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phase. This is the reason why the simple twist is common structure in nature
rather than the double twist.
In the simple twist, the twisting forces in a direction other than the twisted
axis are suppressed as mentioned above. What happens if these forces become
large? Twisting in all lateral directions of molecules results in a structure like
that shown in Fig. 3c. Such an arrangement is called a double twist. Com-
plete double twisting exists only at the central molecule and its surrounds,
that is, the double twist becomes weaker as it spreads radially. The molecules
atandaroundthecenteraremorestablethaninthecaseofasimpletwist,
since twisting in all lateral directions is allowed. The organized structure
formed within such a stable area is the double-twisted cylinder shown in
Fig. 4. Double twisting, if expanded to a broader area, results in a defect. For
this reason, as pointed out earlier, a double-twisted cylinder structure can not
be a basic structure that occupies a space continuously. Blue phases, however,
are built upon such a double-twisted cylinder structure that maintains this
inconsistency, as described in the next section.
5
Structure of Blue Phases
A double-twisted structure is unable to continuously occupy a three-dimen-
sional space. Thus, if such a structure is expanded to a three-dimensional
space, a defect inevitably occurs. Since the generation of such a defect involves
some energy, the entire system becomes unstable. Unless there is some gain
that exceeds such a loss in stability, a phase containing a double twist cannot
become stable. In the case of blue phases, the gain is a strong twisting force.
The stronger the twisting force, the more stable the double-twisted structure
becomes. As the system reaches the temperature of a disorderly isotropic phase,
the loss caused by the defect is relatively alleviated and a double-twisted struc-
ture is more likely to form. In the event that such a gain from a double-twisted
structure exceeds the loss caused by defects, blue phases appear. For this rea-
son, blue phases appear in the temperature range close to that of an isotropic
phase, in a chiral nematic phase, which is shorter-pitched, that is, which con-
tains larger twisting forces. Blue phases are exceptional in that they must
coexist with defects. In short, the local tendency for stability towards a double
twist and the global tendency for stability towards the defect-free space coun-
teract each other. If the former tendency exceeds the latter, blue phases appear.
If the latter prevails, the result is a chiral nematic phase. A system in which the
locally stable structures create such competitive interaction, where the global
ground state does not settle down to a single state, is called a frustration system.
A blue phase is precisely such a system. Among all the phases of liquid crystals,
blue phases were the first to be treated as frustrated phases. Other frustration
systems include spin glasses of magnetic alloys, Frank-Kasper phases of transi-
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