Mench M.M. Fuel Cell Engines

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

30 Basic Electrochemical Principles

where T

and T

are the heat rejection and heat addition reservoir temperatures, respec-

tively. As a result, when the difference between the ambient and operating temperature is

low, heat engines are inefﬁcient. Although an electrochemical reaction engine is not subject

to Carnot limitations, it is important to understand that this does not mean the following:

(a) An electrochemical reaction has no limits on efﬁciency (we will discuss this in

Chapter 3).

(b) An electrochemical reaction always has greater thermodynamic efﬁciency than

its chemical analog. Indeed, depending on the operating conditions, a chemically

based cycle can be more efﬁcient than an electrochemically based cycle.

Many electrochemical reactions do have the potential to be much more efﬁcient and operate

at lower temperatures compared to a chemical reaction. There are many examples where

electrochemical processes are more common than mechanical or chemical alternatives,

including the following:

1. Chemical or Material Production From the early 1800s to around 1900, aluminum

was typically produced through a chemical reduction of aluminum chloride. Alu-

minum was a rare and expensive material produced this way and was treated as

a precious metal. A 2.8-kg pyramid, one of the largest casts of aluminum at the

time, was used to cap the Washington Monument in 1884 [1]. The electrochemical

route, known as the Hall–Heroult process of 1886, greatly reduced cost and ease

of production. The process of recovering aluminum by high-temperature electrol-

ysis of alumina dissolved in a molten salt bath was named after C. M. Hall and

P. L. Heroult, who nearly simultaneously patented the process in the United States

and France, respectively. Considering the importance of aluminum in aviation, it is

doubtful commercial airline travel would be feasible without this electrochemical

process for aluminum production. Other important examples of electrochemical

production include chlorine, hydrogen, oxygen, and other gas-phase species.

2. Batteries According to a 2005 study, over 70 billion batteries are produced a

year with a value of over $38 billion and growing [2]. Although actually small in

comparison to aluminum production, this value should continually increase as the

need for portable and wireless power grows.

3. Electroplating This important electrolytic process includes not only jewelry and

other aesthetic applications but also electrical contacts and coatings for protection

from corrosion (Figure 2.1). Electroplating alone was already a $10 billion market

in 1991.

4. Sensors and Measurement Devices There are many sensors based on electrochem-

ical reactions. A common example is the thermocouple, which exploits the thermo-

dynamically governed relationship between temperature and voltage between the

junction of two dissimilar metals. Other electrochemical-based sensors for physical

parameters, species detection, or other uses are common.

New developments in electrochemical processes continue to occur at a fast pace, and the

ﬁeld is always expanding. The Electrochemical Society (ECS) is one of the oldest technical

societies in America, dating back to 1902. Members of the ECS have included H. H. Dow

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

2.2 Electrochemical Reaction 31

Figure 2.1 The puriﬁcation of copper sheets by electrolysis. Pure copper sheets act as the cathode

and are spaced between impure copper sheets in an electrolyte bath. The process results in growth

of the pure copper sheet. (Image from D. D. Ebbing, General Chemistry, Third Edition, Houghton

Mifﬂin Company, Boston, 1990.)

(Founder of Dow Chemicals), C. M. Hall, and Thomas Edison. The need for electrochemical

expertise and development, including fuel cells, will continue for the foreseeable future.

2.2 ELECTROCHEMICAL REACTION

As discussed in Chapter 1, when an electrochemical reaction occurs, the overall global

reaction and thus the chemical energy difference between the beginning and end states of

the reactants and products are identical to the analogous chemical reaction. However, an

electrochemical reaction circulates current through a continuous circuit to complete the

reaction, while a purely chemical reaction does not. Current is strictly deﬁned as motion

of a charged specie and can be in the form of anions (negatively charged species such as

2−

), cations (positively charged species such as H

), or negatively charged electrons. An

electrochemical reaction also has more requirements than a purely chemical one. Shown in

Figure 2.2 is a basic electrochemical reaction cell. For an electrochemical reaction to take

place, there are several necessary components:

1. Anode and Cathode Electrode The electrochemical reactions occur on the electrode

surfaces. Oxidation occurs at the anode and reduction at the cathode. The reduction

reaction is accompanied by the oxidation reaction, and the pair is often referred to

as a redox reaction. Electrochemical reduction occurs in a reaction that consumes

electrons, reducing the valence state. Electrochemical oxidation results in the loss

of electrons and an increase in the valence state.

The valence state of an element is a measure of the electrons required to reach a ﬁlled outer electron shell.

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

32 Basic Electrochemical Principles

Figure 2.2 Basic reaction circuit.

2. Electrolyte The main function of the electrolyte is to conduct ions from one

electrode to the other. The electrolyte can be a liquid or a solid, and also serves to

physically separate the fuel and the oxidizer and prevent electron short-circuiting

between the electrodes. This is fundamentally different from a chemical reaction

where the fuel and oxidizer react together.

3. External Connection between Electrodes for Current Flow If this connection is

broken, the continuous circulation of current cannot ﬂow and the circuit is open.

When all components are in place, a complete circuit is formed, and continuous ﬂowing

current of ions and electrons can be maintained under the proper conditions. If any of

these components are not present, the circuit is open, and no ﬂow of current will occur.

An example of this is a battery sitting on the shelf at a store. Since the system is missing

an external connection, there is no continuous reaction. It is important to emphasize that

current is not only the ﬂow of electrons in the external connection between electrodes but

also the ﬂow of ions from one electrode to the other through the electrolyte and overall, the

sum of the charges is conserved in the reaction.

Global versus Elementary Reaction An important distinction between reaction steps,

which is needed to understand the material presented in the rest of the book, is the concept

of a global and elementary reaction. Consider the overall fuel cell reaction:

→ H

O (2.2)

We know that in a fuel cell the hydrogen and oxygen are separated by the electrolyte, so this

reaction cannot possibly occur in one step as shown. This is the global hydrogen–oxygen

redox reaction. Next, if we focus on just one electrode, the anode, we also have a global

anodic reaction. For example, consider hydrogen oxidation for an acid electrolyte (PAFC

and PEFC):

→ 2H

+ 2e

−

(2.3)

This looks very simple, but in reality it is still very unlikely to occur in a single step as

shown. Equation (2.3) is the global hydrogen electrochemical oxidation mechanism. The

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

2.2 Electrochemical Reaction 33

following elementary steps are believed to be mainly responsible for this overall oxidation

mechanism in an acid electrolyte:

⇔ 2(H − M)

(2.4)

(

H − M

)

⇔ H

+ e

−

(2.5)

In these equations, M represents the nonreacting catalyst surface. The ﬁrst step is the

hydrogen dissociative chemisorption step, referred to as the Tafel reaction. In this step, the

hydrogen bond is broken and a layer of atomic hydrogen is adsorbed on the catalyst surface.

The second reaction step is responsible for the actual charge transfer and current generation

and is referred to as the Volmer reaction. As a rule, the intermediate reactions must sum to

the overall global mechanism. So even for the simple hydrogen oxidation reaction, there

are multiple reaction steps. For the oxygen reduction reaction, the reaction is much more

complex, can involve dozens of potential reaction steps, and is still a subject of research.

We can, however, summarize the global oxidation and reduction reactions that occur at the

anode and cathode of fuel cells with acid or alkaline electrolytes:

For acid aqueous electrolytes that transport positive ions through the electrolyte (e.g.

PEFC, PAFC):

Anode global hydrogen oxidation reaction (HOR): H

→ 2H

+ 2e

−

(2.6)

Cathode global oxygen reduction reaction (ORR): O

+ 4H

+ 4e

−

→ 2H

O (2.7)

For alkaline aqueous electrolytes that transport negative ions through the electrolyte

(e.g. AFC, MCFC, SOFC):

Anode HOR: H

+ 2OH

−

→ 2H

O + 2e

−

(2.8)

Cathode ORR: O

+ 2H

O + 4e

−

→ 4OH

−

(2.9)

It should be noted that many alternative pathways also exist to describe the oxygen reduction

reaction, and more advanced publications should be consulted for current understanding in

this evolving area.

Conservation of Charge An excess of charge cannot be maintained in equilibrium. Con-

servation of charge is perhaps more difﬁcult to grasp than conservation of energy or mass,

but upon careful consideration, it is just as obvious a physical law. Since electrons and ions

that carry current are discrete physical entities, the units of charge carried are also discrete.

Consider the independent anodic and cathodic reactions of the fuel cell shown in Eq. (2.10):

Anode: H

→ 2H

+ 2e

−

Cathode: 2H

+ 2e

−

→ H

Overall: H

→ H

(2.10)

Although the anode and cathode reactions are independent, they are clearly coupled to

each other by the necessity to balance the overall reaction, so that the electrons produced

in the HOR are consumed in the ORR. Note that the overall balanced chemical equation

has no stray charged species and is identical to the chemical combustion of hydrogen in

air. However, in the electrochemical reaction, the anode oxidation and cathode reduction

reactions are separate and produce or consume the charged species that make up the current.

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34 Basic Electrochemical Principles

When the products of an electrochemical reaction are at a lower chemical energy

state than the reactants, the reaction is thermodynamically favorable, and the reaction

will generate current, a ﬂow of electrons or ions. Such a reaction is termed galvanic.

Thermodynamics, discussed in detail in Chapter 3, can be used to determine if a given

electrochemical reaction is thermodynamically favorable but cannot determine the rate

of reaction. In fact, even a highly thermodynamically favorable reaction may proceed

so slowly that no appreciable current can be detected. Discussion of the determination

of rates of reaction described by electrochemical kinetics is given in Chapter 4. A fuel

cell, a battery, and corrosion are examples of galvanic electrochemical reactions. Galvanic

reactions occur without external input when the proper conditions are met, including all

components necessary for the basic circuit shown in Figure 2.2.

In comparison, some reactions require energy input to occur, and the products are at a

higher chemical energy state than the reactants. Electrical-energy-consuming electrochemi-

cal reactions are termed electrolytic. The generation of hydrogen and oxygen by electrolysis

of water is an example of an electrolytic process. Many industrial processes are also elec-

trolytic, such as gold plating and production of certain chemicals such as aluminum. As an

example, compare the galvanic HOR of a common fuel cell (Eq. 2.2) and the electrolytic

water electrolysis reaction:

Anode: OH

−

→

+ H

O + 2e

−

Cathode: H

O + e

−

→

+ OH

−

Overall: H

O → H

+ 1/2O

(2.11)

The fact that the galvanic HOR of Eq. (2.2) can be reversed is remarkable but is a typical

feature of electrochemical reactions. Consider being able to reverse chemical combustion

and produce gasoline from the tailpipe exhaust of an automobile. Of course, the energy

required to electrolytically return the product water to its reactant state of hydrogen and

oxygen is greater than the chemical energy released in the galvanic process or an unlimited

supply of energy would be possible. However, the fact that the products of reaction can

be returned to the initial chemical state is utilized in some fuel cell applications. In a

reversible fuel cell system, the galvanic reactions of Eq. (2.10) provide power until the fuel

and oxidizer are expended. Then, external power is required for the electrolysis of water to

generate oxygen and hydrogen through the mechanism shown in Eq. (2.11). Thus, the fuel

and oxidizer compartment can be sealed, and no refueling is needed. The reversible fuel

cell system is ideal for space applications, where the cost of delivering weight into orbit can

reach $5000/kg. During orbit, for example, the reversible fuel cell provides power when

solar energy is unavailable, and solar panels provide power to electrolyze water when solar

energy is available. A commercially available portable reversible fuel cell demonstration,

unit is illustrated in Figure 2.3.

A few general conventions are useful to remember considering electrochemical reac-

tions.

1. Current is the ﬂow of charged species through the electrolyte (ions) and through

the external circuit (electrons).

2. Current is deﬁned as the ﬂow of positive charge and is thus movement in a direction

opposite to the electron ﬂow (although this convention is not universal).

3. For both galvanic and electrolytic reactions, electrons are conducted from the anode,

through the external circuit, and to cathode.

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2.3 Scientiﬁc Units, Constants, and Basic Laws 35

Figure 2.3 Reversible fuel cell demonstration kit from Eco Soul of Tustin, California.

4. For both galvanic and electrolytic reactions, oxidation occurs at the anode and

reduction occurs at the cathode. Thus, in a hydrogen fuel cell, the hydrogen is being

oxidized while the oxygen is being reduced.

5. The sign of the electrode depends on type of cell. For a galvanic reaction, reduction

occurs at a higher voltage potential than oxidation and thus the cathode is designated

as the positive electrode. For an electrolytic cell, the opposite is true and the anode

is the positive electrode. In an automotive battery, the cathode is the positive (+),

red-labeled electrode (Figure 2.4).

2.3 SCIENTIFIC UNITS, CONSTANTS, AND BASIC LAWS

Although the reader is assumed to have at least a cursory knowledge of basic chemistry and

electrical engineering concepts, a summary of some of the most basic relations, constants,

and units common to electrochemistry is included to provide an understanding of the

physical meaning of the commonly used parameters and allow us to make some basic

calculations.

2.3.1 Electrical Charge, Current, Voltage, and Resistance

Current and Charge The electricity that powers electric motors, radios, and so on, is

really a ﬂow of current. The ﬂow of electrical current through a circuit, powering an

electrical motor or other device, is analogous to the ﬂow of water in a pipe, powering a

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

36 Basic Electrochemical Principles

Figure 2.4 Cut-away illustration of car battery. (Adapted from http://www.tiscali.co.uk/reference/

encyclopaedia/hutchinson/m0016566.html.)

water wheel and providing mechanical energy, as depicted in Figure 2.5. The electrical

current (I) is the rate of the ﬂow of charged species and is analogous to the mass ﬂow rate

of water in the pipe. The total charge passed is analogous to the total mass of ﬂuid passed

over a given time:

Pipe: Total mass passed = m =



dt =



mdt

Wire: Total charge passed = q =



dt =



Idt

(2.12)

The International System (SI) unit of current (I)istheampere, named after the French

mathematician and physicist Andr

e-Marie Amp

ere (1775–1836) [3]. Note from Figure 2.5

that the electron ﬂow is shown moving in the direction opposite to the current because the

direction of current is deﬁned as the ﬂow of positive charge and thus moves in a direction

opposite to the negatively charged electron ﬂow (although this convention is not universal).

The total electrical charge passed (C) is designated with the SI unit of the coulomb,

after the French physicist Charles Augustin Coulomb (1736–1806). A coulomb is the

conventional unit of charge passed through the circuit and is equivalent to the total charge

passed by the ﬂow of an ampere of electrons in one second:

1C= 6.28 × 10

electrons passed = 1 As (2.13)

Current conductor or water pipe

Figure 2.5 Flow through a pipe or a wire is analogous.

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2.3 Scientiﬁc Units, Constants, and Basic Laws 37

Thus, the charge on a single electron is only −1.6 × 10

−19

C. Since a coulomb is approxi-

mately equal to 6.28 × 10

elementary charges, one ampere is equivalent to 6.28 × 10

elementary charges moving through a surface in one second, or 1 C/s.

Sometimes, it is more convenient to describe total charge passed in units of ampere-

hour (Ah). While this can seem confusing at ﬁrst, examining the units reveals it is simply

a unit of total charge passed:

1Ah= (C/s) · h × 3600 s/h = 3600 C (2.14)

Total energy is often also expressed in a similar fashion. A look at an electric bill or a laptop

computer battery will show the measure often used to deﬁne total energy as a watt-hour,

even though it is really equivalent to a joule.

1Wh= (1 Jh/s)(3600 s/h) = 3600 J (2.15)

Voltage A volt (V) is a measure of the potential to do electrical work. Mechanical work is

done when a weight is moved through a distance, and electrical work is done when current

ﬂows through a resistance. The volt (V) is named after Italian physicist Alessandro Volta

(1745–1827), who demonstrated the ﬁrst electrochemical battery in 1800 [4]. The higher the

voltage, the greater the potential there is to do electrical work. Science students are familiar

with the joule as the standard SI unit of energy. Voltage potential is derived from the same

thermodynamic origin of energy difference between the chemical bonds of the reactants

and products. In this context, we can convert to units appropriate for electrochemical work.

The volt is deﬁned as the measure of potential to do electrical work:

1V= 1J/C (2.16)

A volt is thus a measure of the work required to conduct one coulomb of charge. The higher

the voltage, the higher the potential is available to move this charge. The words potential

and volt in fact are often synonymous with one another. Figure 2.6 illustrates a waterfall

analogy to help understanding. The potential for the water ﬂowing over the waterfall to

do work is proportional to the difference in height between the top and the bottom of the

waterfall and the ﬂow rate of the water. The greater the difference in height between the

top and the bottom, the more work a hydraulic turbine could extract from the same ﬂow.

Similarly, the electrodes in an electrochemical reaction are like the top and the bottom

of the waterfall. The potential to convert chemical bond energy into electrical power is

proportional to the difference in the potential (voltage) between the electrodes, not the

absolute value of the electrodes (imagine if the bottom of the waterfall was only 1 m below

the top—not much of a waterfall). The current is of course analogous to the mass ﬂow rate

of the water going down the waterfall (a trickle of water is not going to generate much

power), and the total charge is analogous to the integration of the mass ﬂow rate over time,

or the total mass passed through the waterfall. Just as the mechanical power generated by

the turbine scales directly with water ﬂow rate and height of the falls, the electrical power

scales directly with current and voltage:

= IV = IE

cell

(2.17)

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38 Basic Electrochemical Principles

cathode

anode

Flow rate over the falls—current

Standard reference: standard hydrogen electrode (SHE = 0.0 V)

cell

= E

cathode

– E

anode

Figure 2.6 Waterfall analogy to voltage potential. E represents the voltage potential.

Since the voltage of a given reaction is a measure of the potential energy for the

reaction, it must be referenced to some standard datum, selected as an arbitrary zero-voltage

point. The standard commonly used in electrochemistry is the so-called standard hydrogen

electrode (SHE). The SHE is the voltage of a platinum sheet electrode immersed in an

aqueous electrolyte solution, with unit H

ion activity i.e., 1 M concentration in contact

with hydrogen gas at 1 atm hydrogen pressure [6]. The SHE is arbitrarily assigned to 0 V.

Thus, other electrodes have an oxidation (negative) or reduction (positive) potential relative

to the SHE. Since most fuel cells operate on hydrogen, the result is that the anode potential

is around 0 V. In practice, the SHE is not always convenient, and many other reference

electrodes with easily reproducible potentials have been devised and can be used instead

of the SHE. The theoretical electrode voltage can be determined based on thermodynamic

considerations, discussed in Chapter 3. The standard electrochemical reduction half-cell

reaction series is shown in Table 2.1 and shows the reduction potential of the given half

reaction relative to the SHE for the reactions shown. The oxidation potential of the reverse

reaction is simply the same value with opposite sign. For a complete cell redox reaction,

the standard cell voltage E

cell

is simply the sum of the oxidation and reduction potentials:

cell

= E

anode

+ E

cathode

(2.18)

If positive, the reaction is galvanic. If the cell voltage (E

cell

) is negative, this is the minimum

applied voltage required to initiate the electrolytic reaction. As an example, consider a

redox couple of the oxidation of zinc and the reduction of hydrogen:

Anode (oxidation):

Zn → 2e

−

+ Zn

Cathode (reduction):

−

+ 2H

→ H

Overall:

Zn + 2H

→ Zn

+ H

From Table 2.1, the reduction potential of the zinc reaction is −0.76 V, so that oxidation

of zinc relative to the SHE at standard conditions is 0.76 V. The cathode is the SHE, so the

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2.3 Scientiﬁc Units, Constants, and Basic Laws 39

Table 2.1 Partial Electrochemical Reduction Potential Series at 298

◦

Half Reaction Voltage E

◦

(V)

+ e

−

→ Ag

+0.799

AgBr

+ e

−

→ Ag

+ Br

−

+0.095

AgCl

+ e

−

→ Ag

+ Cl

−

+0.222

HClO

+ H

+ e

−

→

2,g

+ H

+1.63

+ 2e

−

→ Cu

+0.337

+ 2e

−

→ Fe

−0.440

+ 3e

−

→ Fe

+0.771

+ 2e

−

→ H

2,g

0.000

+ 2e

−

→ H

2,g

+ 2OH

−

−0.830

−

2aq

+ H

+ 2e

−

→ 3OH

−

+0.880

2,aq

+ 2H

+ 2e

−

→ 2H

+1.776

+ e

−

→ K

−2.925

+ e

−

→ Li

−3.05

+ 2e

−

→ Mg

−2.37

2,g

+ 4H

+ 4e

−

→ 4OH

−

+ N

4,aq

−1.16

2,g

+ 5H

+ 4e

−

→ N

−

5,aq

−0.23

−

3aq

+ 4H

+ 3e

−

→ NO

+ 2H

+0.96

+ e

−

→ Na

−2.71

+ 2e

−

→ Ni

−0.28

+ 2e

−

→ Zn −0.76

2,g

+ 4H

+ 4e

−

→ 2H

+1.23

2,g

+ 2H

+ 2e

−

→ H

2,aq

+0.68

2,g

+ 2H

+ 4e

−

→ 4OH

−

+0.40

3,g

+ 2H

+ 2e

−

→ O

2,g

+ H

+2.07

+ 2H

+ 2e

−

→ H

+0.141

3,aq

+ 4H

+ 4e

−

→ S(s) +3H

+0.450

HSO

−

4,aq

+ 4H

+ 2e

−

→ H2SO

3,aq

+ H

+0.170

Source: From [5].

voltage is 0.0 V. Overall, then, the voltage of the cell illustrated in Figure 2.7 at standard

conditions is 0.76 V.

Individual Electrode Behavior In Figure 2.6, a waterfall is shown to illustrate the voltage

potential for the overall reaction. At each electrode, there is an independent half-cell global

reaction coupled with the other electrode reaction only through conservation of mass and

charge. Just as the potential for work from the waterfall is a result of the difference in

location between the top and the bottom, the overall electrochemical cell voltage is a result

of the difference in potential between the anodic and cathodic reactions, not the voltage of

the individual reactions themselves. Consider a hydrogen-ﬁlled cathode and anode from

Table 2.1. This electrochemical reaction circuit would have no overall potential for reaction,

since there would be no potential difference between the two electrodes. This also illustrates

the function of the electrode to separate fuel and oxidizer. If the electrolyte permits passage

of reactants through it, they will mix at the electrodes and reduce voltage potential.