Chemistry Reference
In-Depth Information
beam intensity is usually not very strong. In addition, the small birefrin-
gence of lyotropic liquid crystalline polymers such as PBLG solution causes
further weaker scattering. Fortunately, advanced instruments have been
applied to improve the measurements.
Meyer's group (Taratuta
et al.
, 1985) designed an experiment in which
the liquid crystalline polymers were sandwiched between two glass hemi-
spheres with the director normal to the scattering plane and the incident
beam polarization parallel to both the director and scattering plane. By
adjusting the sample, the scattering amplitude associated with splay defor-
mation is cos
2
(
θ
s
/
2)
/K
11
q
2
(
θ
s
is the scattering angle) while the twist
deformation is responsible for the term sin
2
(
θ
s
/
2)
/K
22
q
2
. The relaxation
time is given by
τ
α
(
q
)
=
K
α
(
q
)
1
η
α
(
q
)
,
(6.23)
where
η
1
and
η
2
are the viscosities of liquid crystals which are actually
a combination of the conventional intrinsic viscosities. The correspondent
elastic constants are designated as
K
α
(
α
=1
,
2). The viscosity of liquid
crystalline polymers will be discussed in detail in the coming section.
In the second experiment, the geometry is the same as the first one
but for rotating the sample along the surface normal so that the director
is parallel to the scattering vector. Thus the scattering arises from a pure
bend deformation, which is proportional to cos
2
(
θ
s
/
2)
/K
33
q
2
. The sample is
switched between the two geometrical configurations while recording data.
The ratio of scattering amplitudes of the two measurements is expressed by
K
22
tg
2
θ
s
.
K
33
K
11
+
K
33
(6.24)
2
By varying the scattering angle one can evaluate elasticity ratios
K
33
/K
11
and
K
33
/K
22
, and accordingly
K
11
/K
22
. Tables 6.5 and 6.6 list
the elasticity ratio of PBG at the volume fractions
φ
=0
.
16 and 0.20 against
the average molecular weight and the degree of polymerization (Lee and
Meyer, 1988, 1990).
These data demonstrate that
K
11
and
K
33
are roughly the same and
are all are greater than
K
22
by an order of magnitude.
K
33
/K
11
increases
initially with an increasing degree of polymerization and then decreases.
Assuming
K
22
constant,
K
11
is approximately proportional to
L/D
while
K
33
increases initially and then saturates at about
L/D
= 50. The per-
sistence length of PBG falls in the range of about
q/D
= 50-100. For a
