A: What are liquid crystals?
So today we embark on a three part journey in trying to understand how LCD screens work. As you can see from the intro picture above, this first part will be dedicated to explaining what Liquid Crystals are as they play a pivotal role in LCD screens. Lets begin!
Liquid vs Crystal vs Liquid Crystal
Once you really start thinking the term liquid crystal is kind of silly as it contradicts itself. What do I think with this? Well lets look at the definitions.
Liquid is a state of matter with the characteristic that it conforms to the container it is held in while maintaining its overall volume . In comparison, a gas will expand to fill the whole volume available. The molecules or atoms that are the constituents of the liquid are not arranged in any specific way and are amorphous, meaning they are uncorrelated.
Crystal is a state of matter in which the constituents are strictly ordered. This means the positions of the constituents are completely correlated.
So liquid crystals are thus correlated while being uncorrelated at the same time, if one infers the true physical nature of the state of matter from the name itself. Well that is actually possible.
Liquid Crystals is a special subset of liquids in which parts of the matter contains some properties of liquids like fluidity, formation of droplets and many others. At the same time the same parts of matter can have anisotropic optical , electrical and magnetic properties which can only be explained by the matter having some order. Depending on the type of ordering we divide the liquid crystal field into several subsets.
Types of liquid crystal materials. The type of liquid crystal is mainly dependent on the shape of the molecule that is the basis of the liquid crystal. 
What are liquid crystals?
Liquid crystals are usually long molecules. Lets go case by case and explain:
Nematic liquid crystals are the most basic type. They are usually very long molecules. The fact that they are much longer than they are wide produces a specific behavior where the molecules prefer to be oriented along the same axis. This axis defines the order of the crystal and can be referred to as the order parameter but in the liquid crystal lingo it is usually refered to as the director. The molecules do not have a tip and a back, meaning that the molecule can be rotated by 180 degrees and the energy of the crystal would still be the same. This means n is not really a vector field but a tensor field, with the following property:
So to recap. Nematic liquid crystals are basically long molecular chains that, because of their shape, like to point in the same direction. Nematics only have directional ordering, but their positional ordering is non-existent.
Cholesteric liquid crystals are still very similar to nematics in the sense that they are very long molecules. But in this case the molecule has some radical that sticks out of the molecule like a sore thumb. This breaking of molecular symmetry means that the molecules cannot simply fit alongside each other to minimize energy. No. The molecules must also twist to a certain extent to basically fit the radical into the free spaces between the molecules. This twist has a period p which defines the cholesteric phase. Still there is no positional ordering.
On to the last liquid crystal type that we are interested in. The smectic liquid crystal is again very similar to the nematic liquid crystal, meaning that the molecules enjoy facing in the same direction. This time no rotations can be sighted like in the cholesteric type. But what we see is that the smectic phase has layers or stratification. This means not only are molecules rotationally correlated but they also show some intra-layer positional correlation. There is still no inter-layer position correlation meaning that layers are independent from each other when it comes to position and can slide freely across each other.
It is maybe interesting to note that the difference between a crystal and a smectic liquid crystal is only the inter-layer positional correlation, while the difference between a liquid and a nematic is that liquids lack the rotational correlation.
Lets just not what the definition of the order tensor is, as it is capable of describing all types of liquid crystal states and defines the properties of that particular phase. Its definition is written in the equation to the right. The sum goes over all molecules inside our small volume at position r which contains N molecules. u is the vector that describes the direction of our choice molecule with index i. It has three components as we are in three-dimensional space. α and β are just telling us which component of the Q tensor we are looking at, meaning:
δ simply the identity matrix, meaning that when α = β then δαα = 1, otherwise it is 0.
This tensor has the nice properties making it suitable for the description of such systems. You can read more about it here .
Now to the last section of this Part 1, where we will talk about boundary conditions of the liquid crystal. This is a very important subject as it is critically important for our LCD screen discussion. We will discuss it on the case of the nematic liquid crystal phase.
Usually the liquid crystal is stored in a little box, like you would expect. How does the box effect the rotation of the molecules on the interface between the box and the liquid crystal. Well normally it doesnt really, but the important thing is that it can if we want. We can impose a specific direction of the molecules on the interface. For example we can impose that all molecules must be perpendicular to surface or horizontal to the surface. In the left figure you can see what the orientation of the molecules throughout the entire sample.
This brings us to an interesting case where we have a sphere shaped box. If we impose perpendicular boundary conditions than all is fine and dandy in the volume of the sphere, but a problem occurs in the center of the sphere. What is the direction of the molecule there? The director n is not defined in the center of the sphere which is what we call a defect. They are interesting creatures as they have very specific topological properties and we all know that things get serious when we start talking about topology. You can read more about it here . The defect in the center of the sphere can be seen in the bottom figure.
Thank you for tuning into the first part as we learn how LCD screens work. Stay tuned for the next two posts coming in the following days.
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