Chemistry Reference
In-Depth Information
Fig. 5
Structures of Blue Phases I and II. The
rods
in (
a
)and(
c
) represent double-twist
cylinder. The
black lines
in (
b
)and(
d
) represent disclination lines
tion metal alloys, and vortex lattices of superfluids and superconductors. Such
frustration systems are known for their peculiar characteristics.
Figure 5 shows the structures of BP I (Fig. 5a,b) and BP II (Fig. 5c,d), iden-
tified through many different experiments and theoretical calculations [4, 5,
12]. BPs I and II have body-centered cubic symmetry and simple cubic sym-
metry, respectively. The cylinders in Fig. 5a and c indicate double-twisted
cylinders, and the black lines in Fig. 5b and d indicate the disclination, defect
lines. These are unusual structures of lattices, and appear as logs stacked up
at right angles. Within each of the double-twisted cylinders, each molecule is
twisted by 90
◦
along its radius. On the outermost circumference of a cylinder,
the molecules are twisted by 45
◦
with respect to the cylinder axis, from - 45
◦
at one end to + 45
◦
at the other. This is equivalent to a quarter pitch, where
a single pitch corresponds to a twist of 360
◦
. The diameter of a single double-
twisted cylinder is typically 100 nm or so. Thus, assuming that the molecular
diameter is 0.5 nm, approximately 200 molecules are gradually twisted. The
lattice parameter for BP I corresponds to 1 pitch of twisting, while that in
BP II corresponds to 0.5 pitches. These pitch lengths usually differ slightly
from those of a chiral nematic phase, which is a lower-temperature phase.
It is amazing that such a complex, hierarchical structure forms in a sort of
self-organized way as a result of repetitions of the twisted arrangement of
molecules. Diffraction peaks appear at (110), (200), and (211), etc., in BP I,
and (100) and (110), etc., in BP II as a result of the long wavelength. These
diffractions satisfy the equation:
2
na
√
h
2
+
k
2
+
l
2
λ
=
,
(1)
where
,
n
,and
a
denote the wavelength of incidence, refractive index, and
lattice constant, and
h
,
k
,and
l
are the Miller indices. In BP I,
h
+
k
+
l
is
an even number. Figure 6 shows an example of the reflectance spectrum of
BP I. Unlike a chiral nematic phase, multiple reflection peaks are present in
λ
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