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where Ch or N* denotes the cholesteric phase, and S I ,S J are the smectic
I and J phase. The asterisk denotes the counterpart chiral phases. The
names smectic A, B, C, etc. were named purely in the chronological
sequence in which the phases were discovered. The letter designation does
not imply any information about the arrangement of the molecules, the
symmetry, or other features.
We now introduce the classification of the liquid crystal phases and their
structural features.
There are two fundamental orderings in the materials: positional order
and orientational order. At low temperatures, matter exhibits a crystal
state. The atoms or molecules are arranged regularly and periodically. Both
position and orientation exhibit a long range order. When heated, matter
may become an isotropic liquid through two ways, by losing the orienta-
tional order first while retaining the translational order, and hence becom-
ing a plastic crystal, or alternatively, by losing the translational order while
keeping the orientational order. These latter materials are liquid crystals.
In fact, with increasing temperature, these materials may not completely
lose their translational order while retaining their orientational order. All
liquid crystals are characterized by their orientational order, but liquid
crystal phases show varying amounts of translational order with the only
exception of nematics. Apart from the above basic symmetries, there is
another important symmetry — bond orientation symmetry. This symmetry
is important when dealing with hexatic phases. Liquid crystals are classified
in terms of following criterion:
(1) translational order
(2) bond orientational order
(3) correlation between smectic layers
(4) with chirality?
(5) cubic structure?
1.4.1. No translational order—Nematics
The nematic liquid crystal, N phase, is the only liquid crystal phase with-
out any long range translational order. Nematics are the most important
member in the family of the liquid crystals and are widely used in the
display industry.
In nematics, the molecules tend to be parallel to each other. The pre-
ferred direction of parallel orientation is characterized by the director,
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