Exchange current density local

Here ir is a local polarization characteristic, referred to as a unit of electrode volume. Sr,i0 are the specific surface and the exchange current density,... 

On an inhomogeneous surface the two currents densities may vary over the surface, and need not balance locally only the total current must be zero. In this case we must replace the exchange current densities in Eqs. (11.40) - (11.42) by the corresponding exchange currents. Because of charge conservation an uneven current distribution on the electrode must be balanced by currents flowing parallel to the surface on both sides of the interface. 

Here subscripts a and c denote anode and cathode respectively, iref is the reference exchange current density, y is the concentration dependence exponent, [ ] and [ ]ref represent the local species concentration and its reference concentration, respectively. Anode transfer current, Ra, is the source in the electric potential equations at the anode/electrolyte interface with positive sign on membrane (electrolyte) side and negative sign on solid (anode) side. Similarly, near the cathode interface, the source on membrane (electrolyte) side is negative of the cathode transfer current, Rc and that on solid (cathode) side is positive of Rc. The activation over-potentials, in Equations (5.35) and (5.36) are given by... 

Owing to the symmetry of the attachment-detachment process on a kink site from eq. (2,21), a local exchange current density (cf. eq. (2.14 a)) may be defined... 

This quantity is independent of the surface profile and directly connected to the exchange frequencies oidep tink or diss,kink od can be considered as a system property giving a key to the kinetics of the metal ion transfer reaction. The local exchange current density as defined by eq. (2.23) is an imaginary quantity assuming a surface fully covered by kink sites. 

The surface, which can be considered as active for this direct transfer, is located, obviously, in the close vicinity of the step. All atoms exchanged at a distance not much greater than one atomic diameter do,Me can be considered as incorporated into the crystal lattice. Under this assumption, all sites denoted as step" in this area are equivalent and roughly equal to the kink sites. Consequently, these sites can be characterized by an exchange current density, t o° ep > which is not very much different from the local exchange current density of kinks (cf. eq. (2.23)). 

The quantity j0 is the exchange current density and is related to the kinetics of the electrochemical reactions considered and the local concentration of the reactants. It also depends on the electrode material. The parameter a is the symmetry factor and typically has a value of around 0.5. The Butler—Volmer... 

O2 diffusion versus proton conductivity, g = I jab Characteristic parameter of O2 diffusion, A cm Exchange current density parameter, A cm Local proton current density, A cm Proton... 

Then, a deeper analysis has been made by performing a parameter estimation, allowing an analysis of the local anode activation effects with variable local fuel utilization and temperature the anode exchange current density of every sector has been the estimated parameter, and its strict relation to the local fuel utilization of every sector (Paragraph 3.1) has been outlined. 

Nevertheless, the activation contribution to the cell voltage sensitivity to FU is neglected in this part of the analysis because of its small effect of the voltage drop [16,21]. In the next Paragraph 6, dealing with parameter estimation of some terms of the cell polarization model, the anode exchange current density will be estimated and a correlation with the local fuel utilization will be outlined. 

Estimation of the Local Anode Exchange Current Density... 

The parameter estimation procedure involved the anode exchange current density, considered in the expression of the anode activation overpotential (equation (18)). As already noticed, in literature there are some expressions which describe the anode exchange current (equations (19) and (20) according to these equations, this parameter should be significantly affected by the fuel utilization values, and the aim is to outline how the distribution of the local fuel utilization (that is, the distribution of fuel) inside the generator affects the activation of the reaction at the anode side in the various sectors. 

The procedure of parameter estimation consisted in the evaluation of the values of the anode exchange current density in each sector of the generator, in order to obtain its distribution inside the stack. In the estimation, the local values of fuel utilization evaluated in... 

In Figure 29 the correlation between the local anode exchange current density and the local fuel utilization (as usual, divided in Power Leads and Ejectors side) is shown. 

Figure 29. Correlation between the local anode exchange current density and the local fuel utilization.

The anode exchange current density depends not only on the local fuel utilization, but it is also influenced by the local temperature. A higher temperature should have a increasing effect on the anode exchange current density. Therefore, in Figure 30 the correlation between the local anode exchange current density and the local temperature (as usual, divided in Power Leads and Ejectors side) is shown. It seems that the correlation with the local temperature is less evident than the correlation with the local fuel utilization, especially at the Ejectors side (fuel inlet). Thus, it seems that the effect of the local fuel utilization is more significant than the effect of the local temperature on the activation of the anodic reaction. 

Finally, in Figure 33 a correlation between the anode exchange current density and the local temperature (grouped by sector running hours), and the mean values for the miming horns (the cell pedigree), are shown. 

The volmnetric exchange current density (A cm ) should not be confused with the superficial exchange current density (A cm ). The first value is a local characteristic of a CCL, proportional to the local concentration of catalyst particles (to be precise, to their active surface) . In contrast, parameter is an integral characteristic of the CL. This parameter includes CL thickness imder variable h(x) the generalization of (1.38) is obvious... 

Here j x) is the local proton current density, is the volumetric exchange current density (the number of charges produced in unit volume per second, A cm ), c is the molar concentration of oxygen, Cref is the reference oxygen concentration, (f> is the conversion function, r] is the local polarization voltage, at is the proton conductivity of the CCL, D is the effective oxygen diffusion coefficient and jo is the cell current. 

However, the ORR rate is also proportional to the local exchange current density. This value includes an active surface of catalyst particles, which in turn is proportional to the catalyst concentration (loading). Is it possible to compensate for the decrease of Cqx along the channel by the increasing catalyst loading along z7... 

Here the axis x is directed from the intercoimect to the electrolyte (Figure 4.18), j x) is the local ionic current density, is the volumetric exchange current density, cm is the molar concentration of hydrogen in the anode, Cref is the reference hydrogen concentration, a is the transfer coefficient, rj is the polarization voltage of the anode side and at is the ionic conductivity of the anode. 

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