Chemistry Reference
In-Depth Information
Figure 2.19. N-I transition temperature
T
c
against the chain length
L
. (From Wang &
Warner, 1986.)
Equation 2.110, we obtain the analytical expression for the pseudo-second-
phase-transition temperature (Wang, 1995a)
15
1
e
−
6
l
)
,
2
T
∗
=
−
l/
6
L
(1
−
(2.119)
which is reminiscent of the numerical calculation of the N-I transition tem-
perature
vs.
the chain length or the degree of polymerization, shown in
Figure 2.19.
The N-I transition temperature, or the pseudo-second-phase-transition
temperature, increases as the chain length increases and then saturates to
a finite value when
L/l
is greater than,
e.g.
, about 1.5. Gri
n
et al
. (1989)
and Blumstein
et al
. (1984) found that for a monomer, dimer, oligomer
as well as a polymer with the same building units displaying a nematic
phase, the transition temperature increases with an increasing degree of
polymerization and then rapidly saturates, as shown in Figure 2.20. Good
agreement was found for the above theory and experimental data.
2.5.5.
Latent entropy at transition
Ignoring the temperature dependence of
ε
, as justified by Jahnig (1979),
the latent entropy ∆
E
for a repeat unit at the transition (Wang & Warner,
1986) is
=1
.
69
R
l
l
,
∆
E
(
T
c
)
N
(2.120)
