FUEL CELLS – PROTON-EXCHANGE MEMBRANE FUEL CELLS | Overview Performance and Operational Conditions

FUEL CELLS – PROTON-EXCHANGE MEMBRANE FUEL CELLS | Overview Performance and Operational Conditions

Overview Performance and Operational Conditions J St-Pierre, University of South Carolina, Columbia, SC, USA & 2009 Elsevier B.V. All rights reserved...

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Overview Performance and Operational Conditions J St-Pierre, University of South Carolina, Columbia, SC, USA & 2009 Elsevier B.V. All rights reserved.

Introduction The proton-exchange membrane fuel cell (PEMFC) industry is currently in the precommercial stage. Because developers are positioning themselves to maximize their competitive advantage, they are particularly sensitive to intellectual property matters and to premature release of potentially key technical details. Thus, for some research and development areas, it is more fruitful to look for information in the patent literature rather than in the technical journal literature. Additionally, fuel cell materials, designs, system configurations, and operating conditions are not yet fixed because many issues still remain such as the high cost of platinum (and the search for cheaper alternatives), cell/stack mass manufacturing (e.g., cell design enabling the use of flexible gas diffusion electrodes and roll-to-roll processes), the need for hydrogen fuel recirculation (maximizing system efficiency and eliminating atmospheric fuel emissions), and the reduction in reactant humidification and increase in operating temperature (system architecture simplification by humidifier elimination and use of a standard size heat exchanger). Under these conditions, it is a challenge to establish state-of-the-art PEMFC general performance and operational conditions. In this context, reference to specific materials, fuel cell designs, and system configurations is minimized to concentrate the discussion on general principles. The discussion is also limited to the steady-state operating conditions. The main fuel cell reactions for a hydrogen-fueled system that contain the necessary details to identify the main performance parameters are as follows: O2 þ 4Hþ þ 4e -2H2 O


2H2 -4Hþ þ 4e


O2 þ 2H2 -2H2 O; DH ¼ 286 kJ mol1


These are electrochemical reactions involving a number of electrons (eqns [I] and [II]). The flow of electrons or current (also equivalent to a reaction rate) and the associated cell voltage are the key parameters. Water is produced (eqn [I]) and its rate is an important consideration to ensure adequate performance, especially in relation to freezing temperatures and the need for the ionomer is to be maintained wet for an acceptable ionic conductivity. Finally, the overall reaction (eqn [III]) is exothermic (DH represents the enthalpy) and, therefore,

heat needs to be removed to maintain the cell at a constant temperature. Other parameters are either derived from these basic ones or complementary, addressing other important requirements.

Performance Parameters Voltage Figure 1 illustrates a typical polarization curve, a depiction of the cell voltage as a function of the current density (based on the geometric surface area covered by the catalyst) or reaction rate (Faraday’s law). Three regions are distinguished. At low current densities, the change in voltage is associated with the irreversibility of the oxygen reduction reaction and follows a logarithmic behavior (Tafel law). At intermediate current densities, an ohmic behavior is observed predominantly due to the resistive nature of the ionomer separating the reactant compartments. At large current densities, the diffusion of the reactants/products between the flow field channels and the catalysts becomes rate-limiting, resulting in an asymptotic behavior (a ‘limiting current’). The opencircuit voltage (zero current) does not correspond to the thermodynamic value (DG/nF, of the Nernst equation); where DG represents the Gibbs free energy (kJ mol1), n the number of electrons exchanged in the electrochemical reaction, and F the Faraday constant (96 485 C mol1). Instead, the cell voltage reduction is due to the presence of other processes influencing the oxygen reduction reaction, including hydrogen crossover by diffusion through the membrane, platinum catalyst oxidation, and possible presence of internal short circuits. All these processes lead to a potential lower than the Nernstian value. The polarization curve is parametrically represented as follows: 0 V ¼ V0 

RT B i lnB @ F 1

1 C C  RO i iA i1


where V represents the cell voltage (V), V0 is a parameter (V), R the gas constant (8.3145 J mol1 K1), T the temperature (K), i the current density (A cm2), il the limiting current density (A cm2), and RO the ohmic resistance (O cm2). The second term on the right-hand side of eqn [1] represents the kinetic and mass transport loss, and the third term the ohmic loss. Equation [1] is valid locally at a



Fuel Cells – Proton-Exchange Membrane Fuel Cells | Overview Performance


Cell voltage (V)


ΔG/nF Vpc,max

Vmax 0.8 Vmin 0.4


Vpc,min imax

Eqn [1] Eqn [2]

0.0 0.0





Current density (A cm−2) Figure 1 Proton-exchange membrane fuel cell (PEMFC) polarization curves generated from eqn [1] (V0 ¼ 0.8 V, T ¼ 70 1C, il ¼ 1.5 A cm2, RO ¼ 0.05 O cm2) and eqn [2] (V0 ¼ 0.8 V, T ¼ 70 1C, RO ¼ 0.075 O cm2, a1 ¼ 8  106 V, a2 ¼ 7 cm2 A1).

given position along the flow field length. For a complete electrode the behavior is slightly different as represented by the following equation (Figure 1): V ¼ V0 

RT lnðiÞ  RO i  a1 expða2 iÞ F


where a1 (V) and a2 (cm2 A1) are parameters. The second term on the right-hand side of eqn [2] represents the kinetic loss, the third term the ohmic loss, and the fourth term the mass transport loss. Equation [2] reflects the local variation in operational parameters along the flow field length, resulting in a smoother observed transition to a limiting current. Ideally, the polarization curve should be as flat as possible. Figure 1 illustrates that the operational current density range defines an operational voltage window. The maximum current is partly dictated by design considerations to avoid overheating of the electrical cables. The minimum current is dictated by the fuel cell system requirements under idle conditions (which is the amount of power necessary to keep the different system components active). Power conversion components are present in some applications (direct current (dc) to dc or dc to alternating current) and usually operate within specified voltage limits, which have to be consistent with the cell operational voltage window. This requirement extends for the whole cell life partly defining the target degradation rate. Figure 1 illustrates that there is a difference between the operational cell voltage range (Vmax, Vmin) and power conversion component range (Vpc,max, Vpc,min, which are reported on a cell basis by dividing the converter operational limits by the number of cells in a stack). The Vmin–Vpc,min difference combined with the system lifetime requirement defines an overall maximum

degradation rate. Other parameters that define the operating voltage window include the geometric requirements (i.e., the defined space allocation for the stack), which lead to compromises between cell area, number of cells, and current density to achieve a specified overall output power. Power Equations [1] and [2] are used to define the power density on an active area basis: P ¼ iV


where P represents the cell output power (W cm2). Equation [3] is illustrated in Figure 2. In this figure, Pmax, Pmin, and Imax, Imin are, respectively, the maximum and minmum power and current densities. The density curve has a maximum particularly important for applications sensitive to the volume of the system such as automotive (cars, buses) and portable. For these applications, it is important to operate as closely as possible to the maximum current density value to minimize the stack size. This is potentially problematic as the maximum current density is located near the mass transport region associated with a relatively fast decay in cell voltage. Power can also be defined in terms of density rather than on an active area basis. The stack volume or weight is selected to define this parameter (combined with eqn [4]) used for stack sizing or assessing whether a specific design meets specified application requirements. Equation [4] also includes geometric parameters needed to complete this analysis: Pstack ¼ nc AiV


Fuel Cells – Proton-Exchange Membrane Fuel Cells | Overview Performance


1.0 Pmax Power density (W cm−2)


0.6 imax 0.4



Eqns [1] and [3] Eqns [2] and [3]

Pmin 0.0 0.0





Current density (A cm−2) Figure 2 Proton-exchange membrane fuel cell (PEMFC) power density curves generated from eqns [1] and [3] (V0 ¼ 0.8 V, T ¼ 70 1C, il ¼ 1.5 A cm2, RO ¼ 0.05 O cm2) and eqns [2] and [3] (V0 ¼ 0.8 V, T ¼ 70 1C, RO ¼ 0.075 O cm2, a1 ¼ 8  106 V, a2 ¼ 7 cm2 A1).

where Pstack represents the stack power (W), nc the number of cells in the stack, and A the cell active area (cm2). The basic parameter is the cell performance. The other parameters allow flexibility in design, including the number of cells to achieve a given voltage range and active surface area (width, length) to meet specific volume/weight requirements.

required, the overall efficiency is also reduced by a value Zpc. Finally, part of the fuel cell power is used to operate system components, thus further reducing the overall efficiency. This parasitic power is in first approximation assumed to be a linear function of fuel cell power:


where Pp represents the parasitic power (W cm2), and a3 (W cm2) and a4 are parameters. The corresponding parasitic power efficiency Zp is

Overall fuel cell system efficiency is dependent on a series of efficiencies. The thermodynamic efficiency Zmax defines the maximum efficiency that can be obtained from the reactants and is defined as the ratio of the Gibbs free energy to the enthalpy: Zmax



The thermodynamic efficiency is reduced by the voltage efficiency ZV, the ratio of the operating cell voltage to the Nernst potential equal to DG/nF: ZV ¼ V



The product of eqns [5] and [6] represents the fuel cell stack contribution to the overall efficiency. It is illustrated in Figure 3 and has the same shape as the polarization curve. The value of DH/nF represents the thermoneutral voltage (Figure 1) and is dependent on the state of the produced water (liquid or vapor). The overall system efficiency is also reduced by the fuel efficiency, the fraction of fuel converted to useful energy or fuel utilization ufuel, and the onboard reformer efficiency (if present), the fraction of raw fuel transformed into fuel cell usable fuel uref . If the electric power is not directly used and conditioning is

Pp ¼ a3 þ a4 Vi

Zp ¼

Vi  ða3 þ a4 Vi Þ a3 ¼ 1  a4  Vi Vi



The maximum efficiency Zmax (eqn [5]) depends on the fuel cell electrochemical reactions and slowly varies with the operating temperature. For an oxygen/hydrogen–based system, Zmax is of the order of 0.8. The voltage efficiency depends on the operating cell voltage (eqn [6]). The Nernst potential DG/nF for an oxygen/hydrogen–based system is of the order of 1.2 V. The fuel utilization ufuel depends on the system configuration and can be as high as B1 for dead end or recirculation operation. For systems including a combustor, the fuel utilization is typically of the order of 0.9. The reformer efficiency uref is equal to 1 for a hydrogen fuel but will reach a value of 0.95 for other fuels requiring reforming. The power conversion efficiency Zpc is also relatively high with a typical value of 0.95. The parasitic power efficiency Zp parameter a3 is of the order of a few percent of the maximum fuel cell power, whereas a4 is of the order of a few percent. The overall fuel cell system efficiency Z is Z¼

nFufuel uref Zpc V  a3  1  a4  DH Vi


Fuel Cells – Proton-Exchange Membrane Fuel Cells | Overview Performance

Energy efficiency (dimensionless)



imin 0.4

Eqns [1], [5], and [6] 0.2

Eqns [2], [5], and [6] Eqns [1] and [9]


Eqns [2] and [9] 0.0 0.0





Current density (A cm−2) Figure 3 Proton-exchange membrane fuel cell (PEMFC) efficiency curves generated from eqns [1], [5], and [6] (V0 ¼ 0.8 V, T ¼ 70 1C, il ¼ 1.5 A cm2, RO ¼ 0.05 O cm2, DH/nF ¼ 1.5 V) and eqns [2], [5], and [6] (V0 ¼ 0.8 V, T ¼ 70 1C, RO ¼ 0.075 O cm2, a1 ¼ 8  106 V, a2 ¼ 7 cm2 A1, DH/nF ¼ 1.5 V). PEMFC system efficiency curves were also generated from eqns [1] and [9] and [2] and [9] (ufuel ¼ 0.9, uref ¼ 1, Zpc ¼ 0.95, a4 ¼ 0.05, a3 ¼ 0.449 W cm2).

Equation [9] is illustrated in Figure 3, which shows that the overall fuel cell system efficiency rapidly decreases at low current densities (near idle conditions), thus defining a maximum value at intermediate current densities. This problem should not be understated especially for automotive systems and city driving that imply significant operating periods at idle conditions. Equation [8] is responsible for that efficiency decrease (last term on the right-hand side). For the specific case illustrated, the system cannot deliver any power in a small current density range above the imin value. A system redesign is, therefore, needed and would include a reselection of system components affecting individual efficiency contributors and fuel cell configuration (number of cells, active area, operating cell voltage window) to better match requirements (power, packaging constraints, etc.). For systems requiring variable power levels such as automotive applications, an average overall efficiency is also computed by taking into account a representative drive cycle, thus averaging over time the effect of current density. Heat Flux The heat generated by eqn [III] is computed as follows: Q ¼i

  DH V nF


where Q represents the generated heat flux (W cm2). Equation [10] is plotted in Figure 4 using both expressions for the cell voltage (eqns [1] and [2]). The end point of each curve at the high current density end corresponds to the maximum heat dissipation (V ¼ 0). Figure 4 shows that the heat generated in the operating regime is approximately proportional to the current

density. The amount of heat is significant, being of the same order as the power generated. Equation [10] indicates that the heat generated depends on the thermoneutral and operating voltage difference. The operating voltage in Figure 1 is located roughly around a value equal to half the thermoneutral voltage. The methods used to remove heat are dependent on power level and consequently application. Natural and forced convection and evaporative cooling (product water) represent the most important heat removal mechanisms. For low-power portable applications, which often have dry reactant feeds, evaporative cooling and natural convection are sufficient to control the stack temperature. For larger power levels, reactants are usually humidified and natural convection becomes less important partly because of the heat transfer resistance offered by the stack size (internal conduction heat transfer limitation) and a relatively low operating temperature. For these cases, a liquid coolant is needed further complicating cell design (additional flow field and manifold) and system design (circulating pump, heat exchanger to reject heat to the environment). Coolant selection is dictated by the anticipated environmental temperature range (above and below 0 1C). The heat can be removed in either the in-plane or through-plane direction (parallel or perpendicular to the bipolar plate plane). The heat can also be used to further increase efficiency, for example, by coupling the system to a water heater (cogeneration). Distribution Effects In previous sections, the defined performance parameters are average values because the stack operating conditions

Fuel Cells – Proton-Exchange Membrane Fuel Cells | Overview Performance


different meaning for the dimensionless parameter a5:

vary along the flow field length (from the inlet to the outlet manifold) for a number of reasons. Total current is usually set leaving both current and voltage distribution across the bipolar plate surface uncontrolled. Reactant stoichiometries have fixed values to minimize the parasitic power needs from the air compressor or hydrogen recirculation pump, thus creating concentration gradients. The same consideration applies to the coolant pump leading to a temperature gradient. The specific example of current distribution with a high hydrogen stoichiometry, a well-humidified membrane, and negligible operating condition gradients (situation close to automotive applications) is illustrated in Figure 5. The general equation describing the distribution is valid for both kinetic and mass transport control at the cathode but with a

  iðxÞ 1 x 1  ¼ a 5 ¯i v


where x represents the dimensionless distance separating the reactant flow field channel inlet and outlet, ¯i the average current density (A cm2), and v the oxidant stoichiometry. For large stoichiometry values, eqn [11] leads to a uniform distribution ðiðxÞ=¯i ¼ 1Þ. Such a distribution is easily obtained with pure reactants like oxygen (rather than air) and hydrogen because composition variations are minimized. For lower stoichiometry values, a gradient is observed with the maximum value located at the inlet. The distribution

2.4 Eqns [1] and [10] Heat generation (W cm−2)


Eqns [2] and [10]



0.8 imax



0.0 0.0




Current density (A



Current density/average current density (dimensionless)

Figure 4 Proton-exchange membrane fuel cell (PEMFC) heat generation computed from eqns [1] and [10] (V0 ¼ 0.8 V, T ¼ 70 1C, il ¼ 1.5 A cm2, RO ¼ 0.05 O cm2, DH/nF ¼ 1.5 V), and eqns [5] and [10] (V0 ¼ 0.8 V, T ¼ 70 1C, RO ¼ 0.075 O cm2, a1 ¼ 8  106 V, a2 ¼ 7 cm2 A1, DH/nF ¼ 1.5 V).

2.0 Air stoichiometry = infinity Air stoichiometry = 1.8 (kinetic regime)


Air stoichiometry = 1.2 (mass transport regime) 1.2


0.4 0.0






Flow field channel length (dimensionless) Figure 5 Proton-exchange membrane fuel cell (PEMFC) current density distributions along the flow field length for different operating regimes generated from eqn [11]: infinite stoichiometry (a5 ¼ 1), kinetic regime (a5 ¼ 1.46), and mass transport regime (a5 ¼ 2.04).


Fuel Cells – Proton-Exchange Membrane Fuel Cells | Overview Performance

polymer structure, leading to failure (loss of both ionomer and its conductivity). The presence of gradients suggests that failure occurs prematurely at higher current density locations. Gradients have other consequences needing careful consideration during fuel cell stack and system design. In this regard, the of cell-to-cell performance differences originates from the presence of operating condition gradients and manufacturing limitations, which can further accentuate nonuniformities. An example of stack performance distribution is given in Figure 7. At low (kinetic control) and intermediate (ohmic control) current densities, cell-to-cell performance variations are relatively small but significantly increase in magnitude at high current densities (mass transport control). In some cases, negative voltages can be observed and depending on their specific cause (e.g., fuel starvation accelerates anode catalyst and catalyst support degradation) limit the maximum current that can be drawn (system control), negatively affecting stack power output. Nonuniform operating condition distributions also have beneficial effects with respect to product water management (eqn [I]). The decrease in pressure due to friction losses in the reactant flow field channels and the increase in coolant temperature due to heat transfer lead

steepness is also generally more prominent under mass transport control. The existence of gradients negatively impacts not only performance parameters but also degradation mechanisms. For example, if it is assumed that the nonuniform distributions illustrated in Figure 5 are associated with neighboring cells in a stack, current conservation dictates that current will redistribute within the bipolar plate separating these two cells (Figure 6). Because the bipolar plate has a finite in-plane resistance value, some power and efficiency is lost to ohmic heating. Hydrogen peroxide is generated at high oxygen reduction reaction overpotentials. This parallel reaction rate is overpotential dependent. Hydrogen peroxide attacks the membrane

Cell j + 1 Bipolar plate Cell j

Figure 6 Current redistribution within a bipolar plate as a result of different neighbor cell performance. Arrow width is proportional to current. Current is conserved at the two illustrated nodes.

0.05 A cm−2


Cell voltage (V)

0.7 A cm−2 0.6



1.4 A cm−2

0.0 0






Cell number Figure 7 Proton-exchange membrane fuel cell (PEMFC) stack performance distribution generated from eqn [2] (T ¼ 70 1C) using normal distributions to define parameter values (mean/standard deviation, V0 ¼ 0.8/0.005 V, RO ¼ 0.075/0.0075 O cm2, a1 ¼ 8  106/ 8  107 V, a2 ¼ 7/0.7 cm2 A1).

Table 1

Typical proton-exchange membrane fuel cell (PEMFC) operating conditions


Current density (A cm  2)

Absolute pressure (oxidant /fuel, kPa)

Temperature (1C)

Relative humidity (oxidant /fuel, %)

Stoichiometry (oxidant /fuel)

Reactant composition (oxidant /fuel, %)


Up to 0.1


Up to 0.5 Up to 1

300/300 300/300

Ambient/0, aqueous solution 100/100 0–100/0

 /B1, 2–3

Stationary Automotive

Ambient to 40 65 80

Air/hydrogen, aqueous methanol Air/reformate Air/hydrogen

2/1.2 2/1.2

Fuel Cells – Proton-Exchange Membrane Fuel Cells | Overview Performance

to an increase in reactant stream water vapor carrying capacity along the flow field channel length. With proper design, liquid water flooding, negatively impacting reactant diffusion to the catalyst and performance, is minimized. Equations [12] and [13], respectively, give the


minimal values of pressure drop and partial water vapor pressure required to achieve an increase in reactant stream water vapor carrying capacity: Dp >

ps ðlÞ >

f ð pð0Þ  ps Þ v

pps ð0Þ   f f ps ð0Þ þ p 1  v v

½12 ½13

where Dp represents the reactant pressure drop between flow field channel inlet and outlet (Pa), f the fraction of electroactive species in the dry reactant, p the reactant pressure (Pa), ps the water vapor saturation pressure (Pa), and l the dimensionless flow field channel length. Other methods based on design are available to manage product water including reactant counterflow operation and use of partly porous bipolar plates. For the latter case, the liquid water coolant circulating on one side of the bipolar plate provides liquid water by evaporation to the reactant circulating on the other side if the relative humidity is o100%. If the reactant stream contains liquid water, the porous material absorbs it. This strategy requires a coolant pressure lower than the reactant pressure.

Figure 8 Angstrom Power V60 prismatic portable protonexchange membrane fuel cell (PEMFC) (5 mm  27 mm  19 mm, 0.38 W, 5 V). Courtesy of www.angstrompower.com/technology_cells.html.

Main Applications Proton-exchange membrane fuel cell stacks have three major applications: portable, stationary, and automotive.

Figure 9 Fraunhofer Institute for Solar Energy Systems portable proton-exchange membrane fuel cell (PEMFC) prototype system developed in 2000 (144 mm diameter, 20 mm height, 500 g, 50 W). Reproduced with permission from Fraunhofer Magazine 2.2000; Laboratory celss attain high energy density.


Fuel Cells – Proton-Exchange Membrane Fuel Cells | Overview Performance

Figure 10 (a) Ballard Power Systems Mark1030TM residential cogeneration proton-exchange membrane fuel cell (PEMFC) (430 mm  171 mm  231 mm, 20.5 kg, 17 L, 1.320 kW). (b) Associated Tokyo Gas system. Courtesy of Ballard Power Systems; MK1030 Stack Picture from Spec Sheet and Associated Generator from Image Gallery/Prototypes.

Fuel Cells – Proton-Exchange Membrane Fuel Cells | Overview Performance


Figure 11 (a) Ballard Power Systems Mark902TM transportation proton-exchange membrane fuel cell (PEMFC) (805 mm  375 mm  250 mm, 96 kg, 75 L, 85 kW, 284 V, 300 A). Courtesy of Ballard Power Systems; MK902 Stack Picture from Spec Sheet and Associated Generator from Car Engine Picture. (b) Associated Ford Focus car system. Courtesy of Ballard Power Systems; Mark902TM Fuel Cell Stack in Ford Focus Fuel Cell Vehicle.

Their respective operating conditions (Table 1) are largely dictated by key system design objectives. For portable applications, system simplification is essential. System components are either minimized (natural convection or a fan rather than an air compressor) or eliminated (no humidifier, reformer, or separate cooling circuit). Under these conditions, performance can be significantly limited by mass transport and/or membrane dehydration resulting in low current densities. Figure 8 illustrates a portable stack and Figure 9 a complete system. For stationary applications, system efficiency and durability constitute the overriding factors. Hence,

current density is low (eqn [6]) and the pressure and temperature are higher than for portable applications to minimize kinetic (fuel contaminants) and mass transport losses, and the relative humidity is high to minimize membrane degradation. Figures 10(a) and 10(b) shows a generator stack for the home and its associated system packaging. For automotive applications, space is severely limited. Thus, achieving high power densities is of primary concern and is obtained by a combination of high current densities and system simplification/optimization. Exposure to freezing temperatures (o0 1C) represents another key concern requiring system protection from ice


Fuel Cells – Proton-Exchange Membrane Fuel Cells | Overview Performance

damage during start-up, shutdown, and nonoperational periods. Many mitigation approaches have been suggested, such as insulation (delay a decrease in stack temperature), dry gas purges, or dry reactant operation before shutdown (liquid water minimization within the stack), heat exchanger bypass coupled with operation at a low cell voltage (eqn [10]) during start-up (minimum heat loss and maximum heat generation), and use of materials able to withstand freezing conditions (ethylene glycol based coolant). Figures 11(a) and 11(b) depicts a car stack and its associated system. It is readily observable that the 1.3 kW, 17 L, 21 kg home generator (Figure 10(a)) has a much smaller volumetric and gravimetric power density than the 85 kW, 75 L, 96 kg car stack (Figures 11(a)). Other PEMFC stack applications exist but are currently considered niche rather than potential mass markets. In this regard, oxygen- rather than air-based systems are considered for space (either regenerative or not) or submarine applications to limit the reactant storage volume. The fuel is also flexible as listed in Table 1 and includes hydrogen, aqueous methanol solutions, and reformed alkanes (methane, butane, etc.).

Conclusions Proton-exchange membrane fuel cell performance parameters were presented including their interdependence with manufacturing processes, design objectives, system considerations, operating conditions, and applications. Other considerations exist such as transient effects (startup, shutdown, drive cycle), including slow degradation processes, but were not considered here because these topics are not as developed and are beyond the scope of this article. Degradation originates from a variety of sources: operating condition selection, loss of system control, faulty design, or insufficient material resistance. For the latter case, predominant modes include catalyst agglomeration/dissolution, catalyst support corrosion, membrane chemical structure degradation, and contamination. Although an average degradation rate is easily defined for steady-state operating conditions, a general definition valid for transient cases remains to be developed because the results are dependent on the operating conditions, which in turn control the predominant degradation mechanisms.

i il imax imin i¯ j l n nc p P Pmax Pmin Pp ps Pstack Q R RX T ufuel uref V V0 Vmax Vmin Vpc,max Vpc,min x DG DH Dp g gmax gp gpc gV n /

current density (A cm  2) limiting current density (A cm  2) maximum operational current density (A cm  2) minimum operational current density (A cm  2) average current density (A cm  2) cell number flow field channel length number of electrons exchanged in the electrochemical reaction number of cells in the stack reactant pressure (Pa) cell output power (W cm  2) maximum cell output power (W cm  2) minimum cell output power (W cm  2) parasitic power (W cm  2) water vapor saturation pressure (Pa) stack power (W) generated heat flux (W cm  2) gas constant (8.3145 J mol  1 K  1) ohmic resistance (O cm2) temperature (K) fuel utilization reformer efficiency cell voltage (V) parameter (V) maximum operational cell voltage (V) minimum operational cell voltage (V) maximum power converter voltage (V) minimum power converter voltage (V) distance separating the reactant flow field channel inlet and outlet Gibbs free energy (kJ mol  1) enthalpy (kJ mol  1) reactant pressure drop between flow field channel inlet and outlet (Pa) overall fuel cell system efficiency thermodynamic efficiency parasitic power efficiency power conversion efficiency voltage efficiency reactant stoichiometry fraction of electroactive species in the dry reactant

Abbreviations and Acronyms

Nomenclature Symbols and Units ak


parameter; units vary for k ¼ 1 (V), k ¼ 2 (cm2 A  1), k ¼ 3 (W cm  2), k ¼ 4 and 5 (dimensionless) cell active area (cm2) Faraday constant (96 485 C mol  1)

ac dc PEMFC

alternating current direct current proton-exchange membrane fuel cell

See also: Fuel Cells – Proton-Exchange Membrane Fuel Cells: Bipolar Plates; Cells; Life-Limiting

Fuel Cells – Proton-Exchange Membrane Fuel Cells | Overview Performance Considerations; Membrane–Electrode Assemblies; Systems; Water Management.

Further Reading Arato E and Costa P (2006) Transport mechanisms and voltage losses in PEMFC membranes and at electrodes: A discussion of open-circuit irreversibility. Journal of Power Sources 159: 861--868. Berg P, C¸ag˘lar A, Promislow K, St-Pierre J, and Wetton B (2006) Electrical coupling in proton exchange membrane fuel cell stacks: Mathematical and computational modelling. IMA Journal of Applied Mathematics 71: 241--261. Berg P, Promislow K, St-Pierre J, Stumper J, and Wetton B (2004) Water management in PEM fuel cells. Journal of the Electrochemical Society 151: A341--A353. Bu¨chi FN, Schmidt TJ, and Inabe M (eds.) (forthcoming) Degradation and Durability of PEFC. New York: Springer. Chang PAC, St-Pierre J, Stumper J, and Wetton B (2006) Reactant flow distribution in proton exchange membrane fuel cell stacks. Journal of Power Sources 162: 340--355. Ferreira PJ, la O’ GJ, Shao-Horn Y, Morgan D, Makharia R, Kocha S, and Gasteiger HA (2005) Instability of Pt/C electrocatalysts in proton exchange membrane fuel cells–a mechanistic investigation. Journal of the Electrochemical Society 152: A2256--A2271. Garland NL and Kopasz JP (2007) The United States department of energy’s high temperature, low relative humidity membrane program. Journal of Power Sources 172: 94–99. Kim GS, St-Pierre J, Promislow K, and Wetton B (2005) Electrical coupling in proton exchange membrane fuel cell stacks. Journal of Power Sources 152: 210--217. Kim J, Lee S-M, Srinivasan S, and Chamberlin CE (1995) Modeling of proton exchange membrane fuel cell performance with an empirical equation. Journal of the Electrochemical Society 142: 2670--2674. Knights SD, Colbow KM, St-Pierre J, and Wilkinson DP (2004) Aging mechanisms and lifetime, PEFC and DMFC. Journal of Power Sources 127: 127--134. Kulikovsky A A, Kucernak A, and Kornyshev A A (2005) Feeding PEM fuel cells. Electrochimica Acta 50: 1323--1333. Lampinen MJ and Fomino M (1993) Analysis of free energy and entropy changes for half-cell reactions. Journal of the Electrochemical Society 140: 3537--3546. Mittal VO, Kunz HR, and Fenton JM (2007) Membrane degradation mechanisms in PEMFCs. Journal of the Electrochemical Society 154: B652--B656. Perry ML and Fuller TF (2002) A historical perspective of fuel cell technology in the 20th century. Journal of the Electrochemical Society 149: S59--S67.


Promislow K and Wetton B (2005) A simple, mathematical model of thermal coupling in fuel cell stacks. Journal of Power Sources 150: 129--135. Rogg S, Ho¨glinger M, Zwittig E, Pfender C, Kaiser W, and Heckenberger T (2003) Cooling modules for vehicles with a fuel cell drive. Fuel Cells 3: 153--158. Sattler G (1998) PEFCs for naval ships and submarines: Many tasks, one solution. Journal of Power Sources 71: 144--149. Sone Y, Ueno M, Naito H, and Kuwajima S (2006) One kilowatt-class fuel cell system for the aerospace applications in a microgravitational and closed environment. Journal of Power Sources 157: 886--892. St-Pierre J (2007) PEMFC in situ liquid-water-content monitoring status. Journal of the Electrochemical Society 154: B724--B731. St-Pierre J and Jia N (2002) Successful demonstration of Ballard PEMFCs for space shuttle applications. Journal of New Materials for Electrochemical Systems 5: 263--271. St-Pierre J, Roberts J, Colbow K, Campbell S, and Nelson A (2005) PEMFC operational and design strategies for sub zero environments. Journal of New Materials for Electrochemical Systems 8: 163--176. St-Pierre J, Wetton B, Kim G-S, and Promislow K (2007) Limiting current operation of proton exchange membrane fuel cells. Journal of the Electrochemical Society 154: B186--B193. St-Pierre J, Wilkinson DP, Knights S, and Bos ML (2000) Relationships between water management, contamination and lifetime degradation in PEFC. Journal of New Materials for Electrochemical Systems 3: 99--106. St-Pierre J, Wilkinson DP, Voss H, and Pow R (1997) Advanced water management techniques for solid polymer fuel cells. In: Savadogo O and Roberge PR (eds.) Proceedings of the Second International Symposium on New Materials for Fuel Cell and Modern Battery Systems, pp. 318--329. Montre´al: E´cole Polytechnique. Taniguchi A, Akita T, Yasuda K, and Miyazaki Y (2004) Analysis of electrocatalyst degradation in PEMFC caused by cell reversal during fuel starvation. Journal of Power Sources 130: 42--49. Thorstensen B (2001) A parametric study of fuel cell system efficiency under full and part load operation. Journal of Power Sources 92: 9--16. Vielstich W, Gasteiger H, and Lamm A (eds.) (2003) Handbook of Fuel Cells – Fundamentals, Technology and Applications (4 vols). Chichester, West Sussex, England: John Wiley and Sons. Weber A Z and Darling RM (2007) Understanding porous watertransport plates in polymer-electrolyte fuel cells. Journal of Power Sources 168: 191--199. Wilkinson DP and St-Pierre J (2003) In-plane gradients in fuel cell structure and conditions for higher performance. Journal of Power Sources 113: 101--108. Yim S-D, Lee W-Y, Yoon Y-G, et al. (2004) Optimization of bifunctional electrocatalyst for PEM unitized regenerative fuel cell. Electrochimica Acta 50: 713--718.