# User:Izeljkov

## History

Friedrich Richard Reinitzer (February 25, 1857- February 16, 1927)- "founding father" of liquid crystals

The study of liquid crystals (LCs) began in 1888 when an Austrian botanist Friedrich Reinitzer experimented on a material known as cholesteryl benzoate. He observed that the aforementioned substance had two distinct melting points. In his experiments, Reinitzer increased the temperature of a solid sample and watched the crystal change into a hazy liquid at 145.5°C. As he increased the temperature further, the material changed again into a clear, transparent liquid at about 178.5°C. Because of this early work, Reinitzer is often credited with discovering a new phase of matter - the liquid crystal phase.

## Liquid Crystals

Liquid crystal is a substance that exhibits properties that are between those of a conventional liquid and a solid. The main characteristic of the LC state is the tendency of molecules to point along a common axis, called the director. As we know, molecules in the liquid phase do not exhibit any intrinsic order. Also, in the solid state molecules are highly ordered and have little to no translational freedom. Therefore, we see that the characteristic orientational order of the liquid crystal state is somewhere between solid and liquid phases, as seen below.

Ordering of molecules in different phases

In order to describe how ordered a certain liquid crystal is, we use a quantity called order parameter (S). Based on the second Lagandre polynomial, S is given by the following equation:

$S = \left \langle \frac{3 \cos^2 \theta}{2} - \frac{1}{2} \right \rangle$

Ordering parameter temperature dependence.

where $\theta$ is the angle between the common direction and the orientation of that particular molecule. The closer S is to unity, the more ordered (and closer to solid structure) the liquid crystal is. When S drops to zero, that means we have transitioned to a liquid state. Typical values of S are between 0.3 to 0.8. This value decreases as you increase the temperature, which makes sense since thermodynamic entropy increases. Order parameter dependence on temperature is shown on the right. As we can see, for small temperatures we approach (but never quite reach) the value of one. On the other hand, as we increase the temperature, we'll have a "breakdown point" at which we reach complete anisotropy. Increasing temperature above this critical point will not change anything.