Chemistry Reference
In-Depth Information
The contribution from Russian scientists is worthy of special mention.
We will introduce their theory later.
It should be pointed out that to meet the second virial approximation,
molecules must have a large
L/D
so that at the transition the solution
is dilute. For molecules of axial ratio less than 10 the theory does not
work well. In addition, the Onsager value of the density difference at the
nematic — isotropic transition is greater than the experimental data.
Introducing higher virial terms may extend the Onsager theory to
concentrated solutions (Khokhlov & Semenov, 1981).
The Flory theory discussed in the next section is another important
theory on rigid liquid crystalline polymers. Because of its clear picture of
the lattice model and the incorporation of the Onsager theory, it has become
a basic method for the theoretical study of liquid crystalline polymers. As a
result of the constant efforts of Flory and his co-workers, the theory has
been applied to binary and poly-disperse systems and also includes the
“soft” interactions.
2.2.
FLORY THEORY FOR RIGID — ROD LIQUID
CRYSTALLINE POLYMERS
2.2.1.
Partition function of a rigid rod solution
Flory (1956, 1984) adopted the lattice model. The Flory theory starts
with the partition function of systems consisting of rigid rods and solvent
molecules.
Assume the long axis of the rigid rods makes an angle
ψ
with respect
to the director of the system and the director is along one principal axis of
the cubic lattice. Divide each rod into
x
basic units of equal width. Each
basic unit occupies one cell in the lattice.
x
is actually the axial ratio of
the rods. For simplicity, suppose that the dimension of a solvent molecule
is compatible to the size of a cell lattice. In this section we adopt the
same assignations as Flory. These may be different from those used in the
preceding section by Onsager.
In order to put a rod into the lattice, a postulate is made, which suggests
that each rigid rod be divided into
y
sub-particles as shown in Figure 2.4b
y
=
x
sin
θ.
(2.28)
Each sub-particle has
x/y
basic unit and its long axis is along the
director. If a particle is perfectly aligned along the director,
y
is zero. As a
