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MINA HEALEY: Hi.

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My name is Mina, and I'll be
teaching about liquid crystals.

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Liquid crystals have a wide
variety of applications

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in modern technology
and science,

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and this is because of
their unique structure.

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They flow like
conventional liquids

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but are arranged in a similar
way to crystalline solids.

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Liquid crystal molecules can
be calamitic or rod shaped.

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They can also be
diskotic, or disc-like.

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In this video, I'll
be talking about

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calamitic liquid crystals.

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Smectic liquid crystals are
arranged in a layered structure

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and have long
range orientational

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order and one-dimensional
translational order.

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Pneumatic liquid crystals have
no long range positional order

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but have long range
orientation order.

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One way to characterize
a liquid crystal

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is with its orientational
order parameter.

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n is the director
or the vector which

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points along the preferred
axis of the liquid crystals'

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molecular orientation.

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p is the non-polar vector which
indicates the orientation.

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Theta is the angle between
the n and p vectors.

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The general equation for
the orientation, all order

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parameter is s is
equal to 2 times

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the average of n dot
p squared minus 1.

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An isotopic liquid
would have an s of 0

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because theta would be random.

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But over the average
of all the thetas,

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n dot p squared would be 1/2.

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A perfect crystal has an s of
1 because n is parallel to p.

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The orientational order
parameter for liquid crystals

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lies somewhere between 0.3 and
0.9 depending on temperature.

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Another descriptor
of liquid crystals

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is the translational
order parameter.

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Sigma is used to
describe the layering

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in smectic liquid crystals.

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In this equation,
z is position and a

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is the distance between layers.

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Sigma is the average of
the periodic function 2 pi

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z over a.

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Many devices that use liquid
crystals such as liquid crystal

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displays or LCDs in TV'S rely
on the specific orientation

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of the liquid crystal
molecules in a sample.

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To be able to do
this correctly, we

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need to know the energy required
to reorient the molecules

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in a specific liquid crystal.

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To reorient the molecules
in a liquid crystal,

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we have to apply a
voltage to the sample

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and observe when the
molecules have aligned.

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To be able to find
the energy it takes

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to reorient a molecule
in an electric field,

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we need to use the equation
for an electric field--

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e equals v over d, with v
being the voltage applied and d

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being the distance across
which the voltage is applied.

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We also need the equation
of the energy of rotation.

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This is derived from the
torque equation-- tau

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equals e cross mu.

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The energy of reorientation
is u equals e times mu times 1

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minus cosine of
theta, with mu being

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the dipole moment of
our sample and theta

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being the angle between
the unrotated molecule

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and the direction of
the electric field.

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In this example, the liquid
crystal experimented on is 5cb.

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The observed switching
voltage is 16 volts.

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The spacing is 2.5 times 10
to the negative fifth meters.

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The dipole moment is 4.9d
multiplied by 3.3 times 10

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to the negative 30.

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And pi over 2 is the average of
all the angles in the sample.

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Plugging these values
into our equation,

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we can see that the
energy of reorientation

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for the liquid crystal 5cb
is about 6.2 joules per mole.

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What we are now looking
at is a visualization

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of the liquid crystal becoming
ordered as an electric field

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as applied.

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As you can see, when the voltage
increases above the switching

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voltage, the liquid crystal
becomes more and more ordered.

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Liquid crystals are used
in many new technologies,

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and learning about their
structure is very important.

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I hope you enjoyed this video
and learned some new things

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about liquid crystals.