CL performance

The K-matrix method is essentially a configuration interaction (Cl) performed at a fixed energy lying in the continuum upon a basis of "unperturbed funetions that (at the formal level) includes both diserete and eontinuous subsets. It turns the Schrodinger equation into a system of integral equations for the K-matrix elements, which is then transformed into a linear system by a quadrature upon afinite L basis set. 

How to balance Nafion ionomer contenf and Pf/C loading is a challenge for optimizing CL performance, due to fhe complexity induced by proton and electron conduction, reactant and product mass transport, as well as electrochemical reactions within the CL. The optimization of such a complex system is mainly implemented through multiple components and scale modeling, in combination with experimental validation. 

Cho et al. [140] examined the performance of PEM fuel cells fabricated using different catalyst loadings (20, 40, and 60 wt% on a carbon support). The best performance—742 mA/cm at a cell voltage of 0.6 V— was achieved using 40 wt% Pt/C in both anode and cathode. Antonie et al. [28] studied the effect of catalyst gradients on CL performances using both experimental and modeling approaches. Optimal catalyst utilization could also be achieved when a preferential location of Pt nanoparticles was close to the PEM side ... 

It ean be seen from Figure 19 that the eatalyst Cl performance is good for three eonseeutive bateh experiments and eonfirm the hypotheses that in the heterogeneous catalyst approach iron ions are in better eontrol than in the homogeneous one. 

S0l., So2 and SHlo refer to the respective source terms owing to the ORR, e is the electrolyte phase potential, cGl is the oxygen concentration and cHlo is the water vapor concentration, Ke is the proton conductivity duly modified w.r.t. to the actual electrolyte volume fraction, Dsa is the oxygen diffusivity and is the vapor diffusivity. The details about the DNS model for pore-scale description of species and charge transport in the CL microstructure along with its capability of discerning the compositional influence on the CL performance as well as local overpotential and reaction current distributions are furnished in our work.25 27,67... 

In 1938, Chandra (Cl) performed experiments with smoky air which confirmed the Rayleigh theory for depths above 1.0 cm (he employed depths from 4 mm to 1.6 cm), but for depths below this he observed a columnar convection for Rayleigh numbers well below the predicted critical value. In 1950, Sutton (S13) repeated the experiments of Chandra with both air and carbon dioxide and confirmed, for both gases, the occurrence of a subcritical columnar convection for depths less than 8 mm. These results appear to be due merely to the anomalous flow properties of smoke-air suspensions. 

The function g(x) in the system of Eqs. (23.24) and(23.7) should be optimized to maximize the CL performance, that is, to minimize fjo for given jV Figure 23.7 compares the x-shapes of the local proton current and overpotential for the uniform and nonuniform (optimal) loadings [22]. As can be seen, the optimal loading nearly doubles the cell current density. 

In this section, it is constant however, this is not necessariiy the case. In Section 2.6 we will see that the gradient of catalyst loading is beneficial for CL performance. 

In PEFCs the cathode side makes the largest contribution to voltage loss. This explains the great interest in CCL performance in these cells. We begin the analysis of CL performance with the cathode catalyst layer of a low-temperature hydrogen fuel cell. However, it should be emphasized that the performance of other catalyst layers of the cells considered in this book can be described by similar equations. The features of particular layers are taken into account by the expression for the rate of the electrochemical reaction. 

In this section, we return to the full system of equations for CL performance, (2.10)-(2.12). We study numerically the effect of the oxygen diffusion coefficient D on the CCL polarization voltage rjo for the general case of the Butler-Volmer conversion function (Kulikovsky, 2009a). 

In this chapter the scope of our discussion was restricted by the macrohomogeneous model of CL performance and its derivatives. The first numerical macrohomogeneous models of CCL for a PEM fuel cell were developed by Springer and Gottesfeld (1991) and by Bernard and Verbrugge (1991). These models included the diffusion equation for oxygen transport, the Tafel law for the rate of ORR and Ohm s law for the proton transport in the electrolyte phase. A similar approach was then used by Perry, Newman and Cairns (Perry et al., 1998) and by Eikerling and Kornyshev (1998) for combined numerical and analytical studies. 

The amount of polyelectrolyte binder used in CLs is not as large as that in membranes [18] however, the amount is important because it is closely related to CL performance, catalyst utilization, and MEA durability [23, 24]. In current PEMFCs, PFSA ionomers are employed in the CL as binders and in the proton conducting electrolyte to extend the formation of the electrochemical three-phase interface [3]. The latter is important for obtaining desirable catalyst utilization and, thus, high performance of MEA. Since the reactant must be transported through the proton conducting electrolyte before it arrives at the reaction sites to carry out reactions, the binder in the CL must be reactant-permeable to avoid reactant mass transport limitations [25]. The reactant-permeable property of the binder is... 

Transient study showed that the porosity of the CL affects the cell performance [66]. When CL porosity gi <0.1, the liquid water effect is obvious, but when ci > 0.1, the liquid water effect is not very apparent. An optimum value appears between ci 0.06 and d = 0.1. Pai et al. found that the CL performance was enhanced by using clay for dispersion in the anode CL [67]. Yoon et al. studied the effect of pore structure in the cathode CL on PEMFC performance [68]. 

Operating conditions. As common sense would suggest, operating conditions such as the temperature, pressure, and humidity of the reactant gases directly affect CL performance. An increase in the operating temperature leads to an increase in flie diffusion rate to reduce the mass transport resistance, and the ohmic-ion conductivity of the binder in the CL also increases. The most important... 

As electrochemical reaction sites, CLs play an extremely important rote in the performance of fuel cell stacks. A CL mainly consists of catalyst, support and binder. The CL is usually coated on the surface of the GDL. Another method has the CL directly applied to the membrane (catalyst coated membrane, CCM). The selection of the components, the proper ratios of those components, the structure of the formed CL and the formation method of the CL are critical factors in the performance of a fuel cell. The stability of the fuel cell performance is directly related to the stabilities of the catalyst, binder and support in flie CL. Degradation of catalytic activity would be due to the agglomeration of the eatalyst particles and their detachment from the support, the degradation of the binder, and the oxidation and corrosion of the support, particularly at the cathode. Further improvement in CL performance is possible. The basic technical considerations include how to maximize the three-phase interface of the CL, how to stabilize the metal particles on the support, and how to reduce the degradation of the components in the CL. 

The goal of DFT modeling is to understand the chain of elementary reaction events in the electrochemical conversion and to calculate the rate constants for these steps. The reaction mechanism and the rate constants, obtained from DFT, are then used to establish and parameterize time-dependent mass balance equations for the adsorbed/desorbed species. The steady-state solution of the surface coverage equations provides the conversion function, which can be used in the simplified current conservation equation in the CL model. The solution of the CL performance model yields the CL polarization curve, which can be used in the fuel cell or stack model. The chain of information transfer looks schematically like... 

The model shows that the electron transport effects do not affect the CL performance if the conductivity of the electron-conducting phase obeys the following requirement ... 

Evaluation of CL performance requires a number of parameters that define the ideal electrocatalyst performance, allowing deviations from ideal behavior to be rationalized and quantified. Ideal electrocatalyst performance is achieved when the total Pt surface area per unit volume, Stot, is utilized and when reaction conditions at the reaction plane (or Helmholtz layer) near the catalyst surface are uniform throughout the layer. These conditions would render each portion of the catalyst surface equally active. Deviations from ideal behavior arise due to statistical underutilization of catalyst atoms, as well as nonuniform distributions of reactants and reaction rates at the reaction plane that are caused by transport effects. This section introduces the effectiveness factor ofPt utilization and addresses the hierarchy of structural effects from atomistic to macroscopic scales that determine its value. 

However, as discussed in the paragraph below that equation, liquid water formation in hydrophobic CLs pores is virtually impossible, requiring huge liquid excess pressures. Therefore, during operation, the saturation s could increase only in secondary pores if they are hydrophilic. The volume fraction of hydrophobic pores will determine whether the CL performance depends significantly on the liquid water saturation. 

In the following, a fixed composition of the CCL will be assumed. This section will present an analytical solution of the MHM in limiting cases (Kulikovsky, 2010b). It will provide expressions for the shapes depicted in Figure 4.2 that could serve as a fingerprint of good or bad CL performance. 

From the structure of Equation 4.275, it follows that any nondecreasing function (rj) improves the CL performance. However, growing functions < >( ) do not describe the limiting case of uniform catalyst and electrolyte loading (g = p = 1). Indeed, g = P = I gives 0=1, and from Equation 4.274 it follows that for all rj, one must have = 1. 

Calculations show that the effect of CL performance optimization by the gradient catalyst loading strongly depends on jo. To characterize the effect, the optimization factor kept is introduced, defined as the ratio of cell currents at optimal and uniform loadings... 

Nonetheless, the simple model above clearly indicates the trends it prescribes that both Nafion and catalyst loadings should grow toward the membrane surface. The optimal Nafion content is almost linear, while the optimal catalyst loading is parabolic-like (Figure 4.39). Calculations show that even non-optimal shapes of similar types improve the CL performance, that is, real shapes could always be chosen in accordance with structural limitations. 

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