Chemistry Reference
In-Depth Information
is, their refractive indices of ordinary and extraordinary light,
n
o
and
n
e
,
are different. The difference of these two refractive indices, the birefringence
denoted as ∆
n
=
n
e
−
n
o
, is generally great, say, about 0.1. Due to the
thermal fluctuation, the optical axes of nematic molecules always vary from
point to point and from time to time. The effect of this phenomenon is much
more significant than the density fluctuation. Little energy is required for
causing the fluctuation of the optical axes of nematic molecules, so that the
thermal fluctuation of the refractive index is significant even at the ambient
temperature. This effect results in strong light scattering. The cross-section
of light scattering in the nematics is expressed by
∝
ε
a
|
δ
n
(
k
)
|
2
σ
N
,
(1.4)
where
ε
a
is the optical dielectric anisotropy (
ε
−
ε
⊥
),
i.e.
, the difference
of dielectric constants parallel and perpendicular to the optical axis.
δ
n
(
k
)
is the Fourier transformation of the optical axis fluctuation
δ
n
(
r
). The
detailed calculation gives the statistical average of
2
|
δ
n
(
k
)
|
as follows
Vk
B
T
Kq
2
2
|
δ
n
(
k
)
|
∝
,
(1.5)
where
K
is an elastic constant associated with the change of optical axis.
According to the estimate made by de Gennes (1973)
K
∼
U/a
and
U/a
3
(
a
is the molecular dimension, about 1 nm,
U
is the binding
energy),
q
is the difference between the incident and scattering wave-vectors
of light. 2
π/q
is about the order of visible light's wavelength. Suppose
ε
∼
B
∼
1, thus the ratio of scattering cross-sections of nematic liquid
crystal and isotropic liquid is
σ
N
σ
I
∝
ε
a
∼
ε
a
ε
2
B
Kq
2
≈
1
(
aq
)
2
≈
10
5
-10
6
.
·
(1.6)
The ratio reaches up to one million times. This explains why the liq-
uid crystal is in fact very turbid while ordinary liquid is transparent.
The light scattering varies for different phases of the liquid crystals. For
example, owing to the suppression of molecules into layers the light scat-
tering of the smectic A phase is less than the nematic liquid crystal. For
the smectic C phase, the fluctuation of the projection of tilted molecules
onto smectic layers (the c-vector) causes stronger scattering than that in
the smectic A phase.
The above analysis is one example of the anisotropic properties of liquid
crystals. It is these anisotropic properties that make liquid crystals and
provide for its wide applications.
