Mench M.M. Fuel Cell Engines

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50 Basic Electrochemical Principles

SOLUTION (a) First we need to solve for the total hydrogen required to provide three

days of power: From Faraday’s law for the anode on pure hydrogen

= λ

= 2 ×

(0.6A/cm

)(20 cm

)

(2 e

−

eq)/mol H

)(96,485 C/eq)

×(3600 s/h)(24 h/day)(3 days) = 32.25 mol H

consumed

(32.25 mol)(2 g mol) = 64.5gH

From the ideal gas law

PV = m

For the hydrogen

V =

(64.5g)[8.314 J/(mol ·K)]

2g/mol



298 K

20,260,000 Pa



= 0.0039 m

= 3.9L

(b) Following along the same methodology for the cathode side,

= λ

= 2.3 ×

(0.6A/cm

)(20 cm

)

(4 e

−

eq/mol O

)(96,485 C/eq)

×(3600 s/h)(24 h/day)(3 day) = 18.51 mol O

consumed

(18.51 mol)(32 g/mol) = 592.2gO

V =

(592.2 g)[8.314 J/(mol · K)]

32 g/mol



298 K

20,260,000 Pa



= 0.002265 m

= 2.27 L

COMMENTS: Note these results are for a very low power (9-W) system. Around 10–20

W is needed for many portable applications, so the storage volume would greatly increase.

Three days of power without a recharge in a portable device is quite difﬁcult to achieve.

Storage volume could be improved with increased performance, higher pressure storage

fuel recirculation, or alternate storage techniques, such as use of liquid fuel.

2.6 THE GENERIC FUEL CELL

Now that the basics of electrochemical reactions are known, we can begin discussion of

basic fuel cell operation. A generic fuel cell is shown in Figure 2.9 with regions labeled A

to H. Each variety of fuel cell has unique materials, structure, and design features, but at a

basic level, all can be reduced to this generic design. Note that the basic components are the

same as shown in Figure 2.9. To reduce ionic and electronic resistive losses and increase

power density, the components in a fuel cell are designed to have the smallest possible path

length for ions and electrons.

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2.6 The Generic Fuel Cell 51

Figure 2.9 Generic fuel cell.

For a single cell, component A in Figure 2.9 is known as the anodic current collector

when the ﬂow is a fuel. In a normal stack arrangement, where the anode current collector is

also the cathode current collector on the opposing side, this is also known as a bipolar plate

or cell interconnect, since it connects the anode and cathode of adjacent cells in series. The

current collector functions as follows:

1. Conducts electrons from anode B to the external circuit or to the adjacent cathode

in a stack.

2. Delivers fuel (liquid or gas) ﬂow through the ﬂow channels labeled “B”. The fuel

diffuses or convects

to the anode electrode C, where fuel oxidation occurs.

3. Provides structural integrity of stack (in most, but not all, designs).

4. Dissipate waste heat generated by inefﬁciencies of the reaction to constant, often

with a coolant ﬂow through the current collector.

Current collector materials for fuel cell stacks of all varieties must satisfy the following

requirements:

1. Lightweight, compact and highly robust.

2. Low-cost raw material and manufacturing process.

3. High electrical conductivity over the expected lifetime of operation.

4. High corrosion resistance in oxidizing and reducing environments.

5. Impermeability to fuel and oxidant ﬂow.

6. No disintegration of material or electrical degradation over lifetime of operation.

7. Suitable thermal expansion properties, which is more of a concern for higher tem-

perature fuel cells.

8. Capable of proper sealing of reactant ﬂow to prevent leakage. This is often accom-

plished with gaskets around the periphery to the cell plate.

Diffusion and convection are speciﬁc modes of mass transport. If the reader is unfamiliar with these, a quick

survey of Chapter 5 or an undergraduate mass transfer textbook is recommended for review.

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52 Basic Electrochemical Principles

Figure 2.10 Examples of various ﬂow ﬁeld designs. (Images courtesy of Soowhan Kim.)

Current collector material and manufacturing engineering are active areas of research and

development. Presently, a variety of materials are used for bipolar plates in fuel cell stacks.

Specially coated metals, graphite, and doped polymers have been used for low-temperature

fuel cells. High-temperature fuel cells have primarily utilized ceramics for this purpose.

Component B in Figure 2.9 is known as the anodic ﬂow ﬁeld, or fuel ﬂow ﬁeld. It is

typically machined or formed directly in the current collector plate, although it can also be

a discrete part. The anode ﬂow ﬁeld main functions are to

1. facilitate transport of fuel to the anode and

2. facilitate removal of products of reaction.

For each variety of fuel cell, many different conﬁgurations for the ﬂow ﬁelds have been

used to optimize heat and mass transfer, current collection, and so on. Because of the

highly coupled interaction between heat, mass, and electrochemical phenomena involved,

ﬂow ﬁeld design is not a straightforward matter. Basic ﬂow ﬁeld patterns include a simple

serpentine arrangement, a parallel arrangement, a parallel serpentine combination, and

others, as shown in Figure 2.10. A great deal of the engineering at the individual cell

level is based on obtaining the best possible ﬂow ﬁeld design to balance reactant and heat

transport, product removal, pressure drop, and machinability. Each design has particular

advantages and limitations that will be discussed in detail in later portions of this text.

Component C in Figure 2.9 is the anode electrode. The anode contains a thin region

of catalyst that greatly facilitates the electrochemical reaction. This region is often referred

to as the catalyst layer, although the region is much more complex than this name implies.

The anode is the location of the fuel oxidation reaction. The basic functions of the anode

catalyst layer are to

1. Enable the fuel oxidation reaction via a catalyst.

2. Conduct ions from the reaction site to the electrolyte region D.

3. Conduct electrons from the reaction site to the anode current collector A.

4. Facilitate reactant transport and product removal to and from the catalyst locations.

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2.6 The Generic Fuel Cell 53

Figure 2.11 Transmission electron micrograph of PEFC catalyst layer [10].

Notice that the catalyst layer must have high electrical and ionic conductivity. The catalyst

enables the electrochemical reaction by providing a facilitated reaction site, and the fuel is

said to be “galvanically burned” at the anode. The catalyst layer is typically quite thin but

is porous and three-dimensional in nature, and is the only interface with reactant, catalyst,

and ion and electron conductors that enables a reaction.

Consider a microscopic view of the anode catalyst layer, labeled in Figure 2.9 as D

and shown in Figure 2.11. As discussed, both the anode and the cathode (labeled F) must

have a high degree of mixed ionic and electronic conductivity and porosity. To achieve

this, the catalyst layers are a highly three-dimensional porous structure consisting of the

catalyst, electrolyte, electron conductor, and voids for reactant transport. Note the high

relative porosity of this layer, typically around 40 to 70% for most fuel cells. The reaction

in this highly porous structure depends on the simultaneous presence of reactant, catalyst, an

ionic conductor with a continuous path to the main electrolyte, and an electronic conductor

with a continuous path to the current collector. This is shown schematically in Figure 2.12.

Although we conveniently use the geometric, or planform,

area of the electrode as the

superﬁcial active area of the electrode for calculation of current density, the true active area

of the porous electrode available for reaction can be orders of magnitude larger due to the

three dimensional nature of the surface.

Traditionally, the highly porous nature of the electrodes is to maximize the concept of a

triple-phase boundary where reaction can occur between (1) the open pore for the reactant,

(2) the catalyst, and (3) the ionic conductor. Increasing the triple-phase boundary (TPB)

within the porous electrode structure leads to increased reaction site density for a given

superﬁcial electrode area and therefore results in a higher performance electrode. In some

solid-phase electrode systems, the TPB concept is directly applicable, but in many systems

such as the PEFC, the concept of the TPB is not strictly accurate, because there is actually

The planform (geometric) area is the above view area.

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54 Basic Electrochemical Principles

Figure 2.12 The simultaneous presence of reactant, catalyst, an ionic conductor with a continuous

path to the main electrolyte, and a continuous path of electrical conductivity is needed or a reaction

will not take place at a catalyst site. A catalyst rendered inactive by these situations is called an

“orphan” catalyst.

a thin ﬁlm of electrolyte coating the catalyst structure that has a limited permeability to

the reactant. Thus, reaction can occur below the thin-ﬁlm surface and is not strictly limited

to TPB locations. Nevertheless, the heuristic concept of a TPB is useful to understand the

engineering trade-offs in an electrode. If there is too little catalyst, or too much catalyst

isolated from the reactant (orphan catalyst), or insufﬁcient pathways for ion or electron

transport exists, not enough reaction sites will be active and performance will suffer. If

the porosity is too low or the electrode is too thick, the reactant will not be as available

and performance will also suffer. Major losses in the catalyst layer can occur from lack

of electrical or ionic conductivity. Based on the parallel needs of high porosity and mixed

ionic and electronic conductivity, it is easy to understand that the catalyst structure is highly

complex, and there is a tenuous balance between the various phase distributions. Although

the structure is microscopic in nature, because the catalyst layer is typically manufactured

using macroscopic methods, such as tape casting, spray coating, or painting, there can be

a high number of orphan catalysts.

Proper catalyst selection is critical for optimal fuel cell performance. Low-temperature

fuel cells typically must utilize expensive noble metal catalysts such as platinum, which

has been an historical barrier in terms of cost. Since higher temperatures more readily

enable electrochemical reaction, less expensive catalysts such as nickel can be utilized for

high-temperature fuel cells such as the SOFC or MCFC.

Consider a reaction coordinate plane for a given galvanic electrochemical reaction

shown in Figure 2.13. Even though the overall reaction is galvanic and will release elec-

trical energy in going from reactants to products, in order to proceed from an equilibrium

state of reactants to another equilibrium state of products, some activation energy is re-

quired to initiate a signiﬁcant reaction. This is somewhat similar to a purely chemical

combustion reaction, where an ignition source is needed to initiate an exothermic reaction

from an initial nonreacting state. For an electrochemical reaction, this activation energy

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2.6 The Generic Fuel Cell 55

Activation

energy

Energy

released

Energy

Stage of reaction

Path with

better catalyst

Total exothermic

release available

for work (electrical

or chemical)

Figure 2.13 Reaction plane for effective and ineffective catalysts.

lost is in the form of lost voltage potential. The more effective the catalyst, the lower the

activation energy barrier for reaction and the lower the voltage penalty. This activation

polarization loss is discussed in detail in Chapter 4. For now, consider this barrier as a mea-

sure of the quality of the electrode structure and materials in the promotion of the desired

reaction.

The catalyst layer must have a high degree of mixed conductivity for both electrons

and ions as well as a highly porous structure to promote reactant and product transport.

Ionic conduction in the catalyst layer is typically provided by addition of electrolyte in the

catalyst layer. This enables transport of ions through the catalyst layer to the main electrolyte

structure and to the opposing electrode. Without this ionically conductive material in the

catalyst layer, the circuit would not be complete. Concomitantly, if there were nothing

in the catalyst layer that conducted electrons, electron ﬂow from the reaction site to the

current collector would not be possible. Electron conductivity is generally through catalyst

and other supporting materials.

Several varieties of fuel cells use an electron-conducting porous DM as an interface

between the catalyst layer and the current collectors. This DM is not shown in Figure 2.9,

since it is not a universal feature of all fuel cells. For example, PEFCs use a carbon-based

porous media for this purpose, as shown in Figure 2.14. Either a woven carbon cloth or a

carbon ﬁber structure bonded with a graphitized thermoset resin is typically used for this

purpose. Alkaline fuel cells also use a similar porous media to aid electron conduction

between the porous electrodes and current collectors.

The electrolyte in a fuel cell (E in Figure 2.9) has three main purposes:

1. To physically separate the reactants.

2. To conduct the charge carrying ions from one electrode to the other.

3. To prevent electronic conduction between the anode and cathode.

The ﬁrst purpose is unique to electrochemical reactions. The separation of reactants pro-

duces a thermodynamic activity difference between the anode and cathode that results in

the voltage potential difference. If there was air on both the anode and the cathode, there

would be no potential for reaction and no voltage difference between the two electrodes.

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56 Basic Electrochemical Principles

Figure 2.14 Close-up scanning electron microscope images of (a) woven carbon cloth and (b)

nonwoven carbon paper bound with graphitized thermoset resin diffusion media used in PEFCs.

The second purpose is obvious but also includes a high resistance to ﬂow of electrons. From

the basic circuit schematic of Figure 2.2, the electrolyte completes the ﬂow of current by

conducting ions. However, the electrolyte must also be a strong electron insulator, or the

effect would be to short circuit the ﬂow of electrons to the eternal circuit.

The cathode catalyst layer (F in Figure 2.9) is essentially the same function and purpose

as the anode catalyst layer; however the catalyst type and loading may be different than

that of the anode, as it is designed to promote the ORR. Additionally, the cathode ﬂow ﬁeld

and current collector, G and H, respectively, serve the same function on the cathode as the

anode, although the design may be different from that of the anode for a variety of reasons

discussed later in this text.

2.7 SUMMARY

The purpose of this chapter was to introduce the reader to the basics of electrochemical

reactions, provide a physical understanding of the basic parameters used in electrochemistry,

and introduce the general operation of a fuel cell. Future chapters will use this groundwork

to expand fundamental understanding and investigate the basic trade-offs in engineering

design. For an electrochemical reaction to take place, there must be an anode,acathode,

an electrolyte, and an external connection. Reactions producing and consuming electrical

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2.7 Summary 57

energy are termed galvanic and electrolytic, respectively. Electrochemical reduction occurs

in a reaction that consumes electrons and electrochemical oxidation results in loss of

electrons from the reactant. The electrical current is the rate of the ﬂow of charged species.

The total electrical charge passed is designated with the SI unit of coulomb.Thevolt

is deﬁned as the work required to conduct one coulomb of charge. Electrical resistance,

measured in ohms, is a measure of the potential losses associated with moving a rate of

charge, and is not an intrinsic material property. Resistivity ρ and its inverse, conductivity,

are intrinsic properties of a material:

ρ =

Current, voltage, and resistance can be related through Ohm’s law in the absence of signif-

icant concentration gradients:

V = IR

Electrical power can be expressed as

= IV

Faraday’s constant F represents the charge per mole of equivalent electrons:

F =

6.023 × 10

electrons/mol eq

6.242 × 10

electrons/C

= 96,485 C/eq

The scaling factor n is deﬁned as the number of electrons transferred per mole of species

of interest:

n =

number of electrons

mole of species of interest

mol

Thus, the combination of nF is the charge passed per mole of specie of interest, and the

units of nF are coulombs per mole. Faraday’s second law of electrolysis can be written as

The Faradic efﬁciency is a measure of the percent utilization of reactant in a galvanic

process

theoretical required rate of reactant supplied

actual rate of reactant supplied

Faradic efﬁciency is often called the fuel utilization efﬁciency (µ

) when applied to the fuel

in a galvanic redox reaction. The anode and cathode stoichiometries are deﬁned as follows:

actual rate of oxidizer delivered to cathode

theoretical rate of oxidizer required

actual rate of fuel delivered to anode

theoretical rate of fuel required

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58 Basic Electrochemical Principles

In this chapter, the basic components, requirements, and functions of a generic fuel

cell were also discussed. The reader should be familiar with the functions of the current

collectors (also known as a bipolar plate or cell interconnect), the ﬂow ﬁelds, the anodic

and cathode electrodes with the concept of the triple-phase boundary, and the electrolyte.

The reader should also understand the ﬂow of current (ionic and electronic) through these

components.

APPLICATION STUDY: DESIGN OF FUEL CELL WITH

STORAGE TANKS AND TYPICAL

MATERIAL/PERFORMANCE PROPERTIES

In this assignment, you will design and compare various fuel storage systems for an

automotive fuel cell application. Assume you need 7 kg of hydrogen onboard to achieve

the desired range. There are several options to store hydrogen, including:

1. Liqueﬁed hydrogen

2. Compressed gas-phase hydrogen

3. Stored as methanol in liquid form and reformed into hydrogen on-board

4. Stored in a metal hydride and released via heat addition

Find reliable sources online or in print and perform a feasibility study of the four options

listed above. Discuss in your report:

1. The volume and weight of the storage tanks required

2. The advantages and disadvantages of each design

3. How refueling would be accomplished in each option

Include the Internet resources consulted and copies of any reports or articles used in

preparation. Note that hydrogen storage is also discussed in Chapter 8.

PROBLEMS

Calculation/Short Answer Problems

2.1 Deﬁne the units of the following in terms of the most

basic SI units:

(a) Vo l t

(b) Ampere

(d) Faraday’s constant

(e) n (as in iA/nF)

2.2 Determine the theoretical open-circuit voltage of the

following fuel cells and determine which reactant would

be the oxidizer and which would be the fuel for a galvanic

reaction.

(a) Oxygen and hydrogen gas

(b) Lithium and oxygen gas

2.3 Determine the minimum theoretical open circuit volt-

age that would be required to generate hydrogen peroxide,

, with hydrogen gas and air.

2.4 Besides the desired hydrogen oxidation and oxygen re-

duction reactions, there are several other potential reactions

listed in Table 2.1 that can occur in a hydrogen/air fuel cell

stack (e.g., they only involve atomic hydrogen, oxygen, and

nitrogen species). List the potential reactions; then deter-

mine the theoretical voltage for these reactions and decide

if they could occur in a fuel cell or not. Could any of these

reactions occur normally? Note, the species besides H

,andH

O must be generated and balanced by the over-

all reaction, so you will have to combine some reactions

to achieve this. Using your results, explain why the hydro-

gen oxidation and oxygen reduction reaction is in fact the

c02 JWPR067-Mench December 19, 2007 17:26 Char Count=

Problems 59

reaction that occurs, rather than other reactions along the

same potential series.

2.5 Demonstrate how Ohm’s law is consistent in units; for

example, show V = IR is self-consistent in terms of units.

2.6 Consider a 10-plate fuel cell stack at an anode stoi-

chiometry of 1.2 with 20 A current generated in the stack

and a stack voltage of 6.0 V. As an engineer, you have a

choice to install a recirculation pump to recycle the unused

hydrogen from the anode exhaust back into the anode to

increase the effective fuel utilization to 100%. However,

the pump required 60 W of parasitic power to operate con-

tinuously. Is installation of the pump justiﬁed? Explain. At

what value of parasitic power does the addition of the pump

become unjustiﬁed?

2.7 Consider a 300-plate fuel cell stack with 150 cm

active

area per plate:

(a) For an anode and a cathode stoichiometry of 1.4

and 2.5, respectively, determine the mass ﬂow rate

of hydrogen and air into the fuel cell per ampere

of current.

(b) If the nominal operating point is an average of

0.6 V per plate with 1.2 A/cm

, determine the

stack voltage and electrical power output.

could be performed with a storage tank contain-

ing 5 kg of hydrogen and limitless air? How much

more output could be achieved if the unused fuel

were recycled so that the effective fuel utilization

became 100%.

(d) Determine how many plates the fuel cell would

have to have at 0.6 V per plate, 1.2 A/cm

,to

generate 150 horsepower for an automotive appli-

cation.

2.8 A given fuel cell has continuous 150 A DC, an operat-

ing voltage of 0.55 V, and an overall internal resistance of

3m at 1.4 A/cm

current density. Calculate:

(a) The potential loss from ohmic resistance, in volts,

at this condition.

(b) The total electrical work produced in 2 h.

watts.

2.9 Describe the concept of the TPB and how this is rele-

vant to fuel cell performance. A sketch will help.

2.10 Determine the single-pass fuel utilization efﬁciency

for a 150-plate fuel cell stack with 120 A current output

and a hydrogen ﬂow rate through the stack of 0.2 g/s of

hydrogen.

2.11 We desire a fuel utilization efﬁciency of >95% on

the anode of a 300-plate, 100-cm

-active-area stack. Deter-

mine the hydrogen mass ﬂow rate required in the stack as a

function of current density.

2.12 It is proposed to develop a fuel cell that runs directly

on propane (C

) at a propane stoichiometry (λ

)of

2.5 and a cathode oxygen stoichiometry (λ

) of 2 [note the

cathode is running on air (79% N

, 21% O

by volume].

The cell operates at 0.3 V at a current density of 0.1 A/cm

The superﬁcial active area of the cell is 25 cm

. The anode

electrochemical reaction is

(

)

+ 6

(

)

→ 20H

+ 20e

−

+ 3CO

The basic cathode electrochemical reaction is

+ 4e

−

+ 4H

→ 2H

The balanced overall electrochemical reaction is thus

(

)

+ 5O

→ 4H

O +3CO

with the following molecular weights:

44 g/mol

018g/mol

32 g/mol

air 28.85 g/mol

28 g/mol

(a) Is the overall cell producing or consuming water—

at what rate in moles per second?

(b) What is the actual supply rate of air at the cathode

in grams per hour?

2.13 Consider a direct methanol fuel cell with a liquid

methanol and water solution in the anode and an air cath-

ode. The anode electrochemical oxidation reaction is

OH +H

O → 6H

+ 6e

−

+ CO

The basic cathode electrochemical reduction reaction is

+ 4e

−

+ 4H

→ 2H

The balanced overall electrochemical reaction is

OH +

→ 2H

O + CO