Chemistry Reference
In-Depth Information
1.2. APPEARANCE AND LIGHT SCATTERING OF
LIQUID CRYSTALS
The liquid crystal state is a state of matter which is different from the liquid
and solid states. Liquid crystals can flow as a liquid does. Typically, the
viscosity of the liquid crystals such as the nematic liquid crystal is in the
order of magnitude of 1
10
−
2
Pa.s., a value greater than that of water
×
10
−
3
Pa.s. Some liquid crystals, such as high
order modifications — smectic liquid crystals, are very viscous. A liquid is
transparent, but a liquid crystal is normally milky. This is because the
fluctuation of the orientation of the molecular long axes of the liquid crys-
tals causes strong light scattering. The scattering of liquid crystals is as
high as one million times that of conventional isotropic liquids. The milky
appearance becomes one of the identifications of the liquid crystals.
As we know, the scattering of matter is caused by the fluctuation of their
refractive index (or optical dielectric constant). The local compression or
dilution of mass density in bulk isotropic liquids modifies in turn the local
refractive index. The change can be expressed in the form of the dielectric
constant as
×
whose viscosity is about 1
ε
(
r
)=
ε
+
ε
φ
(
r
)
,
(1.1)
where
ε
is the average dielectric constant,
φ
(
r
) is the bulk compressibility
and
r
is the distance vector of a point in the material,
ε
is the fluctuation of
the dielectric constant. According to light scattering rules, the cross-section
of light scattering of isotropic liquids,
σ
I
,isgivenby
ε
2
2
σ
I
∝
|
φ
(
k
)
|
,
(1.2)
where
φ
(
k
) is the Fourier transformation of
φ
(
r
), and
indicates the
statistical average. The average in the bracket can be written as
...
=
Vk
B
T
B
φ
(
k
)
2
|
|
,
(1.3)
where
V
is the volume of the sample, 1
/B
is the isothermal compressibility
coecient, and
k
B
is the Boltzmann constant.
Liquid crystals are optically anisotropic media with the exception of the
cubic phases, such as the D-phase and blue phase. The refractive index or
dielectric constant of liquid crystals varies according to the orientation of
the molecular axes (or the optical axes). For example, the nematic liquid
crystals are optically uniaxial and exhibit remarkable birefringence, that
