Chemistry Reference
In-Depth Information
the temperature dependence of the elastic constants and birefringence,
the optical textures of liquid crystals are significantly associated with
temperature.
The disclinations may split or annihilate due to interactions. The discli-
nations of the same sign tend to repel each other while those of opposite
signs attract each other and may eventually annihilate.
Because of the additional translational order, the dislocations can exist
in the cholesteric and smectic liquid crystals, which makes the texture of
these liquid crystals even more complicated. Each liquid crystal phase shows
characteristic textures and thus the optical texture becomes an important
means to differentiate the phase of the liquid crystals. Liquid crystalline
polymers have the same topologically stable defects as small molecular mass
liquid crystals do, but the textures may be different due to the difference in
the energetic stability of the same topological defects in both low molecular
mass and polymeric liquid crystals (Kleman, 1991). In Chapter 3 we will
discuss the textures in detail.
1.6.4. Defects in smectic A phase
The homotopy group of the smectic A phase is
Π
0
(
S
A
)=1
,
Π
1
(
S
A
)=
Z
⊗
Z
2
,
(1.35)
Π
2
(
S
A
)=
Z,
Π
3
(
S
A
)=
Z,
where
Z
is the translational dislocation normal to the smectic layers with
the Burger vector being the multiple layer thickness;
Z
2
, is a cyclic group
of two elements. There is no topological stable singular wall, but there
are topological stable singular lines, composed not only of the disclination
lines associated with
Z
2
but also of the dislocation lines associated with
Z
.
Π
3
(
S
A
)=
Z
implies that there are topological solitons.
The deformations in the smectic A phase liquid crystals are the bending
of the smectic layer (accordingly to the splay of the directors) and the
dilation or compression of the layers. The energy is thus
2
B
∂u
2
+
1
F
=
1
∇·
n
)
2
,
2
K
11
(
(1.36)
∂z
