at E>Eeq and a reduction current (cathodic current) at E[Pg.113]

When the exchange current (i0) is large enough, the electrode potential is very near to the equilibrium potential (Eeq), even when a given current ic flows at the electrode (see t] in Fig. 5.4(a)). When the exchange current is very small, however, the electrode potential must deviate considerably from Eeq (to the negative side for reduction and to the positive side for oxidation) for the current ic to flow (see rj in Fig. 5.4(b)). The difference between the equilibrium potential (i=0) and the potential at a given current value (t=ic) is called overpotential and is denoted by tj. As is evident from Fig. 5.4, p depends on the value of ic. 

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