Creating More Efficient Batteries with New Anodes

Session B9
5064
University of Pittsburgh, Swanson School of Engineering
2015-04-03
1
CREATING MORE EFFICIENT BATTERIES WITH NEW ANODES
Rebecca Ghobrial (rmg65@pitt.edu, Mahboobin 10:00) and Margaret Smith (mrs159@pitt.edu, Mahboobin 10:00)
Abstract— The last several decades have exhibited an
exponential growth rate for technology. In perspective, the
smartphones that are now seen as common household items
administer more effective communication than the President
of the United States held access to only twenty-five years
ago. And, they are capable of delivering data more directly
than any of his technology managed just ten years ago [1].
This ever-expanding technological innovation couples with
an increase in demand for batteries. Batteries are used in a
variety of essential products, ranging from remote controls
and smoke detectors, to products like electric cars and
cellular devices [2]. Following the upward trend of
technology advancements, electric car and cell phone
companies are constantly working towards creating new and
better products. Unfortunately, this trend in innovation did
not carry over into the battery industry. This modern
technology still relies on the same weak battery made in
1990 [3].
This paper will dissect the composition of the current
lithium-ion battery and explore a solution to the problem of
poor battery advancement. It will highlight the advantages
of using different materials in the anode of the battery, such
as lithium and titanium dioxide, to maximize charging
capacity. Such changes will lead to batteries that can hold
power more efficiently, increasing the effectiveness of cell
phones and electric cars. As a result, these newly powered
products will have the capability of improving sustainability
by creating a safer environment and enhancing quality of
life. Ethical issues surrounding the use of these anode
materials will also be considered as well as available
solutions. This will ultimately prove why lithium and/or
titanium dioxide anode batteries can succeed as a substitute
for current batteries, and in turn increase sustainability.
Key Words—Anode, Battery, Cathode, Electrons,
Electrolytes, Graphite, Lithium, Sustainability, Titanium
dioxide
THE NECESSITY OF BETTER BATTERIES
The battery was invented to serve as a means of
producing electrical energy, free from any power
connections or fuel. It has so many applications that the
importance of batteries is often overlooked. The commonly
recognized battery is the lithium-ion battery. This type of
battery is present around the home in devices such as remote
controls, smoke detectors, and flashlights. Military
personnel, firefighters, and emergency response teams
depend on the functionality of these batteries for their radio
communication. Similarly, hospitals and emergency services
rely on pacemakers, defibrillators, and heart monitors--all of
which are most commonly powered by lithium-ion batteries.
To support all these applications, it is pertinent that such a
battery be functional and efficient [2].
One application of batteries that is rising in popularity is
the use of lithium-ion batteries in electric cars. Compared to
gas powered cars, electric cars hold more advantages in
regards to the work they require, the noise they produce, and
the environmental impacts. When cars were first introduced,
both gas powered and electric, those that ran on gas
demanded that the owner use a hand crank to start the
vehicle, and also required a great deal of manual effort to
shift gears. Similarly, gas cars proved to be extremely noisy
upon start up and during driving. Electric cars, in
comparison, produced little noise and were deemed easy to
drive. Due to this, the electric car was extremely popular,
especially among women who did not want to be seen
exerting copious amounts of work just to ride into town.
Unfortunately for electric cars, manufacturers were able to
create a gas-powered vehicle that was significantly cheaper
than the electric car. Coupled with a rise in the oil industry,
this caused the demand for gas cars to skyrocket. However,
gas powered cars produced a foul emission that was harmful
to the environment [4]. Though this was a considerable
problem at the time, it reins today as the most defining
argument against gas powered cars. This extreme number of
gas-powered cars, all emitting foul pollutants into the air, is
destroying the environment. In regards to sustainability, this
cannot continue.
Though sustainability often renders the connotation of
simply helping the environment, its true definition holds a
much stronger weight. Sustainability encompasses three
major areas of interest: the environment, the economy, and
the society. In order to be truly “sustainable”, one must
consider environmental influence, affordability for the
average consumer, and effects to the overall standard of
living [5]. Since electric cars are already significantly better
for the environment, the ultimate obstacles to pursuing
electric cars as a means of improving sustainability are the
better affordability and overall standard of living that gas-
powered cars provide. The most prominent solution is then
to improve the lithium-ion battery in an electric car.
Refining the battery has to potential to produce an electric
car that it is cheaper, which would address affordability.
Similarly, the enhanced battery would allow electric cars to
compete with the power provided by gas-powered cars,
deeming them easier to maintain, which would adhere to
customer satisfaction and ultimately standard of living.
Essentially, electric cars could be a highly successful way of

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Margaret Smith
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increasing sustainability; therefore it is crucial that a more
efficient battery be made.
In the same way, perhaps the most common application
for batteries is the cell phone. The first cellphone, the Nokia
DynaTAC, hit the market in 1984 [3]. With the battery
powering this massive two-and-a-half pound device, users
only had about thirty minutes of talking time before they had
to recharge their phone with a process that took ten hours
[6]. Fortunately, by 1991, scientists were able to shrink the
size of batteries so that they only weighed about 100 to 200
grams [7]. Cell phone companies took advantage of this
smaller sized battery and began trying to create the newest,
sleekest phone. Thus came the Motorola Razr in 2004,
shocking customers with its slim look. This prompted the
2003 BlackBerry phone, which boasted e-mail and Internet
use. Finally, in 2007, the Apple iPhone was created--a
device that managed to hold music, Internet, and phone all in
one. Yet, despite the rapid advancements made in the cell
phone industry that first decade of the 21st century, none of
the advancements included changes to the 1990 battery [3].
This accentuates how batteries have fallen behind the
average growth of today's technology, which is why a
resolution to this problem is important. Making
improvements to the battery, and thus the cell phone, has the
power to increase sustainability by means of improving
quality of life.
Building a more efficient battery would positively affect
the cell phone industry by allowing cell phones to hold a
longer charge. This longer charge capacity means the
consumer has to charge their device less frequently. With the
increasing stress consumers put on cell phones to complete
work tasks, this can greatly benefit the consumers overall
standard of living, emphasizing the significance of
improving the current battery.
CURRENT RECHARGEABLE LITHIUM-
ION BATTERIES
How a Rechargeable Battery Works
A battery uses thermodynamically favored oxidation-
reduction (redox) reactions to produce electricity via the
flow of electrons. The three main components of a battery
are the anode, the cathode and the electrolyte. At the anode
(negative terminal), oxidation takes place, which results in
the production of electrons. The anode is typically made of
graphite or silicon. The electrons produced flow towards the
cathode (positive terminal), where they are accepted through
a reduction reaction. The cathode is generally composed of
lithium manganese oxide or lithium nickel manganese cobalt
oxide. An electrolyte is needed to complete the circuit and
facilitate the continual transfer of electrons. Lithium-ions are
commonly contained within the electrolyte in the form of a
mixture of lithium salts (lithium hexafluorophosphate,
lithium tetrafluoroborate and/or lithium perchlorate) in an
organic solvent (ethylene carbonate, dimethyl carbonate, or
diethyl carbonate). This leads to these batteries being
referred to as lithium-ion batteries [8]. Several additives are
added to the graphite anode, which in turn form a metal
alloy. This is needed in order to accelerate the transfer of
electrons. These additives include vinylene carbonate,
aluminum foil, and dimethylmethanphonat [9].
The electrical energy needed to power devices is
produced via the flow of electrons from the anode to the
cathode. In other words, the reactants for these reactions
have been used up. These chemical reactions will continue
to occur until the same chemical potential is reached in the
anode and cathode. In order to recharge a battery, electrical
energy from an outside source is needed to force the
chemical reaction to reverse, causing the decay of the
products and reformation of the reactants. This forces
electrons to flow backwards, from the cathode to the anode,
which is not thermodynamically favored, hence, the addition
of outside energy. The recharging process is known as
electrolysis [10].
Problems with Current Batteries
There are several shortcomings with current rechargeable
batteries. Electrolysis leads to a decreased charge capacity,
resulting in long charge times and decreased battery life.
These reactions occur slowly because the lithium-ions inside
the battery need to travel a long distance to reach the anode
from the cathode. For instance, the Apple iPhone requires
approximately two hours to fully charge. In a new iPhone, a
full charge leads to a battery life of approximately eight to
ten hours. However, a typical cell phone battery will lose
about twenty percent of its capacity after about four hundred
charge cycles [11]. That is, after thirteen months, the battery
life of an iPhone decreases to approximately six and a half to
seven hours. The decrease in battery life is caused by the
repeated expansion and contraction of graphite during the
charging process. This causes the graphite anode to become
stressed, causing it to decay which leads to eventual battery
failure. In older devices, the battery life decreases so
drastically that it requires the same amount of time to charge
as there are hours of usage. The forced backflow of electrons
from the cathode to the anode during the charging cycle
causes this issue. This leads to the decay of the cathode, as
the electrons are strongly held to the cathode and a
significant amount of energy is necessary to pull the
electrons away. The degradation of the cathode is what
causes devices to gradually lose charging capacity over time.
Overall, the lifespan of lithium-ion batteries is about five
hundred charge cycles, which is equivalent to about two to
three years of typical use [12].
The major issues plaguing the expansion of electric cars
are that their batteries are expensive, take a long time to
charge, and pose the risk of explosion. For example, in the
Tesla Model S, the highest rated electric car, the battery
gives a range of about three hundred miles before a recharge

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Margaret Smith
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is required. These batteries take over nine hours to fully
recharge when attached to a two hundred forty volt outlet
[13]. The cost to replace the battery in a Tesla vehicle is
approximately twelve thousand dollars. Also, lithium-ion
batteries can overheat to the point of fire or even explosion.
Recently, several Tesla cars have caught on fire
spontaneously, leading to safety concerns for consumers
[14]. These issues will be discussed further in the “Risks and
Ethical Issues” section.
POSSIBLE SOLUTONS
Replacing the anodes within batteries is the most
promising solution to improving rechargeable batteries. A
new anode could lead to batteries that have a larger charging
capacity, shorter charge times and longer overall lifespan.
These new batteries could improve the status of current cell
phones and facilitate an increase in the demand for electric
cars. This would greatly benefit consumer’s quality of life,
as they would have to worry less about the need to
constantly charge their devices. Also, the increase of electric
cars could greatly benefit the environment, as there would be
a decrease in the amount of harmful emissions from
gasoline-powered vehicles.
Lithium Anodes
Lithium metal is an ideal anode material to address the
issue of cathode decay and the loss of charge capacity for
rechargeable batteries because of its high electropositivity
and low density. Electropositivity is a measure of an
element's ability to donate electrons and therefore form
positive ions. This is an ideal characteristic for an anode, as
it is the location in which electrons are produced and passed
to the cathode. Also, the low density would allow for a
lighter and more compact battery. Yi Cui, a Stanford
professor of materials science and engineering, states, “Of
all the materials that one might use in an anode, lithium has
the greatest potential. It is very lightweight and it has the
highest energy density. You get more power per volume and
weight, leading to lighter, smaller batteries with more
power” [9].
With lithium anodes, scientists have found that battery
capacity increases by about four times today’s battery
capacity. This translates to a cell phone battery that could
last over thirty hours with moderate to heavy usage. Also,
lithium anode batteries maintain 99% efficiency after one
hundred fifty charge cycles. This leads to a battery life that
will be more consistent for the device, which is a significant
improvement over current rechargeable batteries. Lithium
anode batteries are predicted to have a lifespan of six
thousand charge cycles, which is substantially longer than
current batteries, whose lifespan is about five hundred
charge cycles [14].
Titanium Dioxide Nanotube Anodes
Associate Professor Xiaodong Chen from Nanytang
Technological University in Singapore is leading research
projects into a battery with an anode made from titanium
oxide gel. Research indicates that batteries with these anodes
can charge to seventy percent capacity in two minutes or
five minutes for a full charge, which is a drastic
improvement over current lithium-ion batteries. These
batteries are able to charge faster because the materials for
the anode are shaped into intercalating, neatly dispersed,
nanotubes. The nanotubes themselves are one-thousandth the
size of a strand of hair and have a large surface area of one
hundred thirty square meters per gram. This speeds up
chemical reactions that drive discharging and charging, as
there is an increase in the amount of space for them to occur
while the distance needed to transfer charge is minimized
[15]. Professor Rachid Yazami from Nanytang
Technological University and co-inventor of the lithium-
graphite anode that is used in batteries today stated, “There
is still room for improvement and one such key area is the
power density – how much power can be stored in a certain
amount of space – which directly relates to the fast charge
ability. Ideally, the charge time for batteries in electric
vehicles should be less than fifteen minutes, which Professor
Chen’s nanostructured anode has proven to do” [16].
Figure 1 [16]
This figure shows the relatively easy process by which
titanium dioxide nanotubes are produced.
Titanium dioxide anodes are easily manufactured as
shown above in the bottom row of figure 1. The gels are
produced when titanium dioxide is stirred in with sodium
hydroxide under a constant temperature. A previous attempt
to create a titanium dioxide anode is depicted in the first row
of figure 1. The second method is significantly more
effective as the gels are longer, providing more surface area
for redox reactions. Also, this method is cheaper and faster
than the one depicted in the first row. The manufacturing of
titanium dioxide gel anode batteries is a relatively simple

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Margaret Smith
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and fast process, making it a strong candidate for future
batteries.
RISKS AND ETHICAL ISSUES
Though using different anodes provides ample
improvement to batteries, there are risks and ethical issues to
consider. In order to make a new battery that is sustainable
for future generations, playing to positive environmental
influence, affordability for the average consumer, and
benefits to the overall standard of living, these issues must
be addressed with great severity.
Lithium Anodes
The most prevalent issue in using lithium is the severity
of the lithium anode's expansion when it is being charged,
causing cracking in the battery casing. Essentially, when a
battery is being recharged, the negatively charged anode
attracts the electrolyte's positively charged lithium-ions. The
increase in positive charges leads to expansion in the anode,
no matter what it is made of [9].
In the current lithium-ion battery, this anode is made of
silicon or graphite. These elements have structures that allow
for intercalation of the lithium-ions. Intercalation means that
the lithium-ions are neatly dispersed into the layered
graphite or silicon arrangement as depicted in part (a) of
Figure 2. Therefore, when the graphite or silicon anode
expands, the ions are essentially frozen in place, which
presents little hazard [17].
(Figure 2) [17]
This figure depicts the intercalation of lithium-ions in a
graphite anode (a), and in a lithium anode (b). It also
shows the resulting dendrite formation on a lithium
anode (c).
Unfortunately, a lithium anode does not have the layered
structure of graphite and silicon, which means that the
lithium-ions being received through the electrolyte cannot be
intercalated. Rather, the lithium-ions rest on the surface of
the anode instead, as shown in part (b) of Figure 2. The only
protection the lithium-ions have as they rest on the surface is
the SEI layer. The SEI layer is the Solid Electrolyte
Interphase; it moderates the charge rate, stabilizes the
current, and ultimately acts as protection for the expanding
anode [18]. However, the lithium in a lithium anode expands
irregularly. It expands in such a way that the SEI layer splits
and cracks “like paint on the exterior of a balloon that is
being inflated” [14]. These new cracks provide perfect
means for lithium-ions resting on the anode to escape from
the once protective layer. When the ions escape, they do so
in the form of hair-like structures as illustrated in part (c) of
Figure 2. These structures are called dendrites. Each time
that a lithium anode battery is recharged, these dendrites
increase in size. After just a few charge cycles, they become
so large that they can crack the battery casing, which can
potentially harm the consumer [9]. In contrast, the increasing
growth also has the potential to consume the electrolyte
entirely and connect the anode to the cathode. This
connection results in the battery short-circuiting itself, which
can drastically lower the battery's life span [19].
Another issue in using lithium anodes for batteries is
what is known as “thermal runaway”. Thermal runaway is
the process by which an uncontrollable chain reaction of
overheating begins, destroying the battery and potentially
causing dangerous conditions such as explosions or fire.
Being an alkali metal, lithium has an extremely high
electrochemical potential. This means it produces a lot of
energy, and is released in the form of heat. When a battery
goes through its charging and recharging phase, especially a
battery with dendrite formations, the exchange of lithium-
ions generates heat at such a high temperature that the whole
system starts to overheat. This overheating destroys the cell
and breaks it open, sending heat into the neighboring cell.
This cell will then experience the same deterioration [20].
Essentially, one overheated, damaged cell generates a chain
reaction of overheating, which can result in a fire, or even an
explosion. This problem already occurs in some cases of the
current lithium-ion battery. However, the increased
expansion and extreme dendrite growth in lithium anodes
makes them more susceptible to these dangers [21].
Similarly, lithium offers a high degree of threat as it is a
severe fire hazard and is corrosive to the skin. It is also toxic
to the lungs, nervous system and mucous membranes [22].
With the number of electric cars, cell phones, and other
devices containing rechargeable batteries in the United
States, such problems must be fixed before the proposal for
lithium anodes is applied.
Titanium Dioxide
The Material Safety Data Sheet discusses the health and
safety hazards of chemicals commonly used in laboratories.
Based on this data, titanium dioxide is the safest material
discussed as an anode material. It lacks any fire and
reactivity risks, but can offer mild irritation upon contact
with skin or eyes. Titanium dioxide is an abundant, cheap,
and safe material commonly found in soil. It is frequently
used in food as a preservative and in sunscreen in order to

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Margaret Smith
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absorb ultraviolet waves [15]. The safety of these chemicals
is crucial for battery manufacturers to ensure there are no
potential hazards to consumers.
POSSIBLE SOLUTIONS TO LITHIUM
ANODE RISKS
Researchers believe that creating a protective layer for
the lithium anodes would solve the issues of dendrite
formation and overheating. Stanford professor Yi Cui
explains, “The ideal protective layer for a lithium metal
anode needs to be chemically stable to protect against the
chemical reactions with the electrolyte and mechanically
strong to withstand the expansion of the lithium during
charge.” With that in mind, Cui created carbon nanospheres,
a honeycomb-like microscopic layer, which creates a
flexible non-reactive film to prevent the expansion of the
lithium [14].
Figure 3 [9]
This figure shows how carbon nanospheres protect
lithium anode from expansion
Nanospheres are made from interconnected amorphous
carbon domes. This is an ideal solution because amorphous
carbon is chemically stable, strong and flexible. This allows
the protective layer to move freely up and down as the
lithium expands and contracts during the battery’s charge-
discharge cycle. As shown in Figure 3, the carbon
nanospheres offer a higher level of protection than the SEI
layer alone. Therefore, dendrite formation is minimized and
the battery can continue to function at a high level. Another
advantage is that these nanospheres do not add any bulk to
the battery, as they are just twenty nanometers thick which is
about 1/5000th
the width of a human hair [9]. This
technology solves a major roadblock with lithium anode
batteries and will allow them to be used commercially.
COMPARATIVE ANALYSIS
Cost of Materials
The cost and availability of anode materials is an
important factor in the development of new batteries.
Lithium anodes are by far the most expensive, as pure
lithium costs $1,818.40 per kilogram. Titanium dioxide costs
$180.70 per kilogram and graphite costs $99 per kilogram
[23]. Based on this data alone, the current lithium-ion
batteries are the cheapest to manufacture.
Unlike graphite and lithium, titanium oxide does not
expand or contract during the charging cycle. This allows
the battery to last up to twenty years or ten thousand charge
cycles. This is a sharp increase from current lithium-ion
batteries that have a lifespan of about five hundred charges.
Therefore, when the lifespan of the battery is considered,
titanium dioxide batteries are the most cost efficient [15].
When considering electricity costs, titanium dioxide and
lithium anode batteries are more cost effective than current
batteries. Titanium dioxide batteries can charge to seventy
percent in two minutes, meaning they will require less
electricity to charge. Lithium anode batteries last about thirty
hours between charges meaning they will need to be charged
less frequently than other batteries, saving electricity.
Current batteries with graphite anodes are the least cost
effective in this category, as they require at least two hours
to fully charge and have a battery life of only about eight
hours [12].
In current lithium-ion batteries and lithium anode
batteries, additives are necessary to bind the electrodes to the
anode, which increases the cost to manufacture those
batteries. Titanium dioxide batteries lack these additives,
which makes them more cost efficient. Also, in terms of
availability, pure lithium is by far the most difficult to obtain
as it is highly reactive, making it difficult to isolate.
Titanium dioxide is the easiest to obtain, as it is abundantly
found in soil and much less reactive than lithium. Based on
cost and availability, titanium dioxide batteries are the most
economical choice as an anode [15].
Effect on Electric Cars
Currently, electric cars cost significantly more than cars
powered by gasoline. A Tesla Model S car can cost between
$63,570 and $104,500 [13]. A cheaper alternative option to
the Tesla is the Nissan Leaf, which only costs between
$21,510 and $27,620. However, it can only drive about
eighty miles before needing to be recharged, which can take
at least eight hours. Again, this is an inefficient process and
requires a large amount of electricity. With lithium anode
batteries, Yi Cui theorizes that the price of electric vehicles
will drop to $25,000 with a range of three hundred miles
[14].
Titanium dioxide anode batteries would also decrease the
cost to operate electric cars as they can lead to vehicles that
require less time and electricity to recharge than current
lithium-ion batteries. With these batteries, the range of
electric cars would increase dramatically as the charge times
for the batteries would take about the same amount of time it
takes to fill a normal car with gasoline. Also, the life cycle
of titanium dioxide batteries is significantly longer than
current batteries, saving drivers of electric vehicles
thousands of dollars in battery replacements. The longer life

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Margaret Smith
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cycle also benefits the environment, as there would be a
drastic decrease in the amount of waste generated by
disposing of the toxic lithium-ion batteries [15].
THE FUTURE OF BATTERIES
The hunger for knowledge in today's society has lead to
an immense growth in technology advancements. Scientists
are constantly discovering more efficient ways to create new
products and improve existing ones. Yet, even with all these
innovations, batteries have not been improved since the
1990’s. Clearly, current batteries are not on par with current
technological advances, which is why research is being done
to fix this problem.
Possible solutions to refining the current lithium-ion
battery include replacing the current anode with either
lithium or titanium dioxide. Both these substances offer
significant improvements to the current batteries. Lithium
anode batteries offer increased battery life and an overall
longer lifespan than graphite batteries. Also, they take less
time to charge. Titanium dioxide batteries offer an
exceptionally fast charge time, a twenty-year lifespan, and
unmatched economic benefits.
Improving the battery is a feat in itself, but the true
rewards in doing so stem from the applications of the new
battery. Two products being analyzed for improvements
such as those previously stated are electric cars and cellular
devices. Creating a more efficient battery for use in electric
cars could alter the market for cars drastically. One of the
main issues consumers face with electric cars is the
expensive cost. Though the proposed materials for the
improved battery would at first make the electric car more
expensive, the powerful battery means that the car's lifespan
will increase dramatically, which ultimately saves
consumers money in the long run. Similarly, drivers hesitate
to invest in electric cars because of the limited distance they
can be driven before needing to be recharged. With a more
efficient battery, electric cars will be capable of traveling
further distances, making them more appealing to
consumers. The most important aspect of electric cars is that
with the increase in sales, comes the decrease of gas-
powered cars, resulting in a lower carbon emission. This all
sets a platform of sustainability for future generations,
making electric cars cheaper, easier to use, and better for the
environment.
As far as applications for the cell phone, improving the
battery would have similar effects as the electric car. Having
a more efficient battery for use in cell phones would aid in
the already increasing popularity of mobile devices. The
proposed solutions would allow cell phone companies to
create even newer designs and products to add to the
technological productivity of the world today. In the same
way, using a different anode, like titanium dioxide, provides
a safer alternative to the current lithium-ion battery—for the
consumer and the environment. Titanium dioxide is
commonly found in soil, which means it is a natural and
harmless material—much safer than the explosive lithium-
ion battery. Also, a more efficient battery would allow users
to keep their mobile device for a longer period of time. This
increased lifespan means that devices will be disposed of
less often, which will have positive effects on the
environment and promote sustainability.
The importance of batteries is continuing to increase
substantially as the world becomes increasingly dependent
on electronics for everyday tasks. Electric cars and cellular
devices are two popular applications of batteries that serve
great significance in the field of electronics, however the
scope of batteries goes beyond just electric cars and cell
phones. Developing a better battery will enhance the
functionality of items used everyday—from detecting fire in
a home, to reviving a patient’s heart. On a larger scale, a
better battery can improve the equipment engineers use on a
daily basis—leading to scientific discoveries not even
thought possible with the current lithium-ion batteries.
Creating a more efficient battery with a new anode builds a
sustainable future; it addresses environmental concerns,
makes products like the electric car and cell phone more
affordable to consumers, and increases the standard of
living. In order to progress in the fields of science and
engineering, this is the most crucial aspect, deeming it a
necessity to improve the current battery.
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ACKNOWLEDGEMENTS
We would like to thank our writing instructor, Julianne
McAdoo, for introducing the assignment to us in engineering
analysis, and Amanda Brant for her feedback and comments
on the previous assignments. We would also like to thank
our co-chair, Giselle Baillargeon, for providing feedback on
the previous assignments and assisting us in the writing
process. We would also like to thank our chair Stephen
Bishop for his comments and suggestions on our essay.
Finally, we would to thank our Resident Assistant, Violet
Lawson, for proofreading this essay.

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