Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

how batteries work



At 02:01 PM 7/30/00 -0400, Tom McCarthy wrote:
When I refer to the "produced" electron, I meant the free charge that is
created (there I go again!) in the chemical reaction.

Yes, alas, there you go again.

Clearly, the chemical constituents are neutral to begin with and that
there is a monstrously large positive charge awaiting the electrons return.

That's really not a good way to look at it.

The chemical reaction that produced this situation, created a potential
difference (i.e.., the products of the reaction are at a lower potential
than the reactants).

There are two different potentials in the problem: the electrical
potential and the electrochemical potential. You're not being sufficiently
careful about which is which.

If each battery gives its free electron a certain voltage, then, if this
electron enters another battery, it is given another kick as it
participates in the next batteries chemical reaction, and so on. My
question then is why does a voltmeter measure the extreme voltage, as
though all the electrons traveled through all three batteries, as opposed
to an average?

Basically you're asking for an explanation of the internal workings of a
battery. I can explain that. A good job requires more time than I can
afford right now. Here's a rough outline....

Suppose the circuit in question consists of nickel/alkaline/iron batteries
connected by aluminum wires. Throw away the alkali and throw away the
wires for now. Now you are left with an array of chunks of disconnected
metal: iron, nickel, iron, nickel, iron, nickel. Let them sit there and
come to equilibrium. Fact: at equilibrium, all the iron chunks will be at
a different voltage from the nickel chunks. This is a real
honest-to-goodness voltage difference. It will cause electrical fields in
the gaps between the chunks, which you can observe using Kelvin-bridge
techniques or otherwise.

So here is a diagram of the electrical potential in equilibrium

.............................................................. (zero)


_____ _____ _____
Fe ______ Fe ______ Fe ______
Ni Ni Ni


(Imagine the metal chunks are arranged in a big circle, so we have periodic
boundary conditions on the diagram.)


This is real physics. It's not hard to understand. The electrons want to
be near the metal nuclei. Even if the metal chunk is slightly negatively
charged it will attract electrons. (Indeed even a single neutral hydrogen
atom will attract electrons -- the H- ion in vacuum has lower energy than a
hydrogen atom and electron separately.) You need to worry about where to
put the electrons in the band structure of the metal. The attractiveness
of the metal is a tradeoff between the potential energy (attraction to the
nuclei) and the kinetic energy (band structure). Different metals have
different band structure, hence different attractiveness. This is
summarized by the term Work Function; different metals have different work
functions. You can even make a connection between the work function (a
purely electrical property) and the elastic properties of the metal: when
you squeeze the chunk of metal you squeeze the electron wavefunctions and
that takes energy.

Work function for aluminum: 4.2 eV
Work function for iron: 4.63 eV
Work function for nickel: 5.2 eV

Of course if you put too many electrons on the chunk of metal, they will
repel each other and put an end to the game; this is a capacitive
potential-energy effect -- in addition to the kinetic-energy effects
reflected in the band structure. The capacitance depends on the size and
shape and surroundings of the metal -- unlike the work function which is
more-or-less an intrinsic function of the material.

Now you may have thought that at equilibrium, everything would be
field-free and electrically neutral -- BUT THIS IS NOT THE CASE. Nature
doesn't work that way. In equilibrium, there will be fields between the
metal chunks. All the nickel chunks will be negatively charged, having
stolen some electrons from the iron.

Now suppose we hook up certain pairs using aluminum wire in the usual
clever way. The electrical potential diagram will look like this:

............................................................ (zero)

____ ____ ____
(A) _____| Al | (B) _____| Al | (C) ____| Al | (A')
Fe |_____ Fe |_____ Fe |_____
Ni Ni Ni

The details of the aluminum are not interesting; the only function is to
ensure that the Fe and the Ni remain in equilibrium.

So far there is nothing special about this. Suppose an electron flows
along the path from point (A) via points (B) and (C) to point (A') [which
is the same as point (A), because of things are arranged in a circle]. Its
energy goes up and goes down, but it winds up the same.

Now let's get tricky. Let's put some alkali goop in the gaps. This
substance has the property that it has lots of ion-pairs in it. When we
put an ion-pair in an electrical field, such as in the Ni-Fe gap, the + ion
will move one way and the - ion will move the other way. This process will
continue until the electrical field in the gap is driven to
zero. (Remember a pair of separated charges have a field-line between
them; the field lines created by the moving ions tend to cancel the
equilibrium field created by the metal chunks.)

The result is shown in the following diagram:

............................................................ (zero)
___
____ x |
(A) _____| Al | (B) ____ (C) x |_____ (A')
Fe |_____ _____| Al | _x Ni
Ni Fe |_____ ____|
Ni Fe


It is highly ironic that in the guts of the battery where you the chemical
action is taking place, there is a relatively field-free region. The
chemistry happens one place, and the change in voltage happens in another
place!

So when an electron flows from point (A) to point (A') it most assuredly
does gain energy. Each cell is like a step on a staircase. You wind up
with a voltage between the right (Fe) terminal of cell (C) and the left
(Ni) terminal of cell (A)/(A') at the location shown by the "x"
symbols. This voltage can easily be measured with a voltmeter, and can
power lamps and motors et cetera.

Also note that as each electron flows through a cell, one molecule of
chemical reaction takes place in the gap where the alkali
lives. Otherwise, this gap would just charge up like a capacitor and the
battery would be orders of magnitude less effective at maintaining its
rated voltage. The voltage stays the same (more or less) until you run out
of chemicals. (This is how the unit of charge was initially defined: the
amount of chemical precipitated in such a cell.)

Here's the essential piece of magic: running a wire between a piece of Fe
and a piece of Ni is very different from putting some reactive ionic goop
between them. If you read the diagram from left to right you get
Fe-Al-Ni-goop-Fe-Al-Ni-goop
which is _not_ a palindrome. There is a definite direction to the
structure, and that determines which end of the battery is + and which is -.

NOTE!!! I didn't say anything about charge being "created". It is OK to
create charge _pairs_ by ionizing some previously-neutral chemical, but no
net charge was created, not even temporarily. It is also OK to speak of
charge flowing _through_ the cells. But charge does not flow "out" of the
cells like water pouring out of a bucket. It just doesn't. If an electron
flows out one terminal, you can be sure that an electron flows in the other
terminal at the very same instant.