Quick question about liquid crystals

[skrat]

After some reading, I noticed that everybody likes to mention the order parameter and most of the literature simply adds a graph, for example: http://www.personal.kent.edu/~bisenyuk/liquidcrystals/maintypes2.html

However, many (all of them, to be exact) seem to avoid the exact expression of order parameter S as function of temperature T. This makes me wonder why?
I would like to know the exact $S(T)$, so I can plot it in mathemathica and play with it. Where could I find this? :/

 

[nasu]

So you mean a theoretical formula for the order parameter versus temperature, right?
This will depend on the theoretical model and the specific system. And of course, on how this S is defined for the specific system.
There is no "exact" S(T) that applies to all liquid crystals.
It's more likely to find experimental plots for different materials.

Here you can find results obtained by using Landau's theory of phase transitions applied to liquid crystals (also called Landau-de Gennes in this case).
http://www.shu.ac.uk/research/meri/sites/shu.ac.uk/files/mmg-chapter_2.pdf

But the formula will depend on some parameters which have to be found experimentally.

 

[skrat]

What about Maier-Saupe approximation?

 

[nasu]

What about it?

 

[pmacias]

Thank you for your question about liquid crystals and the order parameter. The order parameter, also known as the degree of order, is a measure of the alignment of the molecules in a liquid crystal. As you have observed, it is commonly shown as a graph in many resources, but the exact expression of the order parameter as a function of temperature is not always provided.

The reason for this is that the exact expression of the order parameter can vary depending on the type of liquid crystal and the specific conditions of the experiment. Additionally, the order parameter may also be affected by external factors such as pressure or electric fields. Therefore, it is not always possible to provide a general expression for the order parameter that applies to all liquid crystals.

However, if you are interested in a specific type of liquid crystal or a particular experimental setup, you may be able to find an expression for the order parameter in the literature. I suggest searching for research articles or textbooks on liquid crystals that focus on the specific system you are interested in. Alternatively, you could also try contacting a researcher or expert in the field for more information.

I hope this helps answer your question and I encourage you to continue exploring the fascinating world of liquid crystals.