Chemistry Reference
In-Depth Information
Figure 2.6.
Phase diagrams for various rod axial ratios. (From Flory & Ronca, 1979a.)
and Equation 2.43, where
φ
and
φ
are the volume fraction of rods in the
liquid crystal and isotropic phase, respectively.
For various axial ratios
x
of the rods the numerical solutions of the above
set of equations are summarized in Figure 2.6.
The following important conclusions can be obtained from Figure 2.6:
(1) Those rigid molecules capable of showing a stable liquid crystal phase
must have the axial ratio greater than
x
=6
.
7. This value is some-
what greater than the estimated value of
x
=5
.
44. We have emphasized
that the estimate of the minimum axial ratio for forming a liquid crystal
phase (
x
=5
.
44) is that at which the partition function starts to take a
maximum.
(2) At the equilibrium state, the volume fraction of rods in the two phases
decreases as the axial ratio
x
increases. The volume fraction of the
liquid crystal phase is slightly greater than that of the isotropic phase,
the ratio between these two critical volume fractions increases with
increasing
x
, but is always less than 1.56.
For enough large
x
, the critical volume fractions are respectively
8
x
,
φ
∗
=
12
.
5
x
φ
=
.
