Overpotentials lower limit

The electrolysis temperature affects the electrolyte conductivity, the overpotential, and the solubility of the electrodeposit in aqueous as well as in molten salt systems. The effect of temperature is particularly important in the latter case. The lower limit of the temperature of operation is set by the liquidus temperature of the bath and the solubility of the solute. Generally, the temperature chosen is at least 50 °C above the melting temperature of... 

From the Eqs. (3-1) to (3-13), the h-pH diagram of sodium sulphide solution is constructed with element sulphxir as metastable phase considering the presence of barrier (about 300kJ/mol) or overpotential (about 3.114 mV) of sulphide oxidation to sulphate and shown in Fig. 3.7. It is obvious that the lower limit of potential of sodium sulphide-induced collectorless flotation of pyrite, pyrrhotite and arsenopyrite at various pH agree well with the potential defined respectively by reactions of Eq. (3-9) producing elemental sulphur. The initial potential... 

This is a lower limit for the size of the actual overpotential as there could be additional barriers for the reaction steps, but these are not included in the analysis. The assumption is that trends are captured by the lower limit. 

The reorganization energy. A, has a large effect on the predicted current-potential response, as shown in Figure 3.6.5. The top frame illustrates the situation for A = 0.3 eV, a value near the lower limit found experimentally. For this reorganization energy, an overpotential of -300 mV (case a) places the Fermi level opposite the peak of the state... 

One can assume therefore that in the conditions indicated in figure 4.32, it is numerically acceptable to split the overpotential into an activation term and a concentration term, even if this has no real physical meaning. For overpotentials lower than 200 mV, the error is below 2% of the limiting current, whereas the maximum error is 10% for an overpotential of around 300 mV. 

Though the limiting cases of Butler-Volmer equations are easy to use, one should be careful about the range of activation overpotential for which these equations are valid. Chan et al. [76] reported the lower limit of activation overpotential for which the Tafel equation can be used as > 0.28 V, and the upper limit for linear current-potential relation ship as 7act < 0.1 V. 

At values of ZoAl ratio lower than 1, the complete diffusion cOTitrol of the electrodeposition process arises at aU overpotentials. The lower limit of the region of the complete diffusion control can be determined as follows it is obvious that the convex shape of the polarization curve characterizes the diffusion control of deposition process and the concave one the activation control of deposition process. The Z/Zl ratio as function of tj is shown in Fig. 1.3 and the Z as a function of in Fig. 1.4. In both cases, the convex shape of curves changes in the concave one at approximately Zo/ l 01> meaning that the diffusion control changes in the activation one at the beginning of the polarization curve at low rj and At larger overpotentials, the diffusion control occurs. Hence, the diffusion ccaitrol at aU overpotentials appears at 0.1 activation control appears at Zq/Zl< 0.1 at low overpotentials. 

Obviously, the Eq. (2.80) becomes valid at the moment of the formation of the new phase, and it can be used for estimating the overpotential, at which the nucleation takes place. In order to calculate this overpotential, the supersaturation must be known. According to Pangarov et al. [22, 49, 50], the work of formation of differently oriented particles can be estimated using supersaturations of four to seven. Considering the nucleation overpotential (for different supersaturations), Klapka [48] assumed ten as the upper limit of supersaturation. The lower limit is obviously one and the Eq. (2.80) in this case becomes identical to the equation of the charge transfer reaction. 

Equations (6.10) and (6.11) are valid in the hydrogen evolution range at overpotentials lower than the critical one for the change of the growth of dendrites. The situation is dramatically different in galvanostatic electrodeposition of powder. In this case, due to the increase of the surface coarseness, the low increase of the limiting diffusion current density caused by the increase of the surface area of a... 

Sviridova et al.[283] have shown that the hydrogen overpotential at a gallium cathode in strongly acidic solutions is elevated because of the decelerating effect of specifically adsorbed water molecules. With increasing temperature this effect weakens therefore the value of the preexponential factor obtained in [262] is somewhat overestimated.- Consequently, we may assume that the ratio of the preexponential factors for Hg and Ga (which is equal to 3) is the lower limit of this value. The above-mentioned overestimation of the preexponential factor probably caused a noticeable upward deviation of the point for Ga from the general dependence shown in Figure 4.6. 

Only a limited number of true metal complex electrocatalysts have been proposed for proton reduction due to the difficulty inherent in the bielectronic nature of this reaction. It is obvious that the design of such electrocatalysts must take into account the lowering of the overpotential for proton reduction, the stability of the catalytic system, and the regeneration of the starting complex. 

All of these effects combine to provide enhanced yield and improved electrical efficiency. Other benefits which will become apparent include increased limiting currents [7,8], lower overpotentials and improved electrodeposition rates [9]. (Efficiency is defined as the amount metal deposited divided by the amount that should be deposited according to Faraday s laws of electrolysis.)... 

It is usual to operate an aqueous-medium fuel cell under pressure at temperatures well in excess of the normal boiling point, as this gives higher reactant activities and lower kinetic barriers (overpotential and reactant diffusion rates). An alternative to reliance on catalytic reduction of overpotential is use of molten salt or solid electrolytes that can operate at much higher temperatures than can be reached with aqueous cells. The ultimate limitations of any fuel cell are the thermal and electrochemical stabilities of the electrode materials. Metals tend to dissolve in the electrolyte or to form electrically insulating oxide layers on the anode. Platinum is a good choice for aqueous acidic media, but it is expensive and subject to poisoning. 

Mass transport within the electrodes is of particular importance in determining the reflection of the porous media structure on the fuel cell performance. In fact, the main results of mass transport limitation is that the reactant concentrations (H2 and CO for the anode, and O2 for the cathode) at the reaction zone are lower than in the gas channel. When applying Equations (3.40) and (3.42), the result is that the lower the concentration of the reactants, the lower the calculated cell performance. The loss of voltage due to the mass transport of the gas within the electrodes is also referred to as concentration overpotential. Simplified approaches for determining concentration overpotential include the calculation of a limiting current, i.e. the maximum current obtainable due to mass transport limitation (cf. Appendix A3.2). 

---