The Fuel Cell Polarization Curve

A sufficiently accurate approximation of the fuel cell polarization curve may be obtained by the following equation ... 

The single characteristic that encompasses phenomena at all scales and in all fuel cell components is the fuel cell polarization curve. The polarization curve of a membrane-electrode assembly (MEA), a single cell, or a fuel cell stack furnishes the link between microscopic structure and physicochemical properties of distinct cell components on the one hand and macroscopic cell engineering on the other. It thus condenses an exuberant number of parameters, which lies in the 50s to 100s, into a single response function. Analysis of parametric dependencies in the polariz-tion curve could be extremely powerful at the same time, it could as well be highly misleading if applied blindly. ... 

If these four equations are substituted into Eqns (9.14), (9.9), and (9.12), a semiempitical equation can be obtained, from which the fuel cell polarization curve can be calculated at a desired temperature, backpressure (obtained using gas partial pressure, according to Eqn (9.9) or (9.12)), and RH. Figure 9.2 shows the calculated polarization curves at two different backpressures (2.0 and 3.0 atm absolute backpressure, respectively). Evidently, the backpressure has an effect on performance. Note that during calculation, the values of both and / m were measured from their... 

The response of the fuel cell is determined by the electrochemical processes and associated kinetics at the electrode and electrode interface. The electrochemical processes depend on the mass and charge transfer between the bulk electrolyte solution and electrode surface. The rates at which these transfers occur are determined by the number of localized phenomena and largely depend on the materials involved. These processes are presented in this chapter and the relations between the fuel cell potential and current density are given in terms of BV and Tafel equations. The key losses in the fuel cell include the activation losses, ohmic losses, mass transport losses, and losses owing to reactant crossover and internal currents that are discussed in this chapter. The fuel cell polarization curve is presented and is discussed for low-temperature and high-temperature fuel cells such as PEMFC and SOFC, respectively. 

There are several fuel cell system dynamic models in the literature that are specifically developed for vehicle propulsion. The simplest dynamic model of a fuel cell stack is the representation of the stack with an equivalent circuit whose operating parameters are based on the polarization curve obtained from the manufacturer data sheet at nominal conditions of temperature and pressure. An equivalent single-cell model with semiempirical equation for the fuel cell polarization curve can also be used for this purpose. 

Based on the fundamental principles of electrochemical engineering (electrochemical thermodynamics and kinetics), the fuel cell polarization curves can easily be understood. 

Sometimes, quick calculations regarding fuel cell efficiency-power-size relationships need to be made. Unlike an equation that describes the fuel cell polarization curve (such as Equation 3-54), a linear approximation may be easily manipulated. For most fuel cells and their practical operating range, a linear approximation is actually a very good fit, as shown in Figure 3-23. 

Another design input is the unit performance best described by the polarization curve. The fuel cell polarization curve is the key for sizing and design of a fuel cell stack. However, as shown in Chapter 5, the fuel cell performance is determined by operational conditions (pressure, temperature, humidity of reactant gases) that must be determined based on the application requirements and constraints. 

FIGURE 27.32 Fuel cell polarization curve of a 50 cm MEA made with the new 3M cast membrane (30 pm). (From 3M, www.3m.com.)... 

Several authors have shown the fuel cell performance with varying PTFE content [103, 106, 108, 109]. Figure 7.16 shows the polarizatirais curves of DMFC with different contents of PTFE on the anode and cathode GDL respectively [82]. An excess of PTFE has an adverse effect on the fuel cell polarization as observed in both graphs. The better performance is attained with different PTFE amounts at the anode and the cathode, indicating that an optimum amount has to be chosen according to the particular material and application. This is related to the fact that different amounts of water are present in the anode and the cathode. While an aqueous solution is fed to the anode, water reaches the cathode mainly by transport from the anode through the membrane, because dried O2 or air is typically supply to the cathode. 

The variation of activity for these catalysts, all made under the same experimental conditions, except for the carbon support, was stunning and is presented as fuel cell polarization curves in Figure 3.25. On the one hand, the specific area of all these catalysts was measured and no correlation with the catalytic activity was found. On the other hand, there was a definite correlation between the catalytic activity and the surface nitrogen concentration measured by XPS. This correlation is illustrated in Figure 3.26. It is obvious that the catalytic activity for ORR increases when the surface of the catalyst is richer in nitrogen atoms. This is a logical result, since the precursor of the Fe-N2/C catalytic site (the most... 

Figure 3.25. PEM fuel cell polarization curves at 80°C of several MEAs made with nonnoble metal cathode catalysts. The cathode catalysts were prepared by adsorption of iron acetate (0.2 wt% Fe) on various untreated (NT) (panel a) or heat treated (T) carbon supports (panel b). The (T) carbon supports were obtained by heat beatment of (NT) carbon supports at 900°C in H2 Ar NH3 (1 1 2). The polarization curve for 5 wt% Pt/C at the cathode is given for comparison (according to Figure 3 in ref. [Ill] reproduced with permission of the American Chemical Society).

Figure 7.14 (a) Cross section through a catalytic layer formed by "self-assembly" of the Pickering emulsion and (b) the corresponding fuel cell polarization curve. 

Electrochemical Reactor Design and Configurations, Fig. 3 Contributions of component overpotentials to a fuel cell polarization curve (a) simulated polarization curve for water-saturated H2 and air at 80 °C and 1 atm. The curves are (—) cell potential E, (— —) reversible potential Erev, ( ) transport-limited overpotential r)n, (— —) ohmic resistive overpotential r), and (— —)... 

Figure 1.27. A sample fuel cell polarization curve obtained from the diagnostic modeling PEM fuel cell with an active area of 192 cm, designed by NRC-IFCI...

Figure 4.2. DMFC polarization behavior using aqueous methanol and solid polymer electrolyte (SPE Nafion 117) [52]. a) Anode half-cell polarization comparison between SPE and 0.5 M H2SO4, PtRu/C 0.5 mg cm, b) fuel cell polarization curve using 2 M CH3OH in water effect of temperature. PtRu/C coated Nafion 117 membrane. Note the anode and cathode catalyst loads in the case of fuel cell experiments were not specified in [52]. (Reproduced Ifom Journal of Power Sources, 47(3), Surampudi S, Narayanan SR, Vamos E, Frank H, Halpert G, LaConti A, Kosek J, Surya Prakash GK, and Olah GA, Advances in direct oxidation methanol fuel cells, 377-85, 1994, with permission fi-om Elsevier.)...

Figure I.6a displays a selection of fuel cell polarization curves extracted from publications that span a period of 125 years. The ordinate depicts the fuel cell voltage Eceii (jo) as given in Equation 1.21. The abscissa represents, on a logarithmic scale (to the base of 10), the fuel cell current density that has been normalized to the surface area-specific mass loading of Pt, mpf.

This chapter mainly deals with the fundamentals of H2/air PEM fuel cells, including fuel cell reaction thermodynamics and kinetics, as well as a brief introduction to the single fuel cell and the fuel cell stack. The electrochemistry and reaction mechanisms of H2/air fuel cell reactions, including the anode HOR and the cathode ORR, are discussed in depth. Several concepts related to PEM fuel cell performance, such as fuel cell polarization curves, OCV, hydrogen crossover, and fuel cell efficiencies, are also introduced. With respect to fuel cell stmctures and components, the material properties and effects on fuel cell performance are also discussed. In addition, several important conditions for fuel cell operation, including temperature, pressure, RH, and gas stoichiometries and flow rates, and their effects on fuel cell operation, are also briefly presented. This chapter provides the requisite baseline knowledge for the remaining chapters. 

The fuel-cell determined mass activities (MA-FC) were also compared with the RDE determined mass activities determined (MA-RDE) (Figure 11.12) in the kinetic region (0.9 V from IR-free fuel-cell I- ceu curves and form RDE curves in 0.1 M HQO4 electrolyte), hi general, the mass activities obtained from RDE and the fuel-cell polarization data showed one trend (i.e., MA decreases with increasing temperature), whereas the specific activities obtained from RDE and the fuel-cell polarization data showed another trend (i.e., SA increases with increasing temperature). 

Fuel cell polarization curves owing to internal losses, activation losses, ohmic losses, and concentration losses. Note that the actual magnitude of each loss is different for each fuel cell design and construction. 

Figure 2.11 Fuel cell polarization curves (empty symbols) and power densities (filled symbols) of Pt cathodes in pure oxygen showing the effect of membrane thickness on...

By introducing Equations (3-23), (3-24), (3-34), and (3-41) into Equation (3-43), a relationship between fuel cell potential and current density, the so-called fuel cell polarization curve, is obtained ... 

H2/AU fuel cell polarization curve is given with the following parameters ... 

Very often, there is a need to optimize the stack efficiency and size. These are two conflicting requirements for a given power output and a given polarization curve. Typical fuel cell polarization curves are shown in Figure 6-2. Most of the published fuel cell stack polarization curves fall within these two lines. 

If a cell is flooded in the cathode catalyst layer, fuel cell polarization curve generated with helox (21% O2 and 79% He) as the cathode gas will he ... 

FIGURE 9-41. Fuel cell polarization curve determines the type of converter needed to match the load voltage. 

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