Limiting-current density, defined

When anodic polarization is appreciable AE 0), the CD will tend toward the value and then remain unchanged when polarization increases further. Therefore, parameter i, as defined by Eq. (13.44), is a limiting CD arising from the limited rate of a homogeneous chemical reaction when Cj drops to a value of zero it is the kinetic limiting current density. 

Potentiostatic current sources, which allow application of a controlled overpotential to the working electrode, are used widely by electrochemists in surface kinetic studies and find increasing use in limiting-current measurements. A decrease in the reactant concentration at the electrode is directly related to the concentration overpotential, rj0 (Eq. 6), which, in principle, can be established directly by means of a potentiostat. However, the controlled overpotential is made up of several contributions, as indicated in Section III,C, and hence, the concentration overpotential is by no means defined when a given overpotential is applied its fraction of the total overpotential varies with the current in a complicated way. Only if the surface overpotential and ohmic potential drop are known to be negligible at the limiting current density can one assume that the reactant concentration at the electrode is controlled by the applied potential according to Eq. (6). 

The limiting current density may be defined as the current density at which the depression of the Na+ concentration at the interface of the membrane s sulphonic and carboxylic layers results in an abrupt rise in cell voltage and drop in current efficiency. 

The last part of the polarization curve is dominated by mass-transfer limitations (i.e., concentration overpotential). These limitations arise from conditions wherein the necessary reactants (products) cannot reach (leave) the electrocatalytic site. Thus, for fuel cells, these limitations arise either from diffusive resistances that do not allow hydrogen and oxygen to reach the sites or from conductive resistances that do not allow protons or electrons to reach or leave the sites. For general models, a limiting current density can be used to describe the mass-transport limitations. For this review, the limiting current density is defined as the current density at which a reactant concentration becomes zero at the diffusion medium/catalyst layer interface. 

Electrochemical window — In electrochemical experiments the range of potentials that is accessible without appreciable current flow, i.e., the potential range in which the electrode may be considered perfectly polarizable . Electrochemical windows depend on the - electrode material, the - solvent, and the - electrolyte. There is no strict definition for the current density defining the potential limits of the electrochemical window. That depends on the experiment, i.e., the signals to be measured. For highly sensitive measurements of very low current densities, the acceptable current densities at the potential limits are much smaller than in cases where high current density signals are measured. The electrochemical window also depends very much on impurities, e.g., traces of water in nonaqueous solvents, or traces of transition metal ions in aqueous electrolyte solutions. The... 

The RRDE is calibrated by determining its collection efficiency N. This parameter is defined as the fraction of a species formed at the disc that arrives at the ring and reacts there. To do this, consider a simple oxidation reaction, say, Fe to Fe. The disc potential is set at a positive value, where the oxidation process occurs at some rate i, while the ring potential is set at a very negative value, at which the oxidized species is reduced at its limiting current density. Assuming that there is initially no Fe in solution, the ring current results... 

Equation (8) gives the limiting, potential-independent current density predicted for complete control of sequence (5b) -h (5c) by the dissociative chemisorption of H2 (process (5b)) at a catalyst surface with a small number of CO-free sites (see 18a). Such a limiting rate of hydrogen electro-oxidation at low anodic overpotentials has been observed recently in RDE experiments with H2/CO mixtures, performed with platinum and PtRu RDEs [18d,e]. This limiting current density (Eq. (8)) explains the PEFC characteristic observed with low CO levels in the fuel feed stream, depicted in Fig. 13. Under such conditions, the fuel cell will exhibit ordinary anode losses up to the current density defined by Eq. (8), but higher current demands would require a... 

The current density at which Co approaches zero is defined as the limiting current density, iL which is given by... 

The finite transport rate of the electroactive species toward the electrode surface implies the existence of a limiting current density, that is the most important consequence of mass transport. This limiting current density is defined by the condition of maximum concentration gradient of the electroactive species, which is achieved when the concentration of this species tends to zero at the electrode j depleted DEL interface (or, more accurately, at the EDL I DEL boundary). 

In this model, the drop of voltage due to a variation of fuel utilization is modelled also considering the effect on the cathode diffusion. The effect of diffusion on the cell voltage sensitivity to fuel utihzation has a significant effect when the limiting current density is approached, or for low value of the air stoichiometry. It should also be noticed that in the equations (34) and (35), as posed in [3], the variable L has not the meaning of excess of oxidant with respect to the stoichiometric requirement, and so it has a different meaning compared to the air stoichiometry Xax as defined and used in this Chapter. 

The value of the limiting current density is defined as the maximum value of applied current density at which all supplied current is used to oxidize the organic species. Its value also indicates another condition that concerns the degree of its utilization. In fact, a low value of limiting current imposes to apply a low current density if its full use for the oxidation of pollutants is imposed. In other words, a low value of limiting current density indicates a low degree of utilization of the adopted anodic surface. As Fig. 1 shows, this condition occurs at the end of treatment, when the wastewater contains low... 

Electrode Kinetic and Mass Transfer for Fuel Cell Reactions For the reaction occurring inside a porous three-dimensional catalyst layer, a thin-film flooded agglomerate model has been developed [149, 150] to describe the potential-current behavior as a function of reaction kinetics and reactant diffusion. For simplicity, if the kinetic parameters, such as flie exchange current density and diffusion limiting current density, can be defined as apparent parameters, the corresponding Butler-Volmer and mass diffusion relationships can be obtained [134]. For an H2/air (O2) fuel cell, considering bofli the electrode kinetic and the mass transfer, the i-rj relationships of the fuel cell electrode reactions within flie catalyst layer can be expressed as Equations 1.130 and 1.131, respectively, based on Equation 1.122. The i-rj relationship of the catalyzed cathode reaction wifliin the catalyst layer is... 

If C, = 0 at a = 0, then is the limiting current density [2]. However, eq. (1.96) is more conveniently used if C = C at x = oo from the cathode surface since the bulk concentration is normally known prior to operating an electrolytic ceE Hence, the current density in this case becomes the limiting current density as defined by... 

Voltammograms obtained by the RDE technique are of common shape (Figure 8.32). They contain a well-defined plateau of limiting current that is observed over a wide region of cathodic potentials (-1.2 limiting current density (ij ) depends on solution composition, and... 

Co(II) complexes are reduced at more negative potentials simultaneously with hydrogen evolution. Therefore, cathodic voltammograms obtained in Co(II) and malic acid solutions contain poorly defined plateau of limiting current density (fn ) [136]. The rate of this partial process grows at an increase in cathodic polarization. Besides, decreases at an increase in the ligand concentration. If an... 

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