00:00:00
the next concept we need to consider in
00:00:02
our electrochemical explorations is that
00:00:04
of electrical potential and
00:00:06
fundamentally what it is so we've seen
00:00:09
potential many times before we've
00:00:11
considered thermodynamic potentials
00:00:12
we've considered chemical potentials and
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in first year we considered the
00:00:16
lennard-jones potential so I'm going to
00:00:19
look at lennard-jones potential because
00:00:20
we had a key definition with it that
00:00:22
definition was the work done to move
00:00:24
molecules from infinity to a point of
00:00:26
interest so when whenever we had our
00:00:28
molecule we start at an infinite
00:00:30
separation and look at how much work we
00:00:32
would need to do to bring it to a
00:00:34
particular position if the potential was
00:00:36
negative that meant that we were getting
00:00:38
energy out of the system and if it was
00:00:40
positive that means we had to put energy
00:00:42
in so if you think about moving a
00:00:44
molecule it will freely fall into this
00:00:46
minimum because that doesn't involve
00:00:48
that releases energy but then we have to
00:00:50
put energy in to drive it up this slope
00:00:52
to squeeze molecules further together
00:00:54
the key definition is that potential is
00:00:57
defined at zero at infinite separation
00:00:59
so we have a negative potential which is
00:01:01
our minimum and we have a positive
00:01:03
potential where we're putting more and
00:01:04
more energy in electric potential has a
00:01:06
very similar definition it looks at the
00:01:09
work required to move a unit positive
00:01:11
charge from infinity to a point of
00:01:13
interest so if we have a positive charge
00:01:16
at infinity and we want to bring it
00:01:18
close to a positive electrode we have to
00:01:20
put energy in that means this electrode
00:01:22
has a positive potential we have to do
00:01:26
work to bring a positive test charge
00:01:28
close to it again it's defined at zero
00:01:30
at infinite separation so everything is
00:01:33
based on that and we can plot our
00:01:35
Coulomb back potential in a very similar
00:01:37
way as we have for the lennard-jones the
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anode has a positive charge so we need
00:01:43
to do work to overcome the repulsion for
00:01:45
a positive charge we need to do work on
00:01:47
that positive charge to bring it close
00:01:48
therefore we have that high potential we
00:01:50
run into a few conceptual issues however
00:01:53
when we start to consider potential
00:01:55
versus electron energies we start to
00:01:58
think things becoming a little bit
00:02:00
confusing because potential is
00:02:01
fundamentally related to a positive
00:02:03
charge
00:02:04
but our electron is negatively charged
00:02:06
therefore if we have a high positive
00:02:08
charge on our electrode we have a high
00:02:10
potential however if we have a high
00:02:13
positive
00:02:14
it has a low electron energy because
00:02:16
it's attracting the electron vice-versa
00:02:18
if our electrode has a high negative
00:02:20
charge it has a low potential because it
00:02:22
there's less work required to bring a
00:02:24
positive charge towards it however a
00:02:26
high negative charge means we have a
00:02:28
high electron energy and we need to do
00:02:30
work to overcome that repulsion one way
00:02:33
to picture this is when an electron is
00:02:34
surrounded by positive charge all those
00:02:36
positive charges have very high
00:02:39
potential but they are serving to lower
00:02:41
the electron energy because they are
00:02:42
stabilizing a potential difference
00:02:44
therefore is the difference in potential
00:02:47
between two areas that's all we're
00:02:50
looking at but you're familiar with the
00:02:51
term potential difference but we need to
00:02:53
understand it rigorously in terms of our
00:02:55
definitions it is simply a statement of
00:02:57
a difference in charge because each
00:02:59
charge carries a potential and each area
00:03:01
will have that different potential any
00:03:03
charge species at all whether it's an
00:03:05
electrode whether it's our ions in
00:03:06
solution they can all cause a potential
00:03:08
difference wherever there's a potential
00:03:10
difference a charge species will migrate
00:03:12
they'll move through that potential
00:03:14
difference to minimize their potential
00:03:15
fundamentally lowering their
00:03:17
electrochemical potential this
00:03:18
electrochemical potential carries a
00:03:20
symbol nu bar it is absolutely related
00:03:24
to the chemical potential that you've
00:03:26
seen before which is why it uses a very
00:03:27
similar symbol considering the fact that
00:03:30
charged particles move to minimize their
00:03:32
electrochemical potential well let's
00:03:35
think about this in terms of the
00:03:36
chemical potential if we have a standard
00:03:39
chemical potential we can simply work
00:03:41
out the electrochemical potential
00:03:42
standard we can simply work out the
00:03:45
standard electrochemical potential by
00:03:47
considering the charge on the iron with
00:03:50
the Faraday constant and the localized
00:03:52
potential Phi so it's relate to this
00:03:55
charge and the potential in that medium
00:03:57
there so using this equation we can
00:03:59
start to visualize what's going on so if
00:04:02
we think that our chemical potential at
00:04:05
any point is equal to the starting
00:04:07
chemical potential or starting standard
00:04:09
chemical potential if we're not under
00:04:10
standard conditions we can simply find
00:04:12
the electrochemical potential by using
00:04:14
our starting chemical potential for a
00:04:16
given situation if you remember from
00:04:18
year 1 that our standard chemical
00:04:20
potential can be found from the sum of
00:04:22
the actual chemical potential and and
00:04:24
the activity of the solution thinking
00:04:26
about these chemical potential
00:04:27
chemical potentials electrochemical
00:04:29
potentials they're all fundamentally
00:04:30
related to free energies so let's think
00:04:33
about what's going on at the interfaces
00:04:35
because the interface is where all the
00:04:37
good stuff happens so understanding that
00:04:39
interface is really important as well so
00:04:41
let's think about energy level diagrams
00:04:43
these are schematic diagrams to show the
00:04:46
energy of the interface by convention
00:04:48
the solid is shown or the electrode is
00:04:50
shown on the left so let's think about
00:04:52
the electron energy in the solid
00:04:55
well the solid electrode has a lot of
00:04:56
electron energy levels all together
00:04:58
existing in something called a band the
00:05:00
highest energy of this band is known as
00:05:02
the Fermi level we don't need to worry
00:05:04
too much about the theory of this at the
00:05:05
moment but the Fermi level is simply the
00:05:07
highest filled level of that band so
00:05:09
that's the area where the electrons are
00:05:10
going to come from the energy level from
00:05:12
which we will liberate electrons at the
00:05:14
electrode if we now look at the electron
00:05:16
energies in solution
00:05:17
these are usually single molecules so
00:05:19
they have discrete energy levels so we
00:05:22
have a lot of different energy levels in
00:05:23
solution but we'll only consider the
00:05:24
frontier energy levels to start with if
00:05:27
we consider an electron presence in this
00:05:29
energy level
00:05:30
remember that electrons will move to try
00:05:32
to minimize that energy so at the moment
00:05:33
we have energies in a higher level in
00:05:35
this fermi level and we have an
00:05:38
available space in solution which means
00:05:41
that the electron can move from the
00:05:43
electrode into solution
00:05:45
so it's minimizing its energy when this
00:05:47
happens we have the solvated species
00:05:50
being spontaneously reduced okay so it's
00:05:52
picking up an electron from the
00:05:54
electrode and therefore being reduced
00:05:56
let's consider a slightly different
00:05:57
situation if the solvated species has a
00:06:00
higher electron energy than the fermi
00:06:02
level the electrons will still move to
00:06:04
minimize energies but this time the
00:06:06
electron will move from the high energy
00:06:09
in solution and it will move to the
00:06:11
electrode which has a fermi level at a
00:06:14
lower energy this means in this case the
00:06:16
solvated species is spontaneously
00:06:18
oxidized it loses its electron to the
00:06:20
electrode in both cases we've
00:06:22
transferred a charge whether we've
00:06:24
transferred the charge due to
00:06:25
spontaneous oxidation or whether we've
00:06:27
transferred a charge due to spontaneous
00:06:29
reduction this spontaneous process
00:06:32
creates a potential difference and
00:06:34
fundamentally causes electron transfer
00:06:36
when we connect the circuit when we
00:06:38
think about electrodes we think about
00:06:40
applying up
00:06:41
difference to them the position of that
00:06:43
fermi-level can be adjusted by applying
00:06:45
a potential to the electrode so however
00:06:48
whatever potential we apply will change
00:06:50
the energies of the electrons in that
00:06:52
electrode if we apply a positive
00:06:54
potential it has the effect of lowering
00:06:56
the Fermi level remember we're
00:06:58
surrounding the electrons by more
00:06:59
positive charge making them more stable
00:07:01
lowering their energy conversely a
00:07:05
negative potential is removing positive
00:07:07
charge it makes the electrons less
00:07:08
stable so it raises that Fermi level so
00:07:11
let's picture what's going on if we
00:07:13
raise the potential we add positive
00:07:15
charge this has this buildup of positive
00:07:18
charge has the effect of lowering the
00:07:19
electron energy in that electrode so the
00:07:21
Fermi level drops what this means is the
00:07:24
Fermi level is now at a lower energy
00:07:26
level than the highest energies of
00:07:28
electrons in solution and that electron
00:07:30
can move and drive spontaneous oxidation
00:07:33
if you think about the opposite case if
00:07:35
we lower the potential we're removing
00:07:36
positive charge from the electrode if we
00:07:39
remove the positive charge the electrons
00:07:40
are destabilized and that raises the
00:07:43
electron energy in the electrode which
00:07:45
raises the Fermi level so in this case
00:07:48
we now have electrons in the electrode
00:07:50
which are now at a higher energy and
00:07:51
they can now move from the electrode
00:07:55
into solution and this drives the
00:07:57
reduction of the solvated species just
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to quickly summarize potential remember
00:08:03
that everything is respect to a positive
00:08:04
test charge so we have this
00:08:07
double-headed arrow going on if we have
00:08:09
a high potential we are adding positive
00:08:11
charge which means we are removing
00:08:14
negative charge fundamentally this
00:08:16
stabilizes electrons and lowers the
00:08:18
electron energy for low potential we've
00:08:20
removed positive charge which
00:08:22
effectively means we've added negative
00:08:24
charge and we've raised the electron
00:08:26
energy so removing positive destabilizes
00:08:28
electrons adding a positive stabilizes
00:08:31
electrons so this causes the movement of
00:08:33
the Fermi level and we can drive our
00:08:35
reduction and oxidation accordingly
00:08:37
let's now look at the energies of the
00:08:39
interface potential can fundamentally
00:08:41
change the electron energy as we've
00:08:43
discussed this creates a potential
00:08:45
difference across the interface but how
00:08:47
is that potential difference distributed
00:08:49
how this charges distribution of X the
00:08:52
kinetics of what's happening at the
00:08:53
electric whether we're looking at
00:08:54
transfer of the electron across the
00:08:57
interface and how the iron gets to the
00:08:59
surface to be reduced and oxidized and
00:09:01
all these factors must be considered
00:09:03
let's firstly look at the charge
00:09:05
distribution at the interface so we're
00:09:07
going to zoom in at the micro scale
00:09:08
Grande zoo min into a small part of that
00:09:10
electrode we're going to say that the
00:09:12
metal electrode has a net positive
00:09:13
charge we're gonna call it QM so the
00:09:15
charge in the nettle so let's populate
00:09:17
this with charges but we're going to now
00:09:20
consider the ionic atmosphere model
00:09:22
we're going to consider solvation of the
00:09:24
electrode so as we add the positive
00:09:27
charges we have to populate the
00:09:30
surrounding solution with negative
00:09:31
charges as well and we can expect this
00:09:34
metal to be solvated as it were with an
00:09:37
equal and opposite charge Q s charge in
00:09:39
the solvent the interface zone that
00:09:42
we've highlighted must be neutral it has
00:09:44
no charge but what we see is we have a
00:09:47
gathering of ions at the surface but
00:09:51
once these have occupy fully occupied
00:09:53
the surface the only way we can get the
00:09:55
extender charged it needed to balance
00:09:57
the charge on the metal is to have them
00:09:59
loosely associated outside so the
00:10:02
interface zone we're looking at has
00:10:04
neutral is neutral has no charge so QM
00:10:06
is equal to negative Q s and we can see
00:10:09
we have two distinct modes of solvation
00:10:11
as it were we have this rigid attachment
00:10:13
to the surface which is an ion pair type
00:10:15
mode and we have something loosely
00:10:18
bonded to the interface this is a bit
00:10:20
more of the ionic atmosphere mode and in
00:10:22
this area we are alive for thermal
00:10:24
motion let's zoom out a bit let's look
00:10:28
at the overall structure of the
00:10:29
interface we have two distinct zones
00:10:32
presence in this interface so in order
00:10:36
to visualize this let's add a few more
00:10:38
ions to visualize the structure so let's
00:10:40
populate the metal with its charges so
00:10:43
we filled up the metal surface with
00:10:45
positive charge let's start bouncing
00:10:47
this charge with an ions so for ions
00:10:50
held directly at the surface these are
00:10:51
rigidly held in position and their
00:10:54
centers define something called the
00:10:56
inner Helmholtz plane this is simply a
00:10:59
construct to visualize the distribution
00:11:01
of charge okay we don't quite have
00:11:03
enough
00:11:04
to balance the charge here so we need to
00:11:06
populate the rest of the space nearby
00:11:08
with anions to balance the charge on the
00:11:10
metal so again considering the same
00:11:12
ionic atmosphere model we start
00:11:14
populating with anions but remember
00:11:17
there's thermal motions there's going to
00:11:19
be cations in here as well the important
00:11:21
thing is the overall charge in this
00:11:23
particular zone must be equal to the
00:11:27
charge in the methyl so this defines
00:11:29
another area of the solvent outside of
00:11:31
this area there's no excess charge so
00:11:34
all the anions and cations balance and
00:11:37
we have an equivalent charge from the
00:11:40
cations as we do from the anions so this
00:11:43
is the structure of the bulk solution so
00:11:45
we want to now look at how the potential
00:11:47
varies across that interface so we've
00:11:50
defined two regions of space and this is
00:11:52
known as a double layer or something
00:11:54
called a diffuse double layer because we
00:11:55
have a diffuse layer in this region it
00:11:59
refers to the two sets of charges that
00:12:01
we're looking at firstly referring to
00:12:03
the rigidly held charges at the inner
00:12:06
Helmholtz plane which are fundamentally
00:12:08
I impaired to the surface but we then
00:12:11
have the remaining charge excess which
00:12:13
is subject to thermal motion and we
00:12:16
would expect to have more of the anions
00:12:19
closer to the electorate than we do
00:12:20
further away from it and this means that
00:12:22
the potential varies with distance from
00:12:24
that surface so if we have a variation
00:12:27
we're immediately thinking we want to
00:12:29
try and visualize this with a graph so
00:12:31
let's plot how the potential varies with
00:12:34
distance from the elector as we look at
00:12:35
this we find that we have a very steep
00:12:38
decrease in the potential to the inner
00:12:39
Helmholtz plane so this is the distance
00:12:41
from the surface to the center of the
00:12:44
rigidly bound anions and then we have a
00:12:47
more gradual decrease to get to the
00:12:49
final potential of the solvent so this
00:12:51
potential of this bulk solvent here so
00:12:53
this is a way of visualizing how that
00:12:55
potential varies with distance in
00:12:57
summary remember that potential refers
00:13:00
to the energy of a positive test charge
00:13:02
a high potential gives us a low
00:13:04
electronic energy while a low potential
00:13:06
gives us a high electron energy so think
00:13:09
about what's going on this is a
00:13:10
potential source of confusion but
00:13:12
remember that if we have a high
00:13:14
potential electrode that means we've
00:13:16
added positive charge to it which is
00:13:17
stabilizing the electron
00:13:18
by applying the electrode potential that
00:13:22
allows to control processes so if we
00:13:24
lower the Fermi level we apply a
00:13:25
positive potential it lowers the Fermi
00:13:27
level which will drive spontaneous
00:13:28
oxidation if we lower the potential
00:13:31
we're removing positive charge remember
00:13:33
that raises the electron energy and that
00:13:36
has the effect of driving spontaneous
00:13:37
reduction at the electrode and finally
00:13:41
thinking about that potential at the
00:13:43
electrode interface that charge
00:13:44
distribution varies with distance and
00:13:46
fundamentally this affects the solution
00:13:48
potential that we want to consider
