Chemistry Reference
In-Depth Information
In Figure 2.34 where
T
(
s
)
ni
= 0, the N branch of the free energy is defined
only to a lowest
φ
since the nematogetic network is diluted with a non-
nematic solvent. If we dilute with a nematic solvent it is possible for the
nematic branch of
F
to extend all the way to
φ
=0if
T<T
(
s
)
ni
.If
T
(
s
)
ni
>
T>T
(
x
)
ni
, the nematic branch of
F
may extend from
φ
= 0 to a maximum
with
φ<
1. How far it can be extended depends partly on how much greater
T
is than
T
(
x
)
ni
as well as on the cross-coupling
v
c
.
The precise structure of the phase diagram depends on the rela-
tive strengths of the couplings, more precisely on the coupling matrix
v
a
. We will now consider a variety of representative examples of
v
c
v
c
v
b
self and cross couplings and their effect on the phase diagrams.
First of all, we will treat the simple case where det(
v
)=0,
i.e.
,
v
c
is the
geometrical mean of the self couplings and, except for unusual molecules,
it approximates the order of that expected for a van der Waals mediated
nematic interactions. Next, we will deal with more unusual behavior where
det(
v
)
<
0 and det(
v
)
>
0, respectively.
In all that follows we shall reduce all coupling constants by
v
a
, that is
when (
v
a
,v
b
,v
c
) are quoted they will be quoted as (1
,v
b
/v
a
,v
c
/v
a
). Tem-
peratures will be reduced by the transition temperature of pure solvents
which is at
T
red
=0
.
22
v
a
/k
B
T
. As a result, in this reduction scheme, the
neat solvent has its transition at
T
=1.
Phase diagram with det
(
)=0
Figure 2.35(a) shows the phase diagram for
v
c
=1
.
1 and thus
v
b
=1
.
21,
that is where the network is a stronger nematic than the solvent. The
strand length
L
= 10 and the isotropic Flory-Huggins parameter
χ
=0
.
4,
correspond to a good solvent. These values will be used through out this
section.
It is shown qualitatively, as in Figure 2.35(a), that the I-N phase coex-
istence extends downwards from the transition at
T
=1
.
21 of the neat
network. There is a triple point i-I-N.
If the network is less nematic than the solvent with
v
c
=0
.
9 and thus
v
b
=0
.
81. Now the N-I coexistence extends upward from the neat net-
work's transition at
T
=0
.
81. Diluting with such a solvent stabilizes the
nematic phase of the network against a temperature increase. The triple
point is now n-N-I, instead and from this point upwards to
T
= 1, there is
n-I coexistence. The vertical phase “chimney” (i-I) extends above
T
=1.
Figure 2.35(b) shows the opposite limit.
v
