MINA HEALEY: Hi.
My name is Mina, and I'll be teaching about liquid crystals.
Liquid crystals have a wide variety of applications
in modern technology and science,
and this is because of their unique structure.
They flow like conventional liquids
but are arranged in a similar way to crystalline solids.
Liquid crystal molecules can be calamitic or rod shaped.
They can also be diskotic, or disc-like.
In this video, I'll be talking about
calamitic liquid crystals.
Smectic liquid crystals are arranged in a layered structure
and have long range orientational
order and one-dimensional translational order.
Pneumatic liquid crystals have no long range positional order
but have long range orientation order.
One way to characterize a liquid crystal
is with its orientational order parameter.
n is the director or the vector which
points along the preferred axis of the liquid crystals'
molecular orientation.
p is the non-polar vector which indicates the orientation.
Theta is the angle between the n and p vectors.
The general equation for the orientation, all order
parameter is s is equal to 2 times
the average of n dot p squared minus 1.
An isotopic liquid would have an s of 0
because theta would be random.
But over the average of all the thetas,
n dot p squared would be 1/2.
A perfect crystal has an s of 1 because n is parallel to p.
The orientational order parameter for liquid crystals
lies somewhere between 0.3 and 0.9 depending on temperature.
Another descriptor of liquid crystals
is the translational order parameter.
Sigma is used to describe the layering
in smectic liquid crystals.
In this equation, z is position and a
is the distance between layers.
Sigma is the average of the periodic function 2 pi
z over a.
Many devices that use liquid crystals such as liquid crystal
displays or LCDs in TV'S rely on the specific orientation
of the liquid crystal molecules in a sample.
To be able to do this correctly, we
need to know the energy required to reorient the molecules
in a specific liquid crystal.
To reorient the molecules in a liquid crystal,
we have to apply a voltage to the sample
and observe when the molecules have aligned.
To be able to find the energy it takes
to reorient a molecule in an electric field,
we need to use the equation for an electric field--
e equals v over d, with v being the voltage applied and d
being the distance across which the voltage is applied.
We also need the equation of the energy of rotation.
This is derived from the torque equation-- tau
equals e cross mu.
The energy of reorientation is u equals e times mu times 1
minus cosine of theta, with mu being
the dipole moment of our sample and theta
being the angle between the unrotated molecule
and the direction of the electric field.
In this example, the liquid crystal experimented on is 5cb.
The observed switching voltage is 16 volts.
The spacing is 2.5 times 10 to the negative fifth meters.
The dipole moment is 4.9d multiplied by 3.3 times 10
to the negative 30.
And pi over 2 is the average of all the angles in the sample.
Plugging these values into our equation,
we can see that the energy of reorientation
for the liquid crystal 5cb is about 6.2 joules per mole.
What we are now looking at is a visualization
of the liquid crystal becoming ordered as an electric field
as applied.
As you can see, when the voltage increases above the switching
voltage, the liquid crystal becomes more and more ordered.
Liquid crystals are used in many new technologies,
and learning about their structure is very important.
I hope you enjoyed this video and learned some new things
about liquid crystals.