Overpotentials calculation

In this case, the operating temperature of the fuel cell (used in the Nemst potential, and overpotential calculations) is assumed to be the outlet cathode gas temperature. Initial fuel cell parameters used in the various simulations are summarized in Table 8.5. 

For RuOi, AG b is the potential-determining step. The overpotential calculated by this analysis is thus the additional potential needed compared to the equilibrium potential ... 

Based on the proposed electrochemical model, the percentage values of the overpotential contributions of the considered electrochemical model (with the anode activation overpotential calculated using the estimated values of the anode exchange current density) at about 180 mA/cm are shown. In Figure 31 the percentage values of the overvoltages for every sector at about 180 mA/cm are shown. 

Figure 5.1 shows the resulting relationship between the rate of the slow discharge-ionization step and overpotential calculated using (5.7). 

Figure 5.1 Plots of current density versus overpotential, calculated from Eq. (5.26), for a single-step charge-transfer process, for three values of p, at low overpotentials. Note that linearity is maintained longer for p = 0.5 than for other values of p.

Smaller values of necessitate the appHcation of voltages greater than those calculated from the Nemst equation to obtain a corresponding set of surface concentrations of electroactive species. These voltages are called overpotentials and iadicate chemically related difficulties with the electrolysis. In other words, electron exchange between the electrode and the electroactive species is impeded by the chemistry of the process itself. 

Overpotential. It has been found by experiment that the decomposition voltage of an electrolyte varies with the nature of the electrodes employed for the electrolysis and is, in many instances, higher than that calculated from the difference of the reversible electrode potentials. The excess voltage over the calculated back e.m.f. is termed the overpotential. Overpotential may occur at the anode as well as at the cathode. The decomposition voltage ED is therefore ... 

It must be emphasised that in evaluating the limiting cathode potential to be applied in the separation of two given metals, simple calculation of the equilbrium potentials from the Nernst Equation is insufficient due account must be taken of any overpotential effects. If we carry out, for each metal, the procedure described in Section 12.2 for determination of decomposition potentials, but include a reference electrode (calomel electrode) in the circuit, then we can ascertain the value of the cathode potential for each current setting and plot the current-potential curves. Schematic current-cathode potential... 

During metal deposition processes the addition of adsorbable species has been found to cause an increase in the deposition overpotential [71 Lou]. Evaluation of the data results in the calculation of an adsorption isotherm. (Data obtained with this method are labelled CT.)... 

Both the frequency of the well and its depth cancel, so that the free energy of activation is determined by the height of the maximum in the potential of mean force. The height of this maximum varies with the applied overpotential (see Fig. 13). To a first approximation this dependence is linear, and a Butler-Volmer type relation should hold over a limited range of potentials. Explicit model calculation gives transfer coefficients between zero and unity there is no reason why they should be close to 1/2. For large overpotentials the barrier disappears, and the rate will then be determined by ion transport. 

In an earlier note (p. 9) we mentioned the occurrence of overvoltage in an electrolytic cell (and overpotentials at single electrodes), which means that often the breakthrough of current requires an Uappl = Eiecomp r] V higher than Ehack calculated by the Nernst equation as this phenomenon is connected with activation energy and/or sluggishness of diffusion we shall treat the subject under the kinetic treatment of the theory of electrolysis (Section 3.2). 

Fig. 23. (a) Experimental IR-free overpotentials in MCFC-based separator. Cell performance 0.25% C02 Feed. All curves calculated [32] (b) C02 production scheme using molten carbonate fuel cell stack. 

Figure 3a is an illustration of the effect of surface overpotential on the limiting-current plateau, in the case of copper deposition from an acidified solution at a rotating-disk electrode. The solid curves are calculated limiting currents for various values of the exchange current density, expressed as ratios to the limiting-current density. Here the surface overpotential is related to the current density by the Erdey Gruz-Volmer-Butler equation (V4) ... 

It is clear from the calculated limiting-current curves in Fig. 3a that the plateau of the copper deposition reaction at a moderate limiting-current level like 50 mA cm 2 is narrowed drastically by the surface overpotential. On the other hand, the surface overpotential is small for reduction of ferri-cyanide ion at a nickel or platinum electrode (Fig. 3b). At noble-metal electrodes in well-supported solutions, the exchange current density appears to be well above 0.5 A/cm2 (Tla, S20b, D6b, A3e). At various types of carbon, the exchange current density is appreciably smaller (Tla, S17a, S17b). 

The classical electrochemical methods are based on the simultaneous measurement of current and electrode potential. In simple cases the measured current is proportional to the rate of an electrochemical reaction. However, generally the concentrations of the reacting species at the interface are different from those in the bulk, since they are depleted or accumulated during the course of the reaction. So one must determine the interfacial concentrations. There axe two principal ways of doing this. In the first class of methods one of the two variables, either the potential or the current, is kept constant or varied in a simple manner, the other variable is measured, and the surface concentrations are calculated by solving the transport equations under the conditions applied. In the simplest variant the overpotential or the current is stepped from zero to a constant value the transient of the other variable is recorded and extrapolated back to the time at which the step was applied, when the interfacial concentrations were not yet depleted. In the other class of method the transport of the reacting species is enhanced by convection. If the geometry of the system is sufficiently simple, the mass transport equations can be solved, and the surface concentrations calculated. 

The use of these expressions is effectual only in cases where there is no extensive deviation in the system behavior due to charge transfer overpotential or other kinetic effects.(l) The calculated threshold or thermodynamic energy requirement (2 ) (AG in the previous equation) is often much lower than actually encountered, but is still useful in estimating an approximate or theoretical minimum energy required for electrolysis. Part of the difficulty in applying thermodynamics to many systems of industrial interest may reside in an inability to properly define the activities or nature of the various species involved in the... 

The computed results of free energy as a function of the solvent coordinate, u-ul (where ug is the value of u at the crossing point of the free energy curves at the overpotential, q =0) for Fe and are given in Fig. 9. The free energy of activation AG from the crossing point of this plot is found to be 0.6 eV, which correlates well with the experimental result of 0.59 eV. Furthermore, simple calculations using the continuum theory expression show that AG (continuum) = 0.23 eV, which is... 

Shown in Fig. 12 is an example of the nonadiabatic rate calculated using the full simulation method [ ]S. (27) and (28)] and the approximate formula [Eqs. (29)-(31)] for the + e Fe " reaction at the water/Pt( 100) interface with r= 10cm". For the reason discussed earlier, the full simulation method can only be used for the high overpotential case. In this region, the agreement between the two methods is quite good. 

To learn how to calculate the rate constant of electron transfer, kd, from a Tafel plot of log I o (as y ) against overpotential r) (as x ). 

The activation overpotentials for both electrodes are high therefore, the electrochemical kinetics of the both electrodes can be approximated by Tafel kinetics. The concentration dependence of exchange current density was given by Costamagna and Honegger.The open-circuit potential of a SOFC is calculated via the Nernst equation.The conductivity of the electrolyte, i.e., YSZ, is a strong function of temperature and increases with temperature. The temperature dependence of the electrolyte conductivity is expressed by the Arrhenius equation. 

What this calculation shows is that the rate of bulk transport observed in a thin film of LSM is at least 3 orders of magnitude too low to explain the performance of porous LSM at low overpotential, assuming an entirely bulk transport path. This calculation echoes prior estimates of Adler and co-workers, who showed that the zero-bias impedance of porous LSM cannot be explained in terms of a bulk path. In addition, estimates of the chemical capacitance based on loroi s impedance for porous LSM yield values of 10 —10 F/cm , which as mentioned previously in section 5.2 are more consistent with a surface process... 

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