Ideal proton transport

This relation was obtained in Section 2.2 for the case of an ideal catalyst layer. Thus, ideal proton transport means that 1. 

Ideal proton transport means that the overpotential gradient is small. Setting in the system (2.10)-(2.12) fj fjo and omitting Eq. (2.11) we arrive at... 

With (2.70) this equation is the general polarization curve for the CCL with ideal proton transport. Of particular interest are the two limiting cases. 

For the case of severely limited oxygen transport and ideal proton transport, one may write... 

A detailed discussion of the diffusion-limited case will be presented in the section Ideal Proton Transport of Chapter 4. In the oxygen-depleted regime, an explicit... 

A general analytical solution to the system of Equations 4.53 through 4.55 has not been found yet. However, in the limiting cases of ideal transport of proton or oxygen, the explicit analytical solutions can be derived. In this section, the case of ideal proton transport in the CCL (infinite cfp) is considered. The CCL performance is, hence, determined by the ORR kinetics and by oxygen transport through the CCL. 

This equation is the polarization curve for the CCL with ideal proton transport (Figure 4.15, dashed curve). Of particular interest are the limiting cases of small and large fo, corresponding to low and high cell current, respectively. In these cases, relations (4.77) and (4.78) can be simplified to express rjo and Id through the cell current jo. 

According to the model above, in experiments of Nordlund and Lindbergh, the approximation of ideal proton transport is justified for currents below 100 mA cm . To show this explicitly, it is advisable to plot the model shape of MOR rate along x. By definition, Rmor = -dj/dx. Using Equation 4.232 here, one obtains... 

Physically, this result is quite clear if the cell current is low, the reaction rate is distributed uniformly over the CL thickness, and the spatial optimization of catalyst/Nafion loading is not necessary. If, however, the dimensionless current is substantial, the reaction runs mainly in a small conversion domain close to the membrane (the section Ideal Proton Transport ). Placing more catalyst and Nation into this domain, greatly improves the performance. 

Besides these generalities, little is known about proton transfer towards an electrode surface. Based on classical molecular dynamics, it has been suggested that the ratedetermining step is the orientation of the HsO with one proton towards the surface [Pecina and Schmickler, 1998] this would be in line with proton transport in bulk water, where the proton transfer itself occurs without a barrier, once the participating molecules have a suitable orientation. This is also supported by a recent quantum chemical study of hydrogen evolution on a Pt(lll) surface [Skulason et al., 2007], in which the barrier for proton transfer to the surface was found to be lower than 0.15 eV. This extensive study used a highly idealized model for the solution—a bilayer of water with a few protons added—and it is not clear how this simplification affects the result. However, a fully quantum chemical model must necessarily limit the number of particles, and this study is probably among the best that one can do at present. 

As illustrated in Figure 2.1b, ideal locations of Pt particles are at the true triple-phase boundary, highlighted by the big star. Catalyst particles with nonoptimal double-phase contacts are indicated by the smaller stars. Pt gas interfaces are inactive due to the inhibited access to protons. Bulky chunks of ionomer on the agglomerate surface build the percolating network for proton conduction in secondary pores. Only individual or loosely connected ionomer molecules seem to be able to penetrate the small primary pores. It is unlikely that they could sustain notable proton conductivity. They merely act as a binder. Proton transport inside agglomerates, thus, predominantly occurs via water-filled primary pores, toward Pt water interfaces. 

The polarization voltage of the cathode side is determined by reaction kinetics, transport of water and oxygen across the cell and by proton transport across the CCL. In this section, we will assume an ideal membrane humidification. We start with the model of the CCL. 

The mobility in the pore includes molecular mechanisms of proton transport in bulk water and along the array of charged surface groups. An idealized two-state approach based on this distinction was considered in [82]. This simple model can reproduce a continuous transition from surface-like to... 

Equations (2.10)-(2.12) describe the CCL performance in the general case of finite transport losses. We see that the problem is controlled by three parameters e, D and join the general case, this system can hardly be solved. However, in the limiting cases of ideal oxygen or proton transport the reduced problems are solvable. Before proceeding to these cases we will establish a general conservation equation, which follows from Eqs (2.11) and (2.12). 

Note that in the case of poor reactants or proton transport in the CL the reaction rate and the respective source of heat are distributed nonuniformly (Chapter 2). In this chapter we ignore these nonuniformities. The solutions for the case of ideal transport derived below provide a reference point for more complicated studies. 

The catalyst layers need to be designed to generate high rates of the desired reactions and minimize the amount of catalyst necessary for reaching the required levels of power output. An ideal catalyst layer should maximize the active surface area per unit mass of the electrocatalyst, and minimize the obstacles for reactant transport to the catalyst, for proton transport to exact positions, and for product removal from the cell these requirements entail an extension of the three-phase boundary. In general, individual property specifications should be a compromise between conflicting requirements. The catalyst layer structure should be optimized with respect to the interactions between components, with trade-offs between several effects. 

This ideal situation corresponds to a priori assumption of ideal reactant transport, which is realized in any electrode at sufficiently small currents. In this case, the local proton current is linear, while the overpotential and the reaction rate are constant along X. 

The prevailing class of PEMs exploits the unique properties of water as aproton solvent and shuttle. As a result of the high concentration of protons and the peculiar nature of hydrogen bonding, liquid water is an ideal medium for proton transport. As a blueprint for this fundamental principle, nature relies entirely on liquid water to facilitate proton transfer in intracellular energy transduction (Kuznetsov and Ultrup, 1999). 

What is the effect of finite A, at high currents In this section, the case will be considered for poor oxygen diffusivity and ideal proton conductivity of the CCL. In this case, the local polarization curve of the CCL is given by Equation 4.87. Substituting Equation 5.41 into Equation 4.87, one obtains the local polarization curve with the term describing oxygen transport in the GDL ... 

An ideal CL should provide passages for proton transport, electron transport, and reactant gas transport and should also be able to remove product water. In general, there are two kinds of CLs hydrophobic CL and hydrophilic CL. The composition ratio in the CL greatly influences fuel cell performance and will be discussed in detail in Chapter 2. 

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