00:00:00
in our last session we looked at
00:00:02
electrode kinetics and how these would
00:00:04
have an effect on the current at an
00:00:05
electrode so now what we're going to do
00:00:08
is examine what happens as we vary
00:00:09
potentials as we apply a potential to an
00:00:12
electrochemical cell we introduced last
00:00:15
time the butler-volmer equation which
00:00:16
showed us how we balanced a reductive
00:00:19
process with an oxidative process
00:00:21
remember that we were talking about J in
00:00:24
terms of current density and the
00:00:26
butler-volmer equation shows how this
00:00:27
varies with respect to the applied
00:00:29
potential this over potential eater the
00:00:32
total current sum is therefore the sum
00:00:34
of the oxidative process and the
00:00:36
reductive process both of these we see
00:00:40
as eat a term this over potential term
00:00:42
appears in both so both are affected by
00:00:44
the potential that we apply
00:00:45
fundamentally the observed current that
00:00:48
we see in our cell only applies on the
00:00:51
exchange current density which this J
00:00:53
zero and our over potential eater our
00:00:56
alpha term that we've expressed here is
00:00:58
simply a measure of the symmetry between
00:01:00
the oxidative and reductive processes
00:01:02
where alpha is 0.5 the rate of reduction
00:01:05
is the same as the rate of oxidation at
00:01:06
each electrode where the number of
00:01:08
electrons exchanged is equal to 1 okay
00:01:11
so now let's look at how current varies
00:01:13
with over potential this graph that we
00:01:16
showed in the last slide simply shows
00:01:18
the anode rate and the cathode rate so
00:01:21
the oxidative current here in red on the
00:01:23
top by convention this is positive while
00:01:27
the cathode current the reduction is
00:01:29
happening here in blue and what we see
00:01:32
is the sum of these two curves this
00:01:33
purple line up the middle shows what
00:01:36
direction the current flows as we apply
00:01:38
different over potentials to our cell so
00:01:41
remember the over potential is simply
00:01:42
the difference between the equilibrium
00:01:43
potential and the potential that we're
00:01:47
applying to our cell what we see very
00:01:49
rapidly is as we get to extreme values
00:01:52
of over potential one component very
00:01:54
rapidly begins to dominate so we're eta
00:01:58
is plus or minus naught point one so if
00:02:00
you have plus or minus naught point one
00:02:02
over a potential applied to our cell we
00:02:04
generally get one term dominating if we
00:02:07
look at the left-hand component we're
00:02:10
saying that this oxidative component
00:02:12
dominates if our
00:02:13
overpotential is greater than plus nor
00:02:16
point one volts while the reductive
00:02:18
process would dominate if our over
00:02:20
potential is less than - nor point one
00:02:22
volts so what this means overall is that
00:02:25
unless we have a very very small over
00:02:27
potential we will really only see the
00:02:29
current coming from either the oxygen
00:02:31
process or the reductive process only at
00:02:34
very small magnitudes of n will we see
00:02:36
our currents actually having competition
00:02:38
between oxidation and reduction what we
00:02:41
now need to do is think about what's
00:02:43
this j0 this exchange current density
00:02:45
and this symmetry component let's we
00:02:49
need to find out what these terms are so
00:02:53
our exchange current density and our
00:02:55
symmetry factor alpha cannot be measured
00:02:58
directly so this exchange current
00:03:00
density is simply what the current is or
00:03:02
the exchange current at equilibrium is
00:03:03
while the Alpha component is simply a
00:03:06
reduction contribution to the Gibbs
00:03:08
energy so the greater alpha remember
00:03:11
this is a proportion it's a fraction the
00:03:13
greater alpha is the greater the
00:03:15
reductive component to the overall Gibbs
00:03:17
energy if we look at a situation where
00:03:19
we have alpha is not 0.5 so this is a
00:03:22
symmetrical situation where the
00:03:24
reductive and oxidative processes are
00:03:25
contributing equally to the overall
00:03:27
current we observe well we see that yes
00:03:30
at these extreme values of our over
00:03:31
potential we have our reduction
00:03:33
dominating at very low over potentials
00:03:36
and we have our oxidation dominating and
00:03:38
very high over potentials so let's
00:03:40
consider what happens when ETA is
00:03:42
greater than 0.1 volts or the magnitude
00:03:44
of ETA is greater than 0.1 volts well if
00:03:48
we say that ETA is greater than not 0.1
00:03:50
plus not 0.1 volts if we look at this
00:03:53
reductive term the reductive term simply
00:03:56
shrinks to zero we get a very simple
00:03:58
format for our overall current density
00:04:00
if on the other hand we consider what
00:04:02
happens when eta is less than - not 0.1
00:04:05
volts now our oxidative term shrinks
00:04:08
into obscurity and we get a simple
00:04:11
expression in terms of the reductive
00:04:13
process now that we've established this
00:04:16
how do we now find our exchange current
00:04:18
density and alpha well we have an
00:04:21
equation here we've seen equations like
00:04:23
this before it's this a very similar
00:04:26
format
00:04:27
Rini equation which you've dealt with
00:04:28
before you've linearized before so so if
00:04:31
we think about linearizing this form of
00:04:33
equation we get on to plotting data on a
00:04:36
graph the name for these plots are
00:04:38
called Tafel plots they're lie the
00:04:40
determination of our fractional symmetry
00:04:43
components and our exchange current
00:04:45
density in order to do one of these
00:04:47
plots we simply plot the log of the
00:04:49
current density against the over
00:04:50
potential so remember we simplified the
00:04:53
butler-volmer equation for a particular
00:04:54
case of high e to high over potential
00:04:57
and remember one of these terms drops
00:05:00
out depending on whether we're negative
00:05:02
not point one or positive not point one
00:05:04
so let's look at the reductive process
00:05:07
to start with so we're dealing with eta
00:05:09
is less than - not point one volts if we
00:05:12
take logarithms of both sides we simply
00:05:14
get up this sort of relationship and we
00:05:16
should immediately recognize this where
00:05:19
we have a y equals MX plus C type
00:05:22
equation where the variable
00:05:25
eita we're plotting against log of J and
00:05:28
we should get a graph with a gradient of
00:05:30
alpha F over RT and sure enough when we
00:05:34
plot these we find that the reductive
00:05:37
component where where eta is less than -
00:05:40
not 0.1 volts we see sure enough we get
00:05:42
a linear range it starts to deviate
00:05:45
that's very low over potentials because
00:05:48
as we said we start to get a
00:05:49
contribution from the oxidative
00:05:50
component so that causes a deviation
00:05:52
from linearity so this gives us an
00:05:55
equation for the reductive component and
00:05:56
we can do the same for the oxidative
00:05:58
component and we get the right-hand side
00:06:00
of the curve we simply plot log J
00:06:03
against the over potential which allows
00:06:04
us to very simply find the exchange
00:06:06
current density if we look at this
00:06:08
remember y equals MX plus C type graph
00:06:11
our intercept should be log of j0 the
00:06:15
log of that exchange current density and
00:06:17
the gradient allows us to easily find
00:06:19
this symmetry component alpha it's
00:06:22
important to remember that at Athol plot
00:06:23
will not be symmetrical so depending on
00:06:25
the value of our symmetry factor alpha
00:06:28
we will get a different shaped Ifill
00:06:30
plot so if alpha is not point two we
00:06:33
enhance the oxidative component we have
00:06:36
a much greater contribution to the
00:06:38
current from the
00:06:38
component while if alpha is much greater
00:06:41
we have the simply factors much greater
00:06:43
that means we have a much greater
00:06:44
contribution from the reductive
00:06:45
component but regardless of what this
00:06:48
value of alpha might be this intercept
00:06:51
will be common to both sides of the
00:06:53
graph and both will give us a value for
00:06:56
that exchange current density let's look
00:06:59
at the features of these Tuffle plots we
00:07:01
said a little bit about this deviation
00:07:03
from linearity they're curved at these
00:07:05
small over potentials because what's
00:07:08
happening is we get both reduction and
00:07:10
oxidation contribute to the current that
00:07:12
we observe if we go to higher over
00:07:14
potentials the competing process tends
00:07:16
to zero and we get increasing
00:07:18
conformation to this linear fit the
00:07:21
straight-line section will allow us to
00:07:23
find our exchange current density J 0
00:07:25
from the intercept and alpha from the
00:07:28
gradient it's worth giving some thought
00:07:29
to these logarithms often when we do
00:07:33
theory we use natural logarithms because
00:07:35
of the prevalence of the exponential
00:07:36
term e but when we do things practically
00:07:39
we almost always plot log base 10 so
00:07:42
often we use this log base 10 but it's
00:07:45
important to remember they are the same
00:07:46
mathematical function and there's a
00:07:47
simple linear relationship between them
00:07:49
where the log of one term J is simply
00:07:53
two point three or three times the log
00:07:54
base 10 of J so always remember that
00:07:58
that these logarithmic relationships are
00:07:59
the same just with a scaling factor the
00:08:03
symmetry factor can be a source of some
00:08:04
confusion so it's worth spending some
00:08:06
time on what this means as well we
00:08:07
introduced it earlier as a free energy
00:08:09
contribution from the reductive process
00:08:11
but it's simply a balance between those
00:08:13
oxidation and reduction currents so at
00:08:16
very low alpha if we look at how the
00:08:18
current responds to the over potential
00:08:21
we see at low alpha the oxide of current
00:08:24
responds much more readily to the
00:08:27
applied over potential than the
00:08:29
reductive current so oxidation will be
00:08:32
favored at low alpha where we see this
00:08:34
positive response and it increases much
00:08:37
more rapidly with the applied over
00:08:39
potential if we go the other way and
00:08:41
consider alpha of 0.7 we see the reverse
00:08:44
is true where we get the reduction
00:08:45
process favored where reduction current
00:08:47
increases much more rapidly with ETA
00:08:49
because that kind of gives an overview
00:08:52
of what this symmetry
00:08:52
factories the exchange current density
00:08:54
however is slightly more unusual to
00:08:57
consider this is simply termed the
00:08:59
equilibrium current exchange it is the
00:09:02
rate of charge transfer at the electrode
00:09:03
at equilibrium so there's no net
00:09:06
transfer but it's a measure of how much
00:09:07
charge comes from the ions at the
00:09:09
surface into the electrode or from the
00:09:11
electrode up to the ions remember those
00:09:13
two terms balance the more readily they
00:09:15
can exchange those electrons the more
00:09:17
readily the system can deliver a current
00:09:19
without significant energy loss
00:09:21
fundamentally what this does is it
00:09:23
affects the over potential required to
00:09:25
deliver a specific current so if we look
00:09:28
at the graph this is showing what
00:09:30
happens it to the current voltage
00:09:32
response and at different exchange
00:09:33
current densities so let's firstly
00:09:36
define a fixed current density of not
00:09:39
0.5 micro amps per square meter so to
00:09:42
deliver this current we find that if we
00:09:44
have a high exchange current density at
00:09:47
our electrode so if our electrode
00:09:49
naturally has a high exchange current
00:09:50
density we only have to apply an over
00:09:53
potential of 0.2 volts however as we
00:09:57
have lower and lower exchange current
00:10:00
densities we find we have to apply a
00:10:02
greater and greater over potential in
00:10:04
order to deliver that same current if we
00:10:08
have a low exchange current density that
00:10:09
means we have a lot less charge transfer
00:10:11
at equilibrium which means we have to
00:10:13
apply this larger over potential to
00:10:14
drive the net current forward so what
00:10:17
kind of factors affect the exchange
00:10:18
current density well we said that there
00:10:21
are electrode processes and we said it
00:10:22
was a characteristic of the electrode
00:10:23
and the solute that we were looking at
00:10:25
so let's consider the kinetics of what's
00:10:27
going on if we think about what's going
00:10:29
on at the electrode if we consider
00:10:31
something with a high exchange current
00:10:34
density so quite a high exchange current
00:10:35
density is 10 amps per square meter so
00:10:38
an example of this is a single electron
00:10:40
process so iron ferrous ion it can be
00:10:42
reduced to another iron ferrocyanide
00:10:44
compound but notice there's only a
00:10:46
single electron going on there and
00:10:48
there's no bonds being broken so there's
00:10:51
no chip no significant change in the
00:10:53
solute so it's very easy for it to pick
00:10:55
up an electron very easy for it to give
00:10:57
it up which leads to us having a higher
00:10:59
exchange current density another thing
00:11:02
which favors a high exchange current
00:11:03
density is having no adsorption
00:11:06
so adsorption is when a species will
00:11:08
chemically bond with the surface so in
00:11:11
this case I've shown hydrogen ions
00:11:13
receiving electron and the hydrogen atom
00:11:15
forms a chemical bond of the surface
00:11:17
this reduces the exchange current
00:11:19
density so if we have no adsorption then
00:11:22
we would tend to get a higher exchange
00:11:23
current density and if the reactant and
00:11:25
product have very similar properties
00:11:26
then again we would expect to have a
00:11:28
high exchange currency easy for those
00:11:30
electrons to exchange across the
00:11:32
interface if however we consider a low
00:11:35
exchange current density the reverse
00:11:36
would apply so if you have a very
00:11:38
complex process we have lots of things
00:11:40
going on at once or if we have to break
00:11:41
a chemical bond or if we had to adsorb
00:11:45
onto the surface these are factors that
00:11:47
would favor a low exchange current
00:11:50
density an example of this where we have
00:11:52
the azide nitrogen couple picking up an
00:11:55
electron the exchange current density is
00:11:58
absolutely miniscule because the
00:12:00
strength of the nitrogen bond makes it
00:12:02
extremely difficult to drive that
00:12:05
process forward the electrode material
00:12:08
also affects the exchange current
00:12:10
density so for a given reaction so I'm
00:12:13
just going to talk about the reduction
00:12:14
of protons in a hydrogen standard
00:12:16
electrode so let's consider this couple
00:12:19
at a platinum electrode we have an
00:12:22
exchange current density of 10 minus 3
00:12:24
so one ten-thousandth of an amp per
00:12:26
square meter while if we deal with a
00:12:28
mercury electrode our exchange current
00:12:30
density drops massively and
00:12:33
fundamentally this happens because of a
00:12:34
different mechanism of exchange a
00:12:36
different way in which the charge is
00:12:38
transferred Platinum fundamentally has
00:12:41
catalytic properties this is something
00:12:42
that should be well known to you and is
00:12:44
dealt with quite extensively in the
00:12:46
inorganic chemistry side of things but
00:12:48
as a result of those catalytic
00:12:50
properties this surface effects the
00:12:51
kinetics of the process so let's explore
00:12:54
the process a little bit our first step
00:12:56
is hydrogen being reduced and absorbed
00:13:01
bringing to the surface so we simplify
00:13:03
on this methyl hydrogen bond here we
00:13:06
then have one of two process that can
00:13:07
then occur either a second hydrogen
00:13:10
which which is adsorbed to the surface
00:13:12
can form a bond directly with the
00:13:14
hydrogen and break the metal hydrogen
00:13:16
bonds and release our h2 gas or what we
00:13:19
can have is
00:13:20
we can have another proton coming in and
00:13:22
being reduced and simultaneously falling
00:13:27
that hydrogen gas release so these are
00:13:31
the three steps that we wish to consider
00:13:32
but depending on the rates of each one
00:13:35
and the rate at which each one occurs
00:13:37
will affect the overall rate of our
00:13:39
reaction for mercury and lead a metal
00:13:44
hydrogen bond is very very weak so that
00:13:46
means that this methyl hydrogen bond
00:13:47
formation becomes the rate determining
00:13:49
step if we consider step B where we have
00:13:54
the adsorbed hydrogen coming together to
00:13:56
form a ch2 gas in platinum
00:13:59
this becomes the rate determining step
00:14:01
because the methyl hydrogen bond is
00:14:03
considerably stronger so this is our
00:14:05
rate determining step in platinum step C
00:14:08
is generally slower because it involves
00:14:11
more species but this can also happen in
00:14:13
platinum as well but we need to factor
00:14:15
in the relative strengths of these
00:14:17
methyl hydrogen bonds and for a good
00:14:19
catalyst it has to strike a balance
00:14:21
between steps it has to strike a balance
00:14:23
between the formation of the methyl
00:14:25
hydrogen bond and then the subsequent
00:14:26
breaking of methyl hydrogen bonds it
00:14:29
just so happens that platinum strikes
00:14:30
its balance and makes it very effective
00:14:32
as a catalyst while for mercury LED and
00:14:36
so on this bond is very weak which means
00:14:39
it doesn't favor the formation and the
00:14:41
surface adsorption of hydrogen when
00:14:46
we're considering our current potential
00:14:48
curves we need to consider both the
00:14:50
oxidation and reduction currents because
00:14:52
they both contribute towards the process
00:14:54
that we measure the symmetry factors the
00:14:57
rate at which oxidation and reduction
00:14:59
contribute affect the shapes of the
00:15:01
curves that we've observed so whether we
00:15:03
have a process which strongly favors
00:15:05
oxidation or strongly favors the
00:15:07
reduction these all work together to
00:15:09
affect the shape of the curve that we
00:15:11
observe and fundamentally when we make
00:15:12
our measurements and look at the rate at
00:15:14
which the current is affected by the
00:15:16
overpotential the shape of the curve
00:15:18
gives us insight to the processes going
00:15:19
on at those electrodes the exchange
00:15:22
current is also something that's worth
00:15:23
looking at as well because the exchange
00:15:25
current affects the ability for a given
00:15:28
cell to deliver a current at a given
00:15:30
over potential and these exchange
00:15:33
currents are affected directly by
00:15:35
solution kinetics and electrode effects
