Mench M.M. Fuel Cell Engines

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160 Performance Characterization of Fuel Cell Systems

Current Density

Vo l t a g e

0 1.08

0.03 1.02

0.07 0.968

0.1 0.925

0.15 0.861

0.25 0.754

0.35 0.648

0.45 0.542

0.55 0.436

0.65 0.329

0.75 0.223

0.85 0.117

0.95 0.011

Data from [13].

completely appropriate, this behavior is approached for a high-temperature fuel cell in the

low to moderate current density regimes.

A solution can be found by solving for the slope of the polarization curve in the main

linear region. First, plot the polarization curve and select the appropriate region. In this case,

because it is a high-temperature fuel cell operating on hydrogen, the overall polarization

curve is quite linear and dominated by ohmic effects.

COMMENTS: This technique should be a maximum possible value for the ohmic re-

sistance, because we have assumed that the slope in the middle region of the polarization

curve is solely a result of ionic losses. In fact, activation and concentration polarization

losses also contribute to the voltage loss in this region, although for these high-temperature

fuel cells the approximation is very close. There are other experimental techniques to more

accurately obtain the ohmic resistance in the cell. Some of these methods are discussed in

Chapter 8 on experimental methods.

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4.3 Region II: Ohmic Polarization 161

Electrolyte—ionic conductivity only

Catalyst layer—mixed conductivity

Figure 4.28 Schematic of electrodes and main electrolyte in generic fuel cell system.

For a well-built fuel cell, the dominating ohmic polarization, η

, is from the electrolyte.

This includes the ionic transport resistance in both the main electrolyte separator and

the electrodes, since the electrodes will have ionic (and electronic) conduction as well.

Otherwise, reactions occurring in the electrode could not conduct the ions through the

electrolyte. Even though the catalyst layer in most fuel cells is only on the order of 5–30 µm,

the mixed conductivity and highly porous nature can result in a signiﬁcant contribution to

the overall ohmic drop of the fuel cells. The reaction in the catalyst layer not only is at the

surface facing the ﬂow ﬁeld but is also distributed throughout the three-dimensional porous

structure. The distribution of current throughout the three-dimensional porous structure of

the catalyst layer is a complex issue that is a function of ionic and electronic conductivity,

reactant concentration, catalyst distribution, and other factors beyond the scope of this

text. In many models, the reaction distribution of the catalyst layer is assumed to occur in

a single plane due to the thinness of the catalyst layer. A simpliﬁcation can be made to

allow us to estimate the resistance losses in the electrode if we assume the average location

of the reaction in the electrode is at the dashed line in Figure 4.28, representing the half

distance through the electrode. This implies a homogeneous current distribution throughout

the thickness of the electrode structure. The effective electrode ionic conductivity can be

written as [14]

i,eff

electrode

(4.76)

where τ is the electrolyte tortuosity, which was determined to be approximately 1 [15] for

PEFCs. In Eq. (4.76), ε

electrolyte

is the volume fraction of electrolyte in the catalyst layer,

which is typically 10–30% in PEFCs. This concept is illustrated in Example 4.7.

Contact Resistance Contact resistance is a result of imperfectly matched material inter-

faces in the fuel cells. At every location where there is a noncontinuous contact between

dissimilar materials, there is an electronic or ionic contact resistance, as illustrated in

Figure 4.29. The contact resistance is a function of the material surface state and roughness

and the contact pressure between the materials (values of area contact resistance are given

in units of  ·m

or  ·cm



contact

loss

( · cm

) (4.77)

contact

loss

contact

() (4.78)

where A

contact

is the contact area between the two surfaces. This leads to an interesting

engineering trade-off in channel design, illustrated in Figure 4.30. The smaller the landing

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162 Performance Characterization of Fuel Cell Systems

Figure 4.29 Schematic of single PEFC assembly, illustrating all contact surfaces. (Image courtesy

of Joseph Scott [16].)

areas, the greater the area available for mass transport, and the lower the ﬂow channel

pressure drop for the same ﬂow rate. However, the smaller the landing area, the higher

the ohmic drop from contact resistance. Therefore, a balance including this and other

competing factors is sought for fuel cell design. Major factors in contact resistance include

the following:

1. State of Contact Surface If contacts are oxidized, as can occur over time in a

oxidative environment, this factor can become signiﬁcant. Special coatings on metal

contacts can be used, such as gold or nitrides that resist surface oxidation.

2. Compression Pressure from Current Collector onto Electrode or Diffusion Me-

dia In larger cells, it is difﬁcult to achieve an ideal state of uniform compression,

and current collection can be biased toward locations with better contact.

L = 2C

(a)

CLCLC

C = 2L

(b)

Figure 4.30 Illustration of trade-off between contact resistance transport. Typical channel to land

ratios in fuel cells range from 1 : 1 to 3 : 1. (a) Wide land, low contact resistnace. (b) Narrow land,

high contact resitance.

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4.3 Region II: Ohmic Polarization 163

3. Tolerance and Flatness of Individual Fuel Cell Bipolar Plates To achieve a uni-

form compression on a stack that can have as many as 300 fuel cells in series, a

very tight manufacturing tolerance on the ﬂatness of individual bipolar plates must

be achieved. The change in a hundred or so micrometers can have a major effect on

the distributed contact resistance.

Example 4.7 Cell Ohmic Loss Limiting Current Calculation Consider an ideal PEFC

with only the ionic ohmic losses in the electrolyte and catalyst layers. Ignore kinetic, elec-

tronic, and other losses for this problem. The OCV is 1.0 V, and the electrolyte conductivity

is 8.3 S/m. The catalyst layers can be assumed to be 40% ionomer equivalent and 30

µm thick.

Consider two cases:

(a) The electrolyte is Naﬁon 112, which is 51 µm thick.

(b) The electrolyte is Naﬁon 117, which is 178 µm thick

Find the maximum current density that each electrolyte can support, ignoring other polar-

izations besides ohmic losses.

SOLUTION From Ohm’s law

R = ρ

σ A

V = I



R = iA



R = i



σ A

= i



max,112

= V





III





−1

= (1.0J





15 × 10

−6

0.4 × 8.3S



51 × 10

−6

8.3S



15 × 10

−6

0.4 × 8.3S





−1

10,000 cm

= 6.58 A/cm

where I, II, and III represent the ionic resistances in the anode catalyst layer, main electrolyte,

and cathode, respectively. The ionic conductivity of the electrodes is reduced by the ionomer

fraction via Eq. (4.76), and the average location of the reaction in the electrodes is assumed

to occur midway through the catalyst layer.

For the Naﬁon 117 electrolyte

max,117

= V





−1

= (1.0J





15 × 10

−6

0.4 × 8.3S



178 × 10

−6

8.3S



15 × 10

−6

0.4 × 8.3S





−1

10,000 cm

= 3.28 A/cm

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164 Performance Characterization of Fuel Cell Systems

As we expect, the thicker electrolyte supports a signiﬁcantly lower maximum current

density. Based on ohmic losses only, if we plotted the predicted polarization curves, they

would look as follows:

COMMENTS: Although low-temperature PEFCs tend to be limited by reactant availabil-

ity (concentration polarization), many high-temperature fuel cells are ultimately limited by

the ionic conductivity of the electrolyte, because mass transport and kinetics are facilitated

at high temperature (e.g., see polarization curve in Example 4.6). Also, note the relative

importance of the electrolyte in the overall loss. Considering that some PEFC electrolytes

can be as thin as 18 µm, the electrode resistance can even be larger than that of the main

electrolyte. Also it should be noted that the use of ionomer percentage to adjust ionic

conductivity is an approximation, as well as the approximation that reaction occurs in the

middle of the catalyst layer. More complex modeling of these reactions and losses are

available in literature but are beyond the scope of this text.

Cell Assembly In terms of the compression pressure on the fuel cell, there are initially high

beneﬁts to increased compression and reduced contact resistance. Think of a stack loosely

held together by gravity. Contact losses would obviously be high, as shown in Figure 4.31.

As the compression is increased, there is a plateau region where optimal contact pressure is

reached. If the compression is increased too far beyond this level, however, the components

in the fuel cell will suffer plastic (permanent) deformation and cause a very sharp drop-off

Cell voltage

Compression pressure

Plateau region

Desired

design point

Figure 4.31 Cell performance at given current as function of stack compression pressure.

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4.3 Region II: Ohmic Polarization 165

in performance that is not recoverable. In a brittle fuel cell or one with signiﬁcant thermal

expansion of the materials such as the SOFC, thermal and compressive stresses can result

in catastrophic failure of components. Different types of fuel cells obviously have different

material limits for plastic deformation, but the qualitative shape is the same as Figure 4.31.

For low-temperature fuel cells, the presence of liquid water does not inﬂuence the contact

resistance since pure water is nonconductive.

Over time, various components may deform to relax the compression stress in the ma-

terials, loosening contacts. Some stacks are designed to be spring loaded at the endplates to

provide consistent compression. Also, since each channel design is different, with different

channel-to-land ratios, it is impossible to state an optimal compression pressure for a fuel

cell. For PEFCs, the compression pressure of 1–2 MPa is generally appropriate, but the

optimal compression pressure must be determined experimentally for a given fuel cell and

components. In general, several criteria can be used to determine the best compression on

a cell or stack:

1. Prescribed Torque or Spring Loading Imposed on All Compression Bolts or Tie-

Downs This method is common in laboratories with single cells. However, this

method is highly unreliable and can lead to signiﬁcant variation in compression

pressure and uniformity, since the compression torque is a function of the inter-

facial friction on the bolt threads or between the nut and washer and the back

compression plate. In general, this method should only be used with caution on a

well-characterized fuel cell.

2. Compression Gap Width The materials under compression will have a measurable

gap width decrease under compression, and the compression force on the fuel cell is

increased until a desired elastic deformation is achieved in the stack. For example,

in the PEFC, many diffusion media work best when compressed by 10–20% of

their original thickness. Another advantage is that the gap width can be measured

at locations around the periphery to ensure uniformity of compression.

3. Compression Pressure Speciﬁcation The compression pressure of the ﬂow ﬁeld on

the fuel cell is prescribed. The compression pressure can be determined experimen-

tally with a load cell inserted in the fuel cell or with pressure-sensing contact paper

as shown in Figure 4.32. The proper compression pressure can then be correlated

with the measured gap width or bolt torque.

Figure 4.32 Pictures of Pressurex pressure-sensing paper used to measure contact pressure distri-

butionin5-cm

fuel cell with different torque on fuel cell bolts. The higher the compression, the

better the electrical contact. At some point, however, the cell will become overcompressed.

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166 Performance Characterization of Fuel Cell Systems

In practice, large stacks of hundreds of cells are assembled using large automated presses

to ensure uniformity of assembly and proper cell sealing.

Example 4.8 Equivalent Ohmic Loss Thermal Network Draw an equivalent ionic

resistance network for a single PEFC.

SOLUTION

COMMENTS: The cell and resistance network above shows all the resistances present,

electronic and ionic. Note the mixed ionic and electronic conductivity required in the

catalyst layer. In most cases except the catalyst layer, the electronic resistance is negligible.

Of the various contact resistances, the electronic contact resistance between the land and

diffusion media tends to become dominant for PEFCs [17].

Example 4.9 Resistance Calculation Consider a PEFC operating at 0.6 V, 1 A/cm

with 500 cm

active area electrodes. Naﬁon 112 (51-µm) electrolyte and a graphite current

collector are used, with 3-mm-thick current collection plates, a 200-µm GDL on the anode,

and a 300-µm GDL on the cathode. The catalyst layers are 10 µm thick on the anode and

20 µm on the cathode and can be approximated as 0.3 fraction ionomer on the anode and

0.35 fraction ionomer on the cathode. The electrolyte ionic conductivity can be assumed

to be 8.3 S/m. The landing to channel area ratio is 1 : 2, and the measured total contact

resistance is 30 m · cm

(a) Estimate η

, the voltage loss from resistance.

(b) Estimate the percentage of total potential power wasted due to ohmic losses at this

condition if E

= 1.25 V.

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4.3 Region II: Ohmic Polarization 167

SOLUTION

(a) We can neglect the electronic resistance in most cases relative to the ionic resis-

tance:

= iA



j=1

= iA(R

anode

+ R

cathode

+ R

electolyte

+ R

contact

+ R

electric

≈ 0)

Plugging in the equations and the current and active area,

= iA



j=1

= (1 A/cm

)(500 cm

)





contact



The contact area is one-third of the active area since the landing to channel ratio is

1: 2:

= iA



j=1

= (500 A)



(5 × 10

−6

m) · (10,000 cm

)

(0.3 × 8.3  · m)(500 cm

)

(51 × 10

−6

) × 10,000

8.3 × 500

(10 × 10

−6

) × 10,000

0.35 × 8.3 × 500

0.03

166.6



 · cm



Resulting in:

= 0.205 V

(b) We can simply compare the electrical power at a condition with no losses to the

condition including our calculated ohmic losses:

= IV = 1.25 V · 500 A = 625 W

= IV = 1.044 V · 500A = 522.0W

Wasted =

(

625 − 522

)

625

= 16.48%

COMMENTS: At a relatively high current density of 1 A/cm

, we see that the ohmic

losses are very signiﬁcant. For a PEFC, the ionic conductivity of the electrolyte is a strong

function of humidity. Lower humidity values greatly increase the impact of ohmic losses,

steepening the slope of the ohmic drop on a polarization curve.

Returning to our ultimate goal of being able to analytically describe the fundamental

physics of the polarization curve, we now have an expression that includes the starting

equilibrium voltage, the departure from this voltage resulting from activation overpotential

at each electrode, and the ohmic polarization:

cell

= E

◦

(T , P) − η

a,a

−



a,c



− η

  

Can now solve

−η

m,a

−



m,c



− η

(4.79)

The only remaining major losses are a result of reactant crossover and concentration

polarization, discussed in the following sections.

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168 Performance Characterization of Fuel Cell Systems

4.4 REGION III: CONCENTRATION POLARIZATION

Concentration polarization is caused by a reduction in the reactant surface concentration,

which reduces the thermodynamic voltage from the Nernst equation and the exchange

current density from the BV equation. Figure 4.33 illustrates the transport of reactants from

the ﬂow channel to the reaction surface in a PEFC. The transport of species in the fuel cell

is discussed in detail in Chapter 5. For now, we consider the effects of reduced reactant

availability at the surface. At the electrode surface, reaction consumes fuel and oxidizer

at the rate determined from Faraday’s law. A rate of transport of reactant must be at least

equal to this or concentration polarization will develop:

consumed

≤

transport

(4.80)

Restriction of the rate of transport to the electrode can occur for a variety of reasons:

1. Gas-Phase Diffusion Limitation The diffusion of reactant in the gas phase is

limited to some value. In principle, we can imagine that there is a maximum rate

that perfume can diffuse from the front of a room to the back of the room. Now

consider the perfume is being consumed at the back of the room. The consumption

rate would be limited to the maximum perfume diffusion rate, as the reaction rate

is limited by reactant availability. At the double layer, a greater polarization will be

required to attract the required adsorbed species for reaction in a limiting condition.

2. Liquid-Phase Accumulation and Pore Blockage Limitation In low-temperature

fuel cells such as the PEFC, liquid water accumulation and blockage in the pores

of the electrolyte, diffusion media, or ﬂow channels of the anode or cathode can

reduce the transport rate of reactant to the catalyst. Voltage loss by this phenomenon

is generically termed ﬂooding. This topic is discussed in greater detail in Chapters 5

Figure 4.33 Schematic of path through diffusion media to catalyst layer in PEFC.

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4.4 Region III: Concentration Polarization 169

and 6. In liquid electrolyte systems such as the MCFC or PAFC, improper electrolyte

control can also restrict reactant access to catalyst sites.

3. Build-up of Inert Gases This is also a gas-phase limitation but is a result of the

accumulation of nonparticipating inert species such as nitrogen. As the oxygen is

consumed in an air cathode, the nitrogen mole fraction increases. Near the electrode,

the nonparticipating species can form an inert boundary-layer-restricting reaction.

4. Surface Blockage by Impurity Coverage In this case, some impurity becomes

adsorbed on reaction sites, preventing adsorption of the desired reactant. This is

commonly seen in low-temperature fuel cells when a CO impurity is present.

Carbon monoxide preferentially adsorbs on platinum catalyst sites in the anode

and has a very high polarization for oxidative removal.

In Chapter 3, we learned that the Nernst equation could be used to predict the change in

equilibrium voltage from concentration changes of the reactants and products. At the time,

we noted that there was also a kinetic effect of the concentration. Once there is reaction

at the electrode, the system is not in thermodynamic equilibrium and these effects must

be considered. From a combination of the thermodynamic (Nernst) and exchange current

density dependency [Eq. (4.31)], the voltage adjustment as a result of the change in oxygen

concentration from the reference value (1 atm) on the cathode can be shown as

V

s,ref



,ref



1/2



,ref



(4.81)

where γ is the ORR order with respect to O

partial pressure at constant overpotential and

ranges between 0.6 and 0.75 for a PEFC [9]. Assuming γ ∼ 0.75, the two can be combined

into the following:

V

s,ref



,ref



(4.82)

This predicts a 47-mV gain in potential for switching from dry air (21% O

) to pure oxygen

at 353 K, a value that matches experimental data well [9].

On the anode, we can write

V

s,ref



,ref





,ref



(4.83)

where the reaction order for hydrogen is 0.25–1.0. In practice, the anode hydrogen concen-

tration effect is often neglected for several reasons:

1. The diffusivity of hydrogen is much more rapid than oxygen, especially in higher

temperature fuel cells, so that transport limitation is rare.

2. The HOR kinetics are facile compared to the cathode so that the cathode polarization

typically dominates.

3. In PEFCs, liquid blockage (electrode ﬂooding) occurs more frequently on the cath-

ode, so that two-phase effects can be mostly ignored for low-temperature fuel cells

at the anode and completely ignored for high-temperature fuel cells.