# 3.10: Summary

• Liquid crystals are characterised by their high orientational and low positional molecular order.
• Molecules capable of forming liquid crystals are always anisotropic – typically they will be calamitic (rod-shaped).
• There are three types of calamitic liquid crystal: nematic, smectic and chiral nematic. They are defined by their differing degrees of positional order.
• The degree of orientational order of a liquid crystal can be quantified using the $\text { order parameter } Q=\left(3\left\langle\cos ^{2} \theta\right\rangle-1\right) / 2$orderparameterQ=(3cos2θ1)/2
• Defects in liquid crystals are given the name disclinations. Each type of disclination is assigned a positive or negative number; the magnitude indicates its strength whilst the sign indicates which disclinations can cancel each other out.
• Disclinations can be viewed directly by polarised light microscopy. For example, in a nematic they appear as schlieren brushes.
• Liquid crystals also exhibit birefringence when viewed through crossed polars.
• The most common modern commercial use of liquid crystals is in liquid crystal displays.

## Going further

#### Books

• Peter J. Collings & Michael Hird, Introduction to Liquid Crystals: Chemistry and Physics, Taylor & Francis, 1997.
• Peter J. Collings, Liquid Crystals: Nature’s Delicate Phase of Matter, 2nd Edition, Princeton University Press, 2002.

#### Websites

• Liquid Crystals: a Simple View on a Complex Matter
A presentation covering the different liquid crystalline mesophases and their appearance under polarised light microscopy.
• PLC Virtual Textbook
Contains an introduction to liquid crystals and their phase transitions, including virtual experiments.
• The Basics About Liquid Crystals
A tutorial created by the Liquid Crystal and Photonics Group of Ghent University, Belgium.
• Liquid Crystal Disclinations Seen Through Cross-Polars
A simulation of the movement of schlieren brushes for different types of disclination in a nematic liquid crystal.
• Introduction to Anisotropy
A DoITPoMS TLP describing the anisotropy found in liquid crystals and other materials in further detail.