Chemistry Reference
In-Depth Information
The free energy in the nematic phase is
=ln
1
−
1
exp[
βaSP
2
(cos
θ
)] sin
θdθ
+
aS
2
2
F
Nk
B
T
.
(2.72)
The last term avoids double counting of the pair interaction in the mean
field theory.
At the transition, the free energy of both nematic and isotropic phases
are equal.
The latent change at the N-I transition is
=
aS
c
2
T
c
∆
E
(
T
c
)
N
=3
.
47 J/mol. K
.
(2.73)
It is illustrated that the N-I transition is of first order. Experimentally,
the latent entropies of small molecular mass liquid crystals, ∆
E
(
T
c
), are
very diverse, ranging from 1.25 to 7.55 J/mol. K. Most fall in the range of
2.50-3.35 J/mol. K. The Maier-Saupe prediction for the latent entropy at
transition is in reasonable agreement with experiments.
It is worthwhile to point out that the Maier-Saupe theory has been
successful in analyzing the behavior of small molecular mass liquid crystals
at transition, such as the temperature change of the order parameter. The
jump of the order parameter at transition,
S
c
=0
.
43 is in reasonable agree-
ment with most experiments. The Onsager and Flory theories, which take
into account the steric effects predict a higher critical order parameter.
2.4.2.
Freely-jointed-rod chains
In a very crude sense, liquid crystalline polymers can be regarded as a
freely-jointed-rod chain, shown in Figure 2.16. The freely-jointed-rod chain
consists of a series of repeated segments of length
l
0
. Each segment is able
to rotate freely. It is assumed that the freely-jointed-rod chain is a replica of
its small molecular mass liquid crystal counterpart in the liquid crystalline
properties.
2.4.2.1. Liquid crystallinity
The application of the Maier-Saupe theory to the polymer system results
in the nematic to isotropic (N-I) transition temperature,
T
c
, the order
