[L4.5 Slide 1] Hi, welcome back.
This is the fifth lecture of the fourth week
of the materials science of rechargeable batteries.
Today I'm going to summarize the fourth week.
Okay, what did we learn this week?
[Slide 2] First, we introduce some elements of--
of reaction theory.
Where we said that one side of the electrode
and the other electrolyte, there's an energy barrier that--
that we will have to overcome in order to inject lithium
into the material or say to plate it, another ways--
in other words there's some energy barrier
that has to be overcome.
And if you do that, if you overcome
that energy barrier you have to then introduce contributions
for forward and backward reaction rate.
At equilibrium, these two balance each other
so that you have some kinetic equilibrium where the rate
of the forward reaction is balanced
by the backward of reaction.
Okay, mathematically that is specified
by introducing the concept of a total current in the system.
That-- Basically the difference between the forward
and backward current where if we apply another potential,
one would expect that the bottom of one
of these wells become more stable.
If you do that what you will find is that the, basically,
the forward current is proportional to the amount
of reactant on the-- on reacted sides.
And minus the amount of vacancies that are available.
If the-- if there are no vacancies available,
basically nothing will come in the opposite direction.
Okay. And if we assume that the reaction is
of a errenious type, then you have
that the forward reaction rate constant is proportional
to driving force, this gives-- keeps the energy of formation.
Driving the system, this gives to this, to the-- and how that--
how this energy barrier changes
as I apply another potential to the system.
We can write the forward and backward reaction.
A free energy driving forces in terms
of what the total overall potential of the system is.
Think of it
as the electrochemical potential of a system.
Okay. Proportion-- And multiplied by this scaler value
that gives me a measure of the strength of that driving force
and the same, of course, in the-- in the backward direction.
This effective overpotential, if you may, is proportional
to the electrical interfacial overpotential.
And the chemical potential difference
between what the curves in the electrode side and the electro--
in the electrolyte side.
[Slide 3] If you include all of these, what you will find is
that this reaction rate is really proportional to the--
to the local applied overpotential in the system.
Okay, so if my overpotential is positive I will favor a material
in one direction.
If-- Because the exponential
of a very large negative number will become effectively zero.
And if instead I apply a negative overpotential,
this in turn will shut down and the other one will turn up.
Will-- will basically turn up its value and this value,
this constant i naught,
the exchange current density it really cor-- It's--
It's a function of the spaces that I have
at both ends of my reaction.
And really controlling the-- the strength of that,
of that process as I'm trying to intercalate material
or plate material in my system.
This relationship was referred
at the Butler-Volmer relationship
but we always also have other types of reactions
that basically add up to-- to this relationship.
[Slide 4] In this case, we have
for example the Butler-Volmer relationship which to,
in addition to that we should add any other side reaction
that may occur.
So just SEI, dendrite formation, they all occur
and they're occurring in parallel.
You can think of it as having additional intermediate wells
to this double well that we just put in the system.
And they would add directly to this reaction in the system.
Okay. These may affect,
impact directly the interfacial impedance
because this overpotential will be proportional
to how large the drop of the interface is.
And if that, the thickness of that interface keeps growing,
you have a potential may grow but the rate
at which mass transfers will also change.
So you really want an interface there
but you don't want it to be too thick.
[Slide 5] Okay. Other things that happen in-- in-- in a battery are,
for example, you have salt precipitation.
Which basically as you take lithium
out of the inner particles and dump them into the electrolyte,
the cathode particles are basically going
to take that material.
Okay. But if you do it too fast, what's going to happen
in the outside you can put too much--
too much lithium in it that will lead to salt precipitation.
Well in this one, you-- what you have
over here is really a two-dimensional model
predicting that.
And this is a one-d Newman type model whereas--
as time progresses lithium accumulates a lot
on the backside of the-- of the anode as you can see here
and on the back it will become completely depleted.
So adjusting with that that if you dump too much lithium
into the electrolyte phase you can lead to the formation
of say this additional crystalized system.
And so really what you want is to have this balance
of charge being exuded into the electrolyte with the amount
of lithium that is being taken
from the electrolyte into the particles.
That unbalance will lead to a change in the-- in--
in the-- in the charge ratio.
So, and-- and if you have in addition
to that this side reaction occurring, then you have
to basically subtract the reversal contribution which--
further unbalance the reactivity of the system.
Now, clearly because this interfacial reactions do matter
we care about the details of those reactions.
[Slide 6] And something we learn this week is
that even though what we want is the lithium in the--
in solution to basically be intercalated lithium.
Sometimes we have that the anode, the material limitations
or the material non-idealities of the electrode itself.
Especially in-- in this case of the anode leads to,
to solvent reduction, formation of non-desireable phases
that can lead to the formation of SEI.
Which if it forms and becomes stable,
it's actually favorable for-- for the, for use in a battery.
But if this layer keeps growing, and becoming thicker
at some point the performance of the cell will drop
because it will be so thick that nothing will come through.
As you can see, if the SEI layer is too small we will have
to make much more effort
to actually put something in the particle.
Limiting with that, also, the performance and--
and if it's too thick then nothing will happen.
So we do care a lot of what happens
and what the structure of this interface is.
[Slide 7] We talked about different of-- different description,
experimental description of what happens in--
in-- in that interface.
In this case this measure, set of measurements by Lu
and Steve Harris on the content of lithium
across a 50 nanometer SEI layer the deposited
on a copper substrate shows you that you have a region
of the SEI that is dense.
Okay, and in front of that you have porous region
through which lithium comes through so
that it comes very close to the--
to the substrate basically reacts
that material can form or-- or play through.
We also learn that this SEI layer is not uniform.
[Slide 8] Okay, that actually as it forms, okay,
even though ideally we want this, the--
the lithium metal to grow uniformly
or intercalate uniformly, instead we find that when it--
if it-- in the case of the a pure lithium electrode
that actually in some cases it bows.
Because it prefers some regions with respect to other ones.
And because the SEI layers happens
to be mechanically stiff, okay, it can break.
Okay. Leading to then inhomogeneities lithium
intercalation and-- and favoring therefore the formation
of dendrite, dendritic-like structures which will lead,
again, to the formation of inhomogeneities
and therefore leading to this basically kinetic instability
that-- that will form, favor the formation of dendrites.
Experimentally, that is observed through FEM.
Through the formation of these like micro--
micron sized boulders under the SEI layer as the material forms.
[Slide 9] Okay. And if instead
of recharging your cell you're trying to-- to discharge it,
you really want to remove lithium from the--
from lithium metal through the SEI out.
Okay. And as that happens,
if this inhomogeneities some regions will plate faster
than others one, leading these depressions on the system
which instead will lead to-- to further breakage.
Okay. Could have, could develop pinching,
deformation of additional phases.
And these inhomogeneities lead to lower efficiencies
of the cell and that can be experimentally of service.
These depressions, micron sized depressions in your substrate
which will indeed lead to poor performance
because now these regions could be electrochemically isolated.
In the anode there's a whole set of aging mechanism
that are detrimental for the performance of the cell.
[Slide 10] Okay. And we find that from this whole list all of them,
all these side reactions become basically detrimental.
That in this case, for example, the decomposition
of the electrode, the formation of SEI can be fixed
by putting additives so that the SEI is stabilized.
This is a good thing.
Okay. The-- Because SEI grows, that increase the impedance and,
of course, that can only be fixed
by putting more stable SEI additives.
And changes is porosity also lead to volume changes
and therefore SEI formation, contact loss
of our active material,
which would also lead to capacity fade.
And what people have done is also add additives,
so basically the gain has focused on the addition
of additives to stabilize the SEI so we don't have to deal
with a power or capacity fade as a result of the SEI
or the side reactions coming out of hand.
Getting out of hand.
Now, this of course, on the-- on the anode side.
[Slide 11] In the cathode side, what you have is
that the particles themselves can
undergo internal structural disorder.
And you can, because of the electrochemical shocks
that the particles are subjected you can--
you can have microcracking in the particles.
You can have loss of contact, the formation of
corrosive phases that will lead
to poor contact with the collector.
And therefore, or--
or the precipitation of additional phases.
That can migrate to the counter electrode
or favor electrode decomposition and form gases that can--
could lead to-- to an unstable, and unsafe battery.
Okay. So you can see, both cathode
and anode not only consists on finding materials
that you can match and particle size and thickens
to have the optimal porosity, tortuosity, and energy density,
but you also want to make sure
that these material phases are compatible so when you put them
in the same system the chemistry
of one doesn't affect the chemistry of the other one.
Or the formation of the SEI doesn't impact the response.
The SEI layer has-- has many implication
on the further stability of the system.
[Slide 12] And the case dendrite formation, what people have found is
that dendrite can grow from the top
as more material comes and accumulates.
Or it can come from the bottom.
Okay, as-- as lithium is basically depositing.
And in this case, this-- these experiments suggest that--
that base growth dendrite really corresponds to the--
to some mechanism that is not well known but it seems
to be controlled by the local electrochemical attractions.
And as we've definitely prove to occur because even
if there is no material for it to attach on the surface,
that dendrite will still be coming out.
[Slide 13] Okay. It's very much position dependent
because even though electrochemically the whole
layer of material can be subjected
to the same electrochemical conditions the inhomogeneities
occurring on the cell will effectively dictate what spots
will become more electrochemically favorable,
leading to the formation spherical, lithium beads.
And as they nucleate, they will form and--
and propagate towards the counter electrode as shown
by Harris and coworkers back in 2010.
[Slide 14] The theoretical description of these systems can summarized
in two large types of models, one by Chazalviel where--
and another one by Newman and Monroe.
Where they, both of them proposed there is a critical
overpotential, a critical driving force for its formation.
They defer on the specific details.
Okay. And then one of them proposes that there's a--
a characteristics incubation time,
while the other one really suggests no
such incubation time exists.
That the moment you apply a large current, they just go.
And in one case they propose that the great--
growth rate really is proportional
to the applied electric field.
And the other one is that they accelerate as--
as they keep going.
[Slide 15] So in order to bring both descriptions into agreement,
okay, a thermodynamic description suggests
that if you account for the three energies of transformation
and the surface contributions that are opposing it's growth,
you can account for an energy barrier
that if you overcome it you will be able to stabilize a nuclei
of lithium for it to grow or shrink.
If you do this, then you can control the size of the barrier
and the characteristic size by applying an overpotential.
So if you apply very, a negative overpotential the size
of the barrier will shrink because you basically pushing
down this contribution.
And-- and if you apply a potential of the opposite,
you make the barrier higher.
Okay. And if-- if that happens and you're able
[Slide 16] to overcome this barrier then you can effectively form that.
The characteristic sizes really depend effectively
on the potential of the gibs free energy formation,
as well as the surface tension.
Okay. So really suggesting that there is a critical size
of which this happened,
also there's will be a critical potential in agreement
with both Newman and Monroe and Chazalviel and coworkers
that will happen as you admit the existence
of an energy barrier that has to be overcome.
[Slide 17] Okay. And depending on what the size of dendrite is
and the conditions of the--
that you're submitting that dendrite to.
You could have that if you--
if the initial size of that dendrite is larger
than critical size it'll grow
until it reaches a terminal velocity.
Or it'll shrink if-- if it's smaller
than characteristic size.
Okay. In both cases they agree with both the results
of Chazalviel as-- as it reaches a terminal velocity,
or Newman as it accelerates.
Okay. And-- You-- you can further discuss this additional
details as-- as you consider a finite domain as compared
to an infinitely sized domain.
If you can think of one specific dendrite
that is it sees a large potential and it accelerates,
the overpotential will increase accelerating its velocity.
So it's all within this framework.
[Slide 18] Okay. Then we found that really we can summarize the different
types of growth that--
that these people have found into five regions.
One of them corresponds to no growth region, which is a region
at which you expect the dendrites are not
thermodynamically stable.
So they will not grow.
One where if you apply a very large overpotential the
dendrites will-- will spend a little time basically overcoming
the barrier, very few time interacting with each other
and then basically taking off.
A region where once you have them thermodynamically stable,
they spend a lot of time growing at the expense
of the smaller ones that they eventually reach the--
the kinetic limit.
And that corresponds to the long incubation time region.
And then once they have reached that-- the growth region,
their growth accelerates until they terminal velocity
in the case of having voltage gradient very far away.
Okay. And well, then the fifth region corresponds
to steady state growth.
Okay. And you can use this as a map to identify those locations
and which growth will happen.
And clearly what you want is to avoid regions that lead to the--
a small barrier for nucleation and small incubation times.
And this why when one charges your devices you really are
trying to be somewhere down here,
where the basically your current large enough to intercalate
or plate something but not large enough to start nucleating
at the region of nucleations.
[Slide 19] It's still a large field where we want
to understand how dendrites are inhibited the cell,
a long walk in order to get there.
But really what you want is
to develop low current density charging, okay, so that--
And we want to increase the-- the limit as to how low is low.
We would like to make that larger.
We want to develop intercalation compounds
and polymeric solid electrolytes
so that we can suppress the conditions
in which dendrite will nucleate.
And also change the chemistry of the substrate
so that this doesn't happen.
This can also be done by coming
up with better lithium anodes or-- or alloy anodes.
And other people have tried things like applying pressure
to the cell, this also seems to be commercially viable.
Or electrolyte stirring.
Okay. And while to this point we have talked
about the individual mechanisms controlling the performance
of the cell, we really haven't put all the pieces together.
We haven't talked yet about the electrolyte
and that's what we're going to do in--
in the fifth week of this course.
Thank you.