Efficiency, Faradic

As noted above, the electrocarboxylation process has been widely investigated for the production of some NSAIDs, starting from parent arylethyl halides [6, 7]. On the other hand, the direct process at conventional cathodes requires quite negative potentials, and gives rise in some cases to moderate faradic efficiencies. Furthermore, attempts to scale-up the process in the case of the reduction of l-(3-phenoxyphenyl)-l-chloroethane [18] and l-(4-isobutylphenyl)-l-chloroethane [16] (which are the precursors of fenopren and ibuprofen, respectively) gave very different results with respect to those obtained in syntheses performed in bench-scale systems. In particular, passivation of the cathode surface was observed, and this resulted in lower yields and selectivities. Similar results were also observed during the electrocarboxylation of chloroacetonitrile [19]. 

It normally must be well in excess of 99% to achieve the hundreds of recharges required in most applications. When this condition cannot be met, high cycle life is still achievable by packaging more than a one-to-one equivalent of the less efficient active material, typically the anode metal. However, this approach entails a substantial loss in energy density. The theoretical loss of capacity as a function of the limiting Faradic efficiency can be calculated by exponentiation of the theoretical efficiency. By example, to calculate n, the number of cycles obtainable, to an arbitrarily chosen 75% remaining of initial capacity from a cell which loses 1 % of its capacity per recharge, solve... 

This quantitative analysis allows a comparison in the product yield, Wq, for the ethanol oxidation reaction between different catalysts. In the discussed example, the three catalysts considered present close yields, with a low CO2 production (for Pt/C and PtRu/C catalysts CO2 is only produced during the positive going scan), whereas acetaldehyde and acetic acid both present a product yield of 60-70 % and 30-40 %, respectively. A shght increase in the acetaldehyde yield can be observed for the PtRu catalyst, leading to a lower Faradic efficiency for the ethanol oxidation reaction, compared to that obtained on Pt/C and PtsSn/C catalysts. 

In addition to the potential losses, the current loss from the theoretical conversion of reactants could be significant. The current (or Faradic) efficiency is defined as... 

The effect of pressure on tlie selectivity and Faradic efficiency (FE) of... 

Planar platinum and Ptyack are examples of effective H2 electrocatalysts. Minimization of I02 is a greater challenge. In the absence of competing redox couples, the faradic efficiency of H2 and O2 evolution approaches 100%, and the 7electrolysis i determined by the current limited VhioC ) ... 

The main advantages of batteries with a liquid electrolyte come from the high conductivity exhibited by the usual concentrated solutions, sulphuric acid and potash, and from the good interface between electrolyte and electrode material, which allows high current densities to be achieved. Electrode materials of these batteries have been in continuous improvement throughout this century they now have a good faradic efficiency and a reasonable cost. 

With equations (5) and (6), we can calculate the Faradic efficiency (Cceii ), energy efficiency (r ceii), and energy density (Sceii, Wh/Kg) of a DMFC single cell from the experimental voltage-current curves. 

The equations of Faradic efficiency, energy efficiency and energy density for a DMFC stack are similar to that of the DMFC single cell. 

Figure 9. Plots of cell voltage, Faradic efficiency and energy efficiency versus discharge current for a DMFC single cell at 60 °C using air as oxidant. The methanol concentrations are A, 0.5M B, l.OM C, 2.0M and D, 3.0M, respectively.

Operating temperature Anodic current density Cathodic current density Cell voltage Faradic efficiency... 

For a given electrochemical system, the increase of the voltage efficiency is directly related to the decrease of the overpotentials of the oxygen reduction reaction, t]c, and alcohol oxidation reaction, T]a, which needs to enhance the activity of the catalysts at low potentials and low temperature, whereas the increase of the faradic efficiency is related to the ability of the catalyst to oxidize completely or not the fuel into carbon dioxide, i.e. it is related to the selectivity of the catalyst. Indeed, in the case of ethanol, taken as an example, acetic acid and acetaldehyde are formed at the anode [10], which corresponds to a number of electrons involved of 4 and 2, respectively, against 12 for the complete oxidation of ethanol to carbon dioxide. The enhancement of both these efficiencies is a challenge in electrocatalysis. 

If the ethanol oxidation reaction is complete, leading to CO2, twelve moles of electrons are exchanged per mole of ethanol consumed. But, this reaction can stop at stages of the mechanism, leading to the formation of acetic acid or aceltaldehyde, for example, with a transfer of only four moles or two moles of electrons involved per mole of ethanol consumed, respectively. In that case, a faradic efficiency will... 

From this equation, it appears that the better way to significantly increase the overall energy efficiency is to increase se (the potential efficiency) and 6p (the faradic efficiency), since 8rev. (the reversible efficiency) is given by the thermodynamics (it can be slightly increased by changing the pressure and temperature operating conditions). 

The potential efficiency ce = 48% (0.55/1.15). The Faradic efficiency cp is associated with the product distribution (catalyst selectivity). For CO2 product, the Faradic efficiency is 100% (12/12), while for acetic acid product, only four electrons are transferred, and the Faradic efficiency is 33% (4/12). Although higher current densities are not necessarily associated with complete oxidation of ethanol, improving the anode catalyst selectivity to CO2 will increase the overall DEFC efficiency and fuel utilization. 

The complete oxidation of two hydrox d groups of ethylene glycol to oxalate without breaking C—C bond is as follows, and the Faradic efficiency is 80%. 

In order to improve the Faradic efficiency and fuel utilization, the desired final product of alcohol oxidation is CO2. However, breaking the C—C bonds of alcohols for direct C2+ alcohol fuel cells remains a great challenge, especially at low temperatures (e.g., <90 °C) and low anode overpotentials. For primary alcohol oxidation, such as ethanol oxidation, nanostructured PtRhSn/C has demonstrated a strong ability to both improve reaction kinetics and break C—C bond. Future research efforts using both combinational chemistry methods and theoretical calculations may lead to the development of efficient ternary or even quarterly PtSn-based catalysts for complete alcohol oxidation. 

Sulfur and selenium also show a similar effect. It is well known that sulfur is a poison for reduction on a platinum surface owing to strong adsorption. Sulfur contamination cannot only hinder the ORR, but can also change the oxygen reduction pathway. When a platinum surface is modified by sulfur or selenium, the faradic efficiency of H O generation can be as high as 100% (Mo and Scherson 2003). 

The oxygen ionic transport number to can also be measured using the Faradic Efficiency method, i.e., to is the ratio between the oxygen ionic current and the total current driven through the sample by an applied electrical field. However, in case of noticeable electrode polarization, the measured transport number can differ from the actual value. 

Fig. 16. (a) Electrochemical cells used for EMF and Faradic Efficiency measurements (b) variation of the average electronic transport numbre of Lao.9Sro.iGao.8Mgo.203-5 determined by different techniques, from [Kharton et al., 2007]. 

There are various metrics utilized to quantify the efficiency of different aspects of an electrochemical reaction. One type of efficiency for a purely electrochemical reaction is based on species consumption. For a galvanic process, there will be a minimum amount of reactant required for a given reaction, as calculated by Faraday s law, Eq. [2.33]. In practice, we are not constrained to provide exactly the minimum amount of reactant. For a given current, there is a calculated minimum amount of reactant, but there is no maximum. The actual flow rate of reactants is a function of the pumps and blowers that are used for reactant dehvery. Obviously, the more flow delivered, the higher the parasitic power required, so we generally seek to dehver something close to the minimum requirement. The Faradic efficiency is a measure of the percent utilization of reactant in a galvanic process ... 

Faradic efficiency is often called the fuel utilization efficiency (Hf) when applied to the fuel in a galvanic redox reaction ... 

Stoichiometric Ratio In fuel cell parlance, the term stoichiometry is defined as the inverse of the Faradic efficiency. Smdents may be confused with this terminology, since the stoichiometric condition typically describes a balanced chemical reaction equation with no excess oxidizer. Here, the term stoichiometry is used slightly differently, and its meaning is similar to the definition of equivalence ratio used in combustion. Unlike chemical reactions, the reduction and oxidation reactions are separated by electrolyte, so each electrode can have a discrete stoichiometry ... 

To avoid confusion the reader should be aware that other symbols for stoichiometty, besides A, are commonly used in the literature, including f and The theoretical rate of reactant required is calculated by Faraday s law, and the actual rate of reactant dehvered is a funchon of the fuel or oxidizer delivery system. One important point is worth mentioning Fuel cells must always have an anode and cathode stoichiometry greater than 1. For a value less than unity, the current specified could not be produced. For reasons explained in Chapter 4, a stoichiometry of exactly 1 is not possible either, so that a Faradic efficiency of 100% is not possible on the anode or cathode for a single pass of reactant. ... 

Fuel recirculators can be used to increase the effective faradic efficiency to 100%, but we are talking about a single pass of reactant tiirough the fuel cell here. 

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