Chemistry Reference
In-Depth Information
First we introduce the isotropic interaction which results from the
mixing of rods and solvents. The previous theory, without the mixing con-
tribution to entropy, is only applicable to an athermal system. If there
is a mixing entropy contribution, the free energy in Equation 2.39 is
implemented by a term
χφn
s
, where
χ
is the Flory-Huggins interaction
parameter. Flory called the mixing term the isotropic “soft” interaction to
distinguish it from the steric interaction of rods.
At the coexistence of the two phases the chemical potentials of the rods
and solvents in both the liquid crystals phase and isotropic phase must be
equal and thus the following set of equations for
φ
,
φ
and
y
holds
φ
)+
φ
1
+
χφ
2
φ
)+
φ
(
y
−
1)
+
2
1
x
y
+
χφ
2
= ln(1
ln(1
−
−
−
x
ln
φ
x
+
φ
(
y
2ln
y
x
+
χx
(1
φ
)
2
−
1)+2
−
−
=ln
φ
x
+
φ
(
x
φ
)
2
.
−
−
1) +
χx
(1
(2.52)
Figure 2.8 shows the numerical result of the rod/solvent system for the
rod axial ratio
x
= 100.
The ordinate is the Flory-Huggins parameter
χ
and the abscissa is
the volume fraction of rigid rods. For negative
χ
, the two phase equilib-
rium is basically independent of
χ
. A positive
χ
has a significant effect
on the two-phase equilibrium. The diagram can be divided into three
regions: in Region I the concentration is small and the system is in a single
isotropic phase; in Region II the system is in the liquid crystal phase; and
in Region III both the liquid crystal and isotropic phases coexist. For
χ
less
than, say, 0.07, the region of biphasic coexistence is narrow,
φ
∗∗
/φ
∗
=1
.
5.
For
χ
greater than 0.07 the volume fraction difference between the two
phases becomes larger.
Figure 2.9 shows the experimental results of the PBLG/dimethyl
formamide(DMF)-methanol system (Nakajama
et al
., 1968). The axial
ratios were 150 and 350, respectively, and the
χ
value was controlled by
varying the concentration of methanol. The more methanol the greater is
χ
.
It was shown that for small concentrations of methanol, the biphasic range
is narrow. As the volume fraction of methanol increases (up to 0.10-0.12)
the biphasic range becomes wider.
