Effectiveness factor agglomerate

As for the first assumption, the electrolyte phase must be treated as a mixed phase. It consists of a thin-film structure of ionomer at the surface of Pt/C agglomerates and of water in ionomer-free intra-agglomerate pores. The proton density is highest at the ionomer film (pH 1 or smaller), and it is much smaller in water-filled pores (pH > 3). However, the proton density distribution is not incorporated in the statistical utilization Tstat, but in an agglomerate effectiveness factor, defined in the section Hierarchical Model of CCL Operation. ... 

The macroscale model is almost identical to the MHM discussed in the section Macrohomogeneous Model with Constant Properties. In the electrochemical source term of the MHM Equation 4.5, a spatial variation in the agglomerate effectiveness factor must be accounted for... 

The model of water-filled nanopores, presented in the section ORR in Water-Filled Nanopores Electrostatic Effects in Chapter 3, was adopted to calculate the agglomerate effectiveness factor. As a reminder, this model establishes the relation between metal-phase potential and faradaic current density at pore walls using Poisson-Nernst-Planck theory. Pick s law of diffusion, and Butler-Volmer equation... 

Values of the agglomerate effectiveness factor, Fagg (x), are found in the range from 0.35 to 0.1, as seen in Figure 4.13. They exhibit their highest values close to the interface with the PEM at moderate current density. 

Figure 4.12b shows the variation of the total effectiveness factor of the CCL with current density for the polarization curves in Figure 4.12a. Fstat and F p are functions of composition and microstructure of the CCL neglecting degradation effects, these parameters should remain constant. However, the agglomerate effectiveness factor decreases with current density. The dependence of the effectiveness factor on current density is stronger at low and high current densities, jo < 0.4 A cm and jo > I A cm . Effectiveness factor values are similar over a wide range of jo for the studies of Suzuki et al. (2011) and Soboleva et al. (2011). However, the higher propensity for flooding of the GDL results in a sharper drop of the effectiveness factor at jo > I A cm in Suzuki et al. (2011).

The analysis below is given for the ORR, since the agglomerate and embedded models mainly examine the cathode reaction at the anode can be derived in a similar manner. The analysis is basically the same as that of reaction and diffusion in a catalyst pellet. For the analysis, an effectiveness factor is used, which allows for the actual rate of reaction to be written as (see eq 55)... 

Since the ORR is a first-order reaction following Tafel kinetics, the solution of the mass conservation equation (eq 23) in a spherical agglomerate yields an analytic expression for the effectiveness factor... 

The other approach is more complicated and requires a deeper knowledge of the agglomerate structure or yields more fitting parameters. In this approach, the porous-electrode equations are used, but now the effectiveness factor and the agglomerate model equations are incorporated. Hence, eq 64 is used to get the transfer current in each volume element. The gas composition and the overpotential... 

Effectiveness Factor of Single Agglomerates Macrohomogeneous electrode theory, described so far, has been successfully explored in fuel cell diagnostics and optimization [17, 122-126], Nowadays, finer details of structure and electrocatalytic mechanisms in CLs and model nanoparticle electrocatalysts are moving into focus [127]. 

Experiments suggest that agglomerates of carbon particles form distinct structural units in the fabrication process. Electrostatic effects control the spatial distributions of electrical potential and reaction rates in agglomerates. Corresponding effectiveness factors of agglomerates have been studied in Ref. 240 as a function of agglomerate radius, composition, and the charge-transfer coefficient. 

On surface it is very simple model but effective concentration of filler includes observation that some layer of polymer is bound to the surface of filler and the mechanisms of this bonding is mathematically expressed by effectiveness factor. The recent model assumes that filler particles are spheres which might be connected to form chain-like agglomerates. Each particle is surface coated with matrix polymer. The elastomeric layer is considered immobilized. The effective filler volume is higher than filler volume fraction by the amount of adsorbed polymer. The effectiveness factors is given by equation ... 

Figure 2.6. Effect of the cathodic transfer coefficient, a, on the reactivity distribution within an agglomerate. For 0=1, the reactivity remains uniform throughout the agglomerate so that an effectiveness of Fa = 1 is obtained. For a = 0.5, relative reactivity drops steeply toward the agglomerate center. The corresponding effectiveness factor is strongly reduced. Fa 0.095, i.e. only 10% of the accessible catalyst is effectively used for reactions in this case.

An effective Tafel equation can be written for the Faradaic current density generated by a single agglomerate, which includes the effectiveness factor... 

The nonuniform distribution of protons and potential in water-filled agglomerates and ultrathin catalyst layers is predominantly an electrostatic effect. It is determined by the Debye length. Ad- Resulting reaction rate distributions and effectiveness factors depend on the characteristic sizes of agglomerates (i a) or ultrathin CCLs ( L) and on the transfer coefficient a. 

At the agglomerate level, discussed in Section 2.5, electrostatic effects determine the radial distributions of proton concentrations and electrode potential. Using these distributions in the Tafel law gives the resulting distribution of the electrochemical rate. It depends on the transfer coefficient a, how uniformly catalyst particles are utilized in the wetted pores of agglomerates. Uniform utilization and, thus, effectiveness factors close to 1 are obtained for a 1. 

Internal wetted pore fraction (nomalized) Volumetric Faradaic current density Effective Volumetric Faradaic current density including effectiveness factor of agglomerates... 

Effectiveness factors of agglomerates and ultrathin catalyst layers Thickness of the effective layer in the CCL Relative permittivity (of water 78)... 

The results showed that the effectiveness factor of agglomerates,, is mainly affected by electrostatic effects, which are determined by flic non-linear distribution of proton concentration and flic radial variation of the electrostatic potential, Ti r ). Figure 8.12(a) shows the radial function (r) for various agglomerate radii. It decreases from the agglomerate surface towards the center over a characteristic length corresponding to. In Figure 8.12 (b), t/a (r)... 

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