Chemistry Reference
In-Depth Information
The above analysis may be summarized with Figure 4.9 and Malus'
equation which relates the intensity
I
of the light detectable by POM. In the
equation,
d
is the thickness of the sample,
d
∆
n
is the relative retardation,
and the angle Ψ is defined by Figure 4.9. PP
and AA
are the vibration
directions of the polarizer and analyzer. FF
is the vibration direction of
the faster ray (ordinary ray in a positive uniaxial liquid crystal). SS
is that
of the slower ray (extraordinary ray in a positive sample). Thus, if
d
∆
n
is
by chance equal to
mλ
(
m
is zero or integral number), the intensity will be
null independent of the angle Ψ even if it is 45
◦
. The angle 45
◦
is what
makes the second sinusoid in the equation the highest value. On the other
hand, if
d
∆
n
happens to be (
m
+1
/
2)
λ
, the intensity will be the highest
whenΨis45
◦
.
In most characterizations the incident light is practically white rather
than monochromic. This often makes the image of a liquid crystal very
colorful. For example, if
d
∆
n
is 400 nm, that is
λ
of the violet band, the
violet band will be extinguished. The color showing will be the compensative
orange. If
d
∆
n
is 700 nm (about
λ
of the red), the color will be blue.
Obviously, the observed color of interference relates to the thickness and
the birefringence of the sample. With an increase of the thickness the color
will become more and more faint because of the increased overlapping of
the extinguished bands. The thickness is practically 10-100 microns in most
POM studies.
4.1.3. Conoscopic observation
In conoscopic observations (Figure 4.4(b)), it is not the image of the sample
but the interference figure that is observed through the eyepiece when the
Bertrand lens is inserted. In this case the parallel rays which have passed
through the sample in any given direction are brought to a focus of the upper
lens of the eyepiece. Conoscopic observations are used to determine the
uniaxial or biaxial character of liquid crystals. A homeotropic liquid crystal
which is extinct under orthoscopic examinations can be differentiated from
isotropic liquids with conoscopic studies. The positive or negative nature of
the sample may be determined by this technique also.
While in orthoscopic studies the parallel incident lights are desirable,
in conoscopic examinations high-aperture condenser and objective are used
so that a wide-angle cone of light is allowed to pass through the sample.
The cone is composed of bundles of parallel rays along different directions.
