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Battery Technology and Markets, Spring 2010
26 January 2010
Lecture 1: Introduction to Electrochemistry
1. Definition of battery
2. Energy storage device: voltage and capacity
3. Description of electrochemical cell and standard cell potential
5. Calculating capacity- Faraday’s Law
Approach to this part of the course
In the first part of this course, about four weeks, we’ll be studying and learning about
basic concepts involved in electrochemistry. We recognize that people are coming from very
different backgrounds in this course, and so what is already familiar to some students may be
very new to others. The idea is that in this part of the course, you’ll become familiar with the
basic physics involved in batteries. If you ever are having problems with the material because we
are assuming background knowledge that you don’t have, come talk to us. If you find that you
are interested in this subject and want to learn in much more detail, we hope that this class will
function as a good primer for Professor Newman’s class in the fall.
1. Definition of batteries
The first thing we’re going to do is to define a battery as an electrochemical storage
device- something that stores electricity in chemical bonds. This is a functional definition- you
can have batteries made of many different systems because like the battery is defined in terms of
what it does and not the materials that make it up. This means you encounter many different
material systems (Lead oxide / Lead sulfate, Graphite / Lithium Iron Phosphate, Metal hydride /
Nickel hydroxide). A similar example is a solar cell. A solar cell captures sunlight and turns it
into electricity, and can be made any of a number of materials- silicon or organics, GaAs.
Main idea of electrochemical devices is that chemical energy is converted directly to electrical
energy. Chemical energy can be converted to other forms as well; for example, in combustion
processes, the chemical energy of combustion is converted to mechanical energy by an engine.
Or, in nuclear power plants, the chemical energy of nuclear fission is converted to heat and then
to electricity. Electrochemical devices are unique in that they convert chemical energy directly
to electrical energy. Because electrochemical processes do not involve the transfer of heat,
Carnot limitations are avoided and processes can be very efficient. For example, the round-trip
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energy efficiency (for example, the amount of energy you get out of battery compared to the
amount of energy used to charge it) for a battery is typically greater than 85%.
2. The energy storage device- some basic definitions
Batteries are energy storage devices. What physical properties do we care about for energy
storage? Energy, power, mass, and volume. Energy is a fundamental quantity and has units of
Joules. Power is energy/time, and has units of Watts, which is Joules / second 1 Wh = 3600 J.
Mass and volume usually, but not always, go together (think: automotive versus microdevice
applications. Are mass and volume equally important?). We use specific energy for energy per
unit mass and energy density for energy per unit volume. We can talk about power density and
specific power as well. These four properties are not specific to batteries, but rather general for
all energy storage systems: liquid fuels, thermal, etc.
Let’s do an example of how to calculate the energy that is contained in a consumer battery.
Crack open the cell phone you have in your pocket – what are the two numbers that are given on
the battery? Voltage and capacity. These properties are specific to electrochemical energy
storage systems (i.e. batteries).
Voltage is the electric potential energy, and has units of Volts. A volt is equivalent to J/C.
Capacity is a measure of an amount of electric charge, and has units of Coulombs. In battery
literature, we often use a different unit of Amp-hours instead of Coulombs. 1 Ah 1 C/s*3600 s/hr
= 3600C. Despite the similar-sounding name, capacity is NOT the same thing as capacitance.
Fuel cells and batteries differ greatly in that capacity is specified for a battery but not for a fuel
cell. Why is that?
Quick example: if you are given the voltage and capacity of a battery, how would you calculate
the energy of the battery? Say you have a battery with 3.7 V and 1000 mAh.
3.7 J/C * 3600 C = 13320 J = 13.3 kJ = 3.7 Wh
How much does your battery weigh and cost? For comparison, the combustion of a gallon of
gasoline releases 35-40 kWh; you would need around 10,000 of those batteries to match the
energy in a gallon of gasoline.
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What is the power of your battery? From basic circuits: P = IV. Why isn’t the current written on
the battery? It’s complicated, but the short answer is that I = V/R, and neither of those is
constant- they depend on rate, temperature, history, and other factors.
3. Description of the electrochemical cell, with examples
So we’ve just seen the properties we care about in our battery- power and energy, which are
determined by voltage and capacity. How are those two numbers determined for any given
system? The basic framework for any battery is the electrochemical cell. Every electrochemical
cell is made up of the following components: Anode, cathode, electrolyte, separator, external
circuit. Typically a cell also includes a current collector.
[go to Daniell cell handout, drawing]
This is an image of the Daniell cell. The Daniell cell was invented in the 1830s by the British
chemist Daniell, and had some commercial success in telegraph systems. An electrochemical cell
is a set of reactions, each involving an electron, that are separated by an electronically insulating
layer. This is really important- you cannot measure a voltage without having two reactions
involving electrons. So if you are ever doing any problem involving electrochemistry, your first
step in understanding what is going on is almost always to define the reactions. Current flows in
the form of electrons through an external circuit, and in the form of ions through the separator.
Therefore, the current must change phases as it moves through the electrodes. Current is
movement of charge, not electrons, like we’re used to thinking of- mobile ions or protons can be
charge carriers instead. For every electron that goes through the external circuit, we need to
balance with ionic charge that goes through the battery. This will mean understanding:
thermodynamics, for the driving force behind the reactions; transport, for the movement of ions
inside the battery; and kinetics, for the rates of reactions that occur at the electrodes. The
simultaneous presence of all these phenomena is what makes batteries so complicated, and, for
some people, so interesting.
Here are some important definitions:
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Anode: an electrode at which oxidation occurs; electrons are produced. We also use the phrase
“anodic reaction.”
Cathode: an electrode at which reduction occurs; electrons are consumed. We also use the
phrase “cathodic reaction.”
Electrolyte: a phase that has mobile ions to carry current. An electrolyte typically contains a
solvent (such as water) in addition to a salt (such as KOH). An exception to the solvent/salt
system is something like Nafion.
Separator: a region that separates the two electrodes, and which is electronically insulating. A
separator may also help provide mechanical rigidity to a cell.
Positive electrode: Electrode that is at a more positive electric potential. Electrons move
spontaneously towards more positive potentials.
Negative electrode: Electrode that is at a more negative electric potential.
Galvanic cell is one in which energy is spontaneously produced by the reactions. (Discharging a
battery)
Electrolytic cell is one in which energy is consumed to drive the reactions. (Charging a battery)
We also have an external circuit, and a current collector. Sometimes the current collectors are
separate from the electrode, but here they are the electrodes.
Practice question: When switch from charging to discharging a battery, what changes? The
location of the anode and cathode, or the location of the positive and negative electrodes? Why
don’t electrons always flow towards the positive electrode?
Little bit of nomenclature about batteries and cells- battery is technically made up of several
electrochemical cells. Applicable- many batteries you buy are more than one cell wired in either
series or parallel (e.g. car, laptop, 9V). For our purposes, we talk about batteries as the
application (and thus business, policy, manufacturing), cells when referring to the universal
physics. If you go into other areas of electrochemistry, you’ll find electrochemical cells used for
all kinds of things besides energy storage. Trivia fact- inventor of nomenclature was Ben
Franklin, in analogy to a battery of cannons.
What is the voltage of the cell? It will depend on the identity of the reactions. In the cell above
we have the reactions
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Zn ↔ Zn 2+ + 2e −
Cu 2+ + 2e − ↔ Cu
Depending on which direction the reaction goes, it can be either anodic or cathodic. Note that if
we add these reactions together we get
Zn + CuSO 4 ↔ Cu + ZnSO 4
This shows that the overall reaction is chemical, and that electrons serve as an intermediary in
the process. Every reaction has a potential associated with it, which is a measure of the energy
of the change that occurs when the reaction proceeds. We’ll discuss more about this next lecture.
A voltage really measures an energy difference; the reactions in tables of standard reduction
potentials are typically given relative to a standard hydrogen electrode (SHE), which is an acidic
solution at unit concentration at 25°C and 1 atm.
The potential of a cell is defined as
E 0cell = E 0cathode − E 0anode
The symbol 0 refers to the standard conditions at which these measurements are made; these are
25°C and 1 atm. We can look up the potential of this reaction in a table that gives standard
potentials.
E 0cell = 0.34 − (−0.76) = 1.10V
We can get these values from Appendix B of Linden. Note that the values in this table are
equilibrium potentials. Roughly speaking, an equilibrium potential is the potential at which the
rate of the forward and reverse reactions are equal. As written in Appendix B of Linden, if the
actual potential is higher than the equilibrium potential, the reverse reaction will be favored,
while if the actual potential is lower than the equilibrium potential, the forward reaction will be
favored.
Knowing how to look up the standard electrode potential is an important skill. Let’s do another
example here. What are the reactions in a lithium (not lithium-ion) battery?
Li ↔ Li + + e −
LiCoO 2 + 0.5e − ↔ Li 0.5 CoO 2 + 0.5Li +
E 0cell = 0.7 − (−3.01) = 3.71V
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4. Calculating the capacity of a battery
So far we’ve covered half of what you’ll find on your cell phone battery: the voltage. What
about the other part, the capacity of the battery? In particular, how do we relate the size of the
batteries and the chemicals that are inside it with the amount of charge that it can store?
One Ah is defined as one amp that is passed for one hour. An Ah has the same units as the
Coulomb, the fundamental unit of electrical charge. One Coulomb is the charge of 6.24 x 1018
electrons.
1 Ah = 1 Amp*hour = 1 C/s *3600s = 3600C
Note that the amount of electrical charged that is passed can be directly related to the change in
the amount of chemicals in the system by the use of Faraday’s law.
Ni =
si It
nF
Here are definitions:
Ni = Number of moles of species i
si = stoichiometric coefficient of species i (see convention below)
I = current
t = time
n = number of electrons involved in the reaction
F = Faraday’s constant, with value 96487 C/mole. Equal to Avogadro’s number * charge of
electron.
The convention that we use to define the value of the stoichiometric coefficients is
∑s M
i
zi
i
↔ ne −
i
Here, Mi refers to the identity of species i, and zi is the charge number of that species. Example:
sZn = 1, zZn = 0, sZn2+ = -1, zZn2+ = 2, n = 2
Zn ↔ Zn 2+ + 2e −
Another example is water splitting.
O 2 + 4H + + 4e − ↔ 2H 2 O
sO2 = -1, zO2 = 0, sH+ = -4, zH+ = 1, SH2O = 2, zH2O= 0, n = 4
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Note that Faraday’s law is nothing more than a relation between the number of electrons and the
number of moles in an electrochemical reaction: if a certain number of electrons have been
passed, that means a certain number of moles have passed.
Let’s do an example with our Daniell cell. Assume we have 1 gm each of zinc. What is the
capacity of the zinc electrode?
1 gm Zn = 0.015 mol Zn
It =
nFN Zn
=
s Zn
C
⋅ 0.015mol
mol
= 0.82 Ah
C
3600
Ah
2 ⋅ 96487
What is the specific capacity of the zinc electrode? 0.82 Ah/ 1gm = 820 mAh/gm . If we did
something impossible that halved the molecular of zinc so that only 0.5 gm were needed for 0.82
Ah, what would happen to the specific capacity of the entire battery? What does that imply for
research on high energy-density battery materials?
You should be able to use this procedure to calculate all the capacity values in Table 1.1 in
Linden.
So, to summarize: we talked about the definition of a battery, that it is defined not by what it is
made of but by what it does, store electricity via chemical reactions. Two key properties for
energy storage are voltage and capacity. To figure out how those are determined for a battery, we
introduced the electrochemical cell and some terms for it- anode, cathode, etc. Voltage- comes
from what the reactions are (which chemicals), more next lecture. Capacity- comes from reaction
rate, and the formula used for this is Faraday’s Law.