Mass transfer effects limiting current density

In electrochemistry, spherical and hemispherical electrodes have been commonly used in the laboratory investigations. The spherical geometry has the advantage that in the absence of mass transfer effect, its primary and secondary current distributions are uniform. However, the limiting current distribution on a rotating sphere is not uniform. The limiting current density is highest at the pole, and decreases with... 

It is an experimental fact that whenever mass transfer limitations are excluded, the rate of charge transfer for a given electrochemical reaction varies exponentially with the so-called overpotential rj, which is the potential difference between the equilibrium potential F0 and the actual electrode potential E (t) = E — Ed). Since for the electrode reaction Eq. (1) there exists a forward and back reaction, both of which are changed by the applied overpotential in exponential fashion but in an opposite sense, one obtains as the effective total current density the difference between anodic and cathodic partial current densities according to the generalized Butler-Volmer equation ... 

The diffusion layer thickness is controlled by the hydrodynamics (fluid flow). Although more details on mass transfer effects are discussed in Chapter 5, it is worthwhile to point out here that the diffusion-limited current density is independent of the substrate material. 

In the above section, all the equations we derived are based on pure electron transfer kinetics. Unfortunately, in reality, mass transfer (e.g. hydrogen diffusion inside a porous fuel ceU CL) will have an effect on the overall reaction rate, and sometimes can become the rate-determining step. To address this mass transfer effect, we need to introduce another concept, called limiting diffusion current density, which can be expressed as in Eqns (1.35) and (1.36) [9] ... 

The maximum concentration gradient gives the maximum current density called limiting current density l owing to concentration or mass transfer effects... 

As discussed in Chapter 4, fuel crossover is typically measured as an effective crossover current density. The mass transfer limiting hydrogen crossover current density is the maximum current density that could be achieved if all of the hydrogen crossover were used as fuel. This corresponds to a limiting current density of... 

In Example 5.8, we solved for the mass transport limiting current density of an electrode based on the resistance to gas-phase transport only. In the PEFC and some other fuel cells, a thin layer of liquid or ionomer may cover portions of the catalyst surface, resulting in an additional film resistance. Symbolically show this simation to form a more precise model of mass transfer limited current density at an electrode. Ignore convective effects and Knudsen diffusion in this problem. 

Henry s constant His a strong function of temperature for liquids. At a phase boundary, the concentration of the reactant is decreased in the liqnid or solid phase according to Henry s law and then must diffuse to the catalyst. Any small film resistance on the catalyst of liquid effectively floods the catalyst location, so that almost no reactant can reach the catalyst. For ionomer coverage of the catalyst in a PEFC, some reactant penetration is desired. Although a high reactant diffusivity in the catalyst layer electrolyte is beneficial to increase the mass transfer limiting current density, it is deleterions for reactant crossover discussed in Chapter 4, so that a proper engineering balance of ionomer content in the electrolyte is used. 

The phenomena are common to every value of fuel utilization. Evidently, the increase in fuel utilization emphasizes the effects on the charge transfer mechanism and especially on the mass transport in fact, the limiting current density drops significantly at higher values. 

Figure 12(b) shows the local current distribution of first and second order reactions and applied over potentials ° for the coupled anode model without the mass transfer parameter y. The figure also shows the effect of a change in the electrode kinetics, in terms of an increase in the reaction order (with respect to reactant concentration) to 2.0, on the current distribution. Essentially a similar variation in current density distribution is produced, to that of a first order reaction, although the influence of mass transport limitations is more severe in terms of reducing the local current densities. 

Two impedance arcs, which correspond to two relaxation times (i.e., charge transfer plus mass transfer) often occur when the cell is operated at high current densities or overpotentials. The medium-frequency feature (kinetic arc) reflects the combination of an effective charge-transfer resistance associated with the ORR and a double-layer capacitance within the catalyst layer, and the low-fiequency arc (mass transfer arc), which mainly reflects the mass-transport limitations in the gas phase within the backing and the catalyst layer. Due to its appearance at low frequencies, it is often attributed to a hindrance by finite diffusion. However, other effects, such as constant dispersion due to inhomogeneities in the electrode surface and the adsorption, can also contribute to this second arc, complicating the analysis. Normally, the lower-frequency loop can be eliminated if the fuel cell cathode is operated on pure oxygen, as stated above [18],... 

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