Chemistry Reference
In-Depth Information
〈
P
2
〉
and
〈
P
4
〉
in Equations 6.30 and 6.31 are substituted by
〈
P
2
〉
app
and
app
to distinguish from the molecular distribution by the thermal
fl uctuation. The orientational order parameters describing any molecu-
lar distribution is given by [28,29]
〈
P
4
〉
2
Π
Π
2
Π
()
(*)
L
(
)
=
L
*
(
)
(
)
D
ϕθχ
,,
∫
∫
∫
D
ϕθχ
,,
f
ϕθχ
,,
d
ϕ
sin
θ θ χ
d d
.
(6.51)
1
m
0
m
0
0
0
0
D
m
L
0
()
(
)
ϕθχ
,,
is the Wigner rotation matrix and (
) is the Euler
angle describing the rotational transformation from the molecular fi xed
coordinate frame to the apparent orientational center axis.
ϕ
,
θ
,
χ
〈
P
2
〉
app
and
〈
app
are related to the biaxial orientational order parameters by the
following equation:
P
4
〉
L
=
∑
()
(
)
L
*
P
=
D
ϕθχ
,,
.
(6.52)
L
m
0
app
mL
The distribution function
f
1
can be obtained by this equation when
f
dir
is given experimentally or theoretically. Conversely,
f
1
can be evalu-
ated if
f
dir
is given.
6.6.4 The V-Shaped Switching of Ferroelectric Liquid Crystal
Ferro- and antiferroelectric smectic liquid crystals (Sm
C
* and
Sm
C
)
are widely investigated for the application to LCD. It was found that
some ferroelectric or antiferroelectric smectic liquid crystals show the
V - shaped electro - optic response [29 - 32] . They show neither threshold
nor hysteresis occurring uniformly without any boundary movement
(Figure 6.18). The V-shaped switching is very attractive due to the fast
response to the electric fi eld [33,34] .
The “ random switching model ” [30,35 - 37] was proposed for the
mechanism of the V-shaped switching (Figure 6.19a). The frustration
and the competition between the ferro- and antiferroelectric behavior
bring about the reduction of the interlayer molecular interaction in the
particular case. Thus, the Langevin-type reorientation process of the
c
-
directors occurred. On the other hand, Takezoe et al. [38], Park et al.
[39], Rudquist et al. [40], and Clark et al. [41] asserted that the charge
stabilization and/or the highly collective rotation of the local in- plane
directors on the Sm
C
* tilt cone in the macroscopic scale, and that the
frustration did not play any essential role (Figure 6.19b). The molecular
distributions expected by the random model and the collective model
are different. Therefore, the models can be verifi ed by the molecular
distribution at the tip of V.
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