Faradaic efficiency

The faradaic efficiency (sometimes referred to as the coulombian efficiency or coulombic efficiency) over a charge/discharge cycle is the ratio between the number of electrons delivered (or the amount of electricity delivered) and the number of electrons (or amount of electricity) injected into the secondary battery. 

From the user s point of view, the faradaic efficiency is the product of a discharge efficiency by a charge efficiency. Without some means of internal analysis, there is no way of separating the two. 

The faradaic efficiency must be considered over a discharge/charge cycle. If, by a rapid discharge, less electricity is extracted than by a slow discharge, less electricity will need to be injected during the next recharge. 

52 Here, we are indeed dealing with an element with no associated electronics. In reality, this situation is rare with Uthium technologies because, usually, the elements are coimected in a pack including a battery management system (BMS) which consumes current and degrades the faradaic efficiency as seen by an outside observer. 

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In most cases, oligomers are initially generated in solution,61-64 but most rapidly precipitate onto the electrode surface and/or couple with adsorbed chains, and become oxidized 62,63,65 As a result, an oxidized (p-doped) polymer film is deposited on the electrode surface with, in most cases, high faradaic efficiency. Since ca. 0.3 electrons are required to dope the film to the polymerization potential, the overall polymerization + deposition process consumes ca. 2.3 electrons per monomer unit. 

Although the term non-Faradaic process has been used for many decades to describe transient electrochemical processes where part of the current is lost in charging-discharging of metal-electrolyte interfaces, in all these cases the Faradaic efficiency, A, is less than 1 (100%). Furthermore such non-Faradaic processes disappear at steady state. Electrochemical promotion (NEMCA) must be very clearly distinguished from such transient non-Faradaic processes for two reasons ... 

How can one explain such a huge Faradaic efficiency, A, value As we shall see there is one and only one viable explanation confirmed now by every surface science and electrochemical technique, which has been used to investigate this phenomenon. We will see this explanation immediately and then, in much more detail in Chapter 5, but first let us make a few more observations in Figure 4.13. It is worth noting that, at steady-state, the catalyst potential Uwr, has increased by 0.62 V. Second let us note that upon current interruption (Fig. 4.13), r and UWr return to their initial unpromoted values. This is due to the gradual consumption of Os by C2H4. 

As already noted, the enhancement factor or faradaic efficiency, A, is defined from ... 

Figure 4.22. Effect of the rate of O2 supply to the catalyst electrode on the increase in the rate of C2H4 oxidation on Pt deposited on YSZ.1,4 Dashed lines are constant faradaic efficiency, A, lines. Reprinted from ref. 4 with permission from Academic Press.

Figure 4.22 shows the steady-state effect of current, or equivalently rate, I/2F, of O2 supply to the catalyst on the rate increase Ar during C2H4 oxidation on Pt/YSZ. According to the definition of A (Eq. 4.19), straight lines passing from the (0,0) point are constant faradaic efficiency A lines. 

For A l, the Faradaic efficiency A has, as already noted, an interesting physical meaning50 For oxidation reactions it expresses the ratio of the reaction rates of normally chemisorbed atomic oxygen on the promoted... 

One of the first steps in understanding electrochemical promotion was the observation1 that the absolute value jA of the Faradaic efficiency A of different catalytic reactions could be approximated by (Fig. 4.23)... 

Figure 4.53. Effect of temperature on the faradaic efficiency, A, values measured in electrochemical promotion (NEMCA) studies of C2H4 oxidation on various metals.30 Reprinted with permission from Academic Press.

Time Constants During Galvanostatic Transients and Faradaic Efficiency... 

The faradaic efficiency, A, can be computed in every NEMCA experiment from its definition, i.e. ... 

There exists, however, a second, approximate, way of estimating A on the basis of galvanostatic rate transients as outlined in section 5.2 and shown in Figure 5.6a. This approximate method is useful for gaining additional physical insight on the meaning of the faradaic efficiency A and for checking the internal consistency of experimental data with the ion backspillover mechanism. 

After the discovery of electrochemical promotion in the 1980 s1213 it took only a short time6 to find the means (i.e. Eq. (4.20)) for rationalizing and predicting the magnitude of the absolute value of Faradaic efficiency A, i.e. 

The oxidation of CO on Pd is another reaction exhibiting NEMCA.36 Faradaic efficiency factor A values of the order of 103 have been measured at T=290°C, pCo=3xl0 2 kPa and po2=15 kPa.36 This reaction is well known to also exhibit oscillatory behaviour37 and deserves further examination. 

Methanol oxidation on Ag polycrystalline films interfaced with YSZ at 500°C has been in investigated by Hong et al.52 The kinetic data in open and closed circuit conditions showed significant enhancement in the rate of C02 production under cathodic polarization of the silver catalyst-electrode. Similarly to CH3OH oxidation on Pt,50 the reaction exhibits electrophilic behavior for negative potentials. However, no enhancement of HCHO production rate was observed (Figure 8.48). The rate enhancement ratio of C02 production was up to 2.1, while the faradaic efficiencies for the reaction products defined from... 

Figure 8.68 shows a typical galvanostatic transient under oxidizing gaseous conditions. The reaction rate is enhanced by a factor of 20 (p=21) and the faradaic efficiency A (=Ar/(I/2F)) is 1880. The behaviour is clearly electrophobic (dr/dV Xi) and strongly reminiscent of the case of C2H4 oxidation on Pt/YSZ (Fig. 4.13) with some small but important differences ... 

At t=0 a constant anodic current I=5mA is applied between the Pt catalyst film and the counter electrode. The catalyst potential, Urhe, reaches a new steady state value Urhe=1.18 V. At the same time the rates of H2 and O consumption reach, within approximately 60s, their new steady-state values rH2-4.75T0 7 mol/s, ro=4.5T0 7 mol/s. These values are 6 and 5.5 times larger than the open-circuit catalytic rate. The increase in the rate of H2 consumption (Ar=3.95T0 7 mol H2) is 1580 % higher than the rate increase, (I/2F=2.5T0 8 mol/s), anticipated from Faraday s Law. This shows clearly that the catalytic activity of the Pt catalyst-electrode has changed substantially. The Faradaic efficiency, A, defined from ... 

Figure 9.26 shows the steady state effect of applied current I on the induced changes, ArH2(=rH2 -r 2) and Ar0(=ro-io )> in the rates of consumption of H2 and O respectively, where the superscript o always denotes open-circuit conditions. The dashed lines in Fig. 9.26 are constant Faradaic efficiency, A, lines. The maximum measured A values are near 40 at low current densities. This value is in excellent qualitative agreement with the following approximate expression which can predict the magnitude of A in NEMCA studies ... 

Figure 9.28 also shows the Faradaic efficiency, A0(=Aro/(I/2F)), corresponding to each closed-circuit point A0 reaches values up to 30 for high po2 values. The constant A0 curves shown in Figs. 9.28 and 9.29 are computed from the equation ... 

The addition of a spillover proton to an adsorbed alkene to yield a secondary carbonium ion followed by abstraction of a proton from the C3 carbon would yield both isomers of 2-butene. The estimated faradaic efficiencies show that each electromigrated proton causes up to 28 molecules of butene to undergo isomerization. This catalytic step is for intermediate potentials much faster than the consumption of the proton by the electrochemical reduction of butene to butane. However, the reduction of butene to butane becomes significant at lower potentials, i.e., less than 0.1V, with a concomitant inhibition of the isomerization process, as manifest in Fig. 9.31 by the appearance of the maxima of the cis- and tram-butene formation rates. 

The steady-state effect of positive current on ArH2 and Ar0 is shown in Fig. 10.2. The faradaic efficiency A exceeds 20 (2000%) fow low currents. Fig. 10.3 shows the corresponding effect of catalyst potential UWR=Urhe on rH2 and r0, together with the dependence of I on E. 

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. 

It must be emphasized, however, that since the Faradaic efficiency A is on the order of 2Fr0/I0, one anticipates to observe NEMCA behaviour only for those systems where there is a measurable open-circuit catalytic activity r0. Consequently the low operating temperatures of aqueous electrochemistry may severely limit the number of reactions where Non-Faradaic A values can be obtained. 

In a recent patent Anastasijevic and coworkers11 have described the use of electrochemical promotion to produce ammonium polysulfide, (NH4)2SX, is an efficient manner. The novel electrochemically promoted process leads to faradaic efficiency, A, values of at least four11 and p(=r/r0) values of at least eight.11... 

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