Chemistry Reference
In-Depth Information
Figure 4.25.
DSC heating curve of a biphasic sample of
4
.
5
showing T
N-I
=
97
◦
C
,
T
C-I
= 103
◦
C.
vacancy will be filled by an electron falling from a higher energy shell (L, M,
etc
.). Since the energy levels of the different shells are quantized, a coherent
ray is emitted in the form of an X-ray photon with energy equal to the differ-
ence in energy levels of the two shells. The X-rays resulting from the fall of
electrons from the L and M shells into the K shell are known as K
α
and K
β
radiations. The K
α
radiation of Cu has a wavelength of 0.154 nm. It is most
frequently used in X-ray diffraction studies on polymers and liquid crystals.
The information obtainable from X-ray diffraction studies includes degree
of crystallinity, crystal lattice, crystal size, molecular orientation, and vari-
eties of structural defects. For liquid crystals, it is widely used to identify
a smectic phase from a crystal, a nematic liquid, and other smectic phases.
X-rays are diffracted at crystal planes since the distance between the
planes is comparable to the wavelength of the X-ray. The X-ray diffraction
conditions may be illustrated by Figure 4.26.
As depicted in Figure 4.26, the path difference between waves reflected
by the two-neighboring lattice planes is 2
d
hkl
sin
θ
. If the path difference is
equal to the wavelength of the X-ray used, or some integral multiple of it,
the reflected beams are in phase and a constructive interference is formed
between the reflected beams. Therefore, if 2
d
hkl
sin
θ
=
nλ
, an intense
diffracted wave is produced in the direction
S
which is defined by
θ
. The
intensity decreases abruptly with any deviation from the critical value of
θ
because of destructive interference. In polymers the reflection with the
strongest intensity is frequently found for
n
= 1, that is, 2
d
hkl
sin
θ
=
λ
.
The reflection condition can also be expressed in terms of the reciprocal
lattice which is defined as follows. If
a
,
b
,
c
are the primitive translations
of the real crystal lattice, and
a
∗
,
b
∗
,
c
∗
are those of the reciprocal lattice,
then
a
∗
is perpendicular to both
b
and
c
;
b
∗
is perpendicular to both
a
and
c
;
c
∗
is perpendicular to both
a
and
b
. These mutually perpendicular
