Chemistry Reference
In-Depth Information
n
Figure 1.5.
The nematic liquid crystals.
denoted by a unit vector
n
. The director
n
actually has the up and down
symmetry. The nematic liquid crystal is shown in Figure 1.5.
This phase has a symmetrical axis
C
∞
along the director. In addition,
there is a reflection-symmetry plane perpendicular to the axis
C
∞
and a
mirror-symmetry plane through the
C
∞
axis. Therefore, the local symmetry
of nematics can be expressed by the
D
∞h
group. Of course, nematics have
three dimensional translational symmetry.
The structural factor of the nematic phase reflects the breaking of the
rotational symmetry. The large X-ray scattering angle sphere (short dis-
tance) shrinks toward the circle perpendicular to the director while the
small scattering angle intensity is compressed along the
n
axis. There are
two X-ray diffuse spots at
q
=
q
0
n
with
q
0
=2
π/l
(
l
the molecular length)
and two diffuse rings around
q
=
q
1
n
×
k
with approximately
q
1
=2
π/a
(
a
the distance between neighboring molecules).
1.4.2. One-dimensional translational order—Smectic
A and C phases
As the temperature is further cooled, the molecules begin to segregate into
planes giving rise to a smectic A or smectic C phase. In addition to the
orientational order that the nematic phase shows, the smectic A and C
phases exhibit a one-dimensional translational order, and can therefore form
layered structures. There is a liquid-like motion of the rods in each layer
and no correlation of the molecular positions from one layer to the next. In
each layer, the mass centers of the molecules are randomly distributed as
