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This is how batteries
are engineered.

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This is why we have a
revolution in batteries.

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So this is a couple
of years old.

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There so many great
review articles

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on battery technologies.

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This is the cathode.

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By the way, what is a battery?

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Well, a lithium battery
is basically two sponges.

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And one of them
is usually carbon.

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And when you're
running your battery,

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lithium ions are going in.

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And the carbon is
so strong and able

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to hold those lithium
in and not break down.

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So we often use carbon
on the anode side.

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And then when we
charge it up, we

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push them back over to where?

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Where they came from.

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That's the cathode, which
is a lithium compound.

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But it has to be a material
that can hold lithium

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in it, hopefully at
very high concentration,

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but also be OK to lose it
and not completely collapse.

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And so you've got
lithium ion phosphate,

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those are these ones.

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You've got manganates.

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You've got cobalts,
cobalt oxide materials.

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There are so many
battery materials.

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They all work the same way.

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If it's a lithium
battery, the lithium

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is going to leave some crystal
that has lithium in it.

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But the crystal has to stay.

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So it's like a sponge that
loses something from it

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but stays intact.

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And that's something
goes over to the anode.

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It gets soaked up there.

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And you can recharge,
discharge, recharge,

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as you're just pushing these
lithiums back and forth.

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Oh, but you're pushing
them back and forth.

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You are diffusing them.

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That's what you're doing.

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You are diffusing them
through whatever structure

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you're putting them into.

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So if it's the
cathode, and you're

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trying to get the lithium to
come back in or to go back out,

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then you can imagine that the
barriers and the dimensionality

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itself are crucial.

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What is an activation
energy for a lithium

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atom in a given material?

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And does it take a 1 D path?

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It turns out these can
be extremely efficient.

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Look at those.

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They're practically
holes, they're

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lines in the lithium
ion phosphate.

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It's a really nice
cathode material,

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because you've got
these channels.

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These high conduction
channels, these highways.

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But then you say, well,
but maybe I need 3D voids.

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Maybe it shouldn't
have channels.

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It should have voids, so
it can choose more paths.

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Maybe we have planes.

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Maybe it's a layered structure
where they have these 2D

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planes they can travel through.

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What's the best?

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Well, it's not
trivial, because it's

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one of these, as
usual, constrained

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optimization problems, where,
when you make the pathway

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faster, you might need
to have more voids where

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you'll lose material.

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Or maybe you make the
material unstable.

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So you want it to have
a really high density.

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The lithium diffusion
and a battery material

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is related to the charge time.

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So here's another paper
from a few years ago.

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If you plot materials-- now,
here's the specific power.

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And so that's how much
power, watts per weight.

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Here's the watt hours.

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So that's the energy per weight.

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And this is the charge rate.

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This is the charge rate.

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And notice, so you want it to
be very, very fast-charging.

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And these are good materials.

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There's the lead-acid battery
that's still in your car.

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These are nickel metal
hydrides and so forth,

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other technologies.

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Here are the lithium
ion batteries.

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This is what's in
your cell phone.

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Notice something, as I get
up to faster charge rates,

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more open voids in material,
I lose energy density.

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I go this way.

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I don't want to go that way.

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I want to go this way.

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Constrained optimization,
these are the things.

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What goes into
solving these problems

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is calculating diffusion
barriers and energy densities

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and all the other
things that matter.

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But if you want to
target fast charging,

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you've got to know the
diffusion barriers.

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One of the number one
challenges in battery design

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is to keep that high while
continuing to push up that way.

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Polymers, you could imagine
that a polymer is slower.

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It makes sense, right?

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Because it's
harder-- as we talked

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about when we talked
about polymers,

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it's harder to make
crystalline polymers,

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to keep a polymer from
having some amorphous region.

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After all, you've got these
100,000-unit long strands

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of spaghetti.

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So it kind of makes
sense that the diffusion

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is going to be
lower in a polymer

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than in one of these
crystals, like an olivine,

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lithium ion phosphate.

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So that makes sense.

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But polymers would be great,
because they're lighter.

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And they can be flexible.

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And so we like polymer
batteries a lot.

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We want them for
many applications.

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So these are the kinds of
tradeoffs that you think about.

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And D is right there in the
center, because none of us

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want a battery that
takes two days to charge.