Nematic Phase
The nematic phase of liquid crystal contain rod-shaped molecules that have no set positional order. These molecules all tend to point in the same direction but have no specific order to their arrangement. If you shook a box of matchsticks, they would all become displaced but still point in the same direction. Molecules in the nematic phase behave in a similar fashion.
Chiral Nematic Phase
There is a distinct class of liquid nematic crystals known as chiral nematic. Chiral molecules position themselves in a twisted shape, that usually reflect light in colors that grow brighter or weaker, depending on the temperature. As stated on the Nobel Prize website, chiral molecules are used in thermometers for their heat-reactive behavior. Chiral molecules are also referred to as cholesteric.
Smectic Phase
The smectic stage of liquid crystal lies close to the solid stage. Smectic crystals are ordered into layers of rods. The liquid crystals float around freely within each layer, but are unable to move from one layer to another. Molecules in the smectic stage tend to align themselves in the same direction.
Smectic Phase Sub-Divisions
The smectic phase is divided into many sub categories, each of which have slightly different properties. The most common of these phases is the smectic-A mesophase, where molecules show no specific positional order within each layer. In the smectic-B mesophase, molecules are patterned as a field of hexagons within individual layers, as stated on the Polymers and Liquid Crystals website. In the smectic-C phase molecules are patterned in a similar way to the smectic-A stage, but lie at a tilted angle.
In certain smectic mesophases, the behavior of molecules change according to the layers positioned above or below them, demonstrating a degree of three-dimensional order. The smectic-G mesophase is an example of this stage.
Columnar Phases
Liquid crystals in the columnar mesophase are shaped like disks rather than rods. Columns are closely aligned together to form two dimensional crystalline shapes. The position of molecules within each column and the pattern of the columns themselves results in new mesophases being created.