Biomedical Engineering Reference
In-Depth Information
−
0.10
(a)
(b)
140
PBLG-DMF
120
−
0.05
100
I
LC
I
80
0
60
LC
40
LC + LC
0.05
20
0
I + LC
0.10
I + LC
−
20
−
40
0.15
0
0.2
0.4
0.6
0.8
1.0
0
0.2
0.4
0.6
0.8
1.0
φ
φ
Flory
s theoretical prediction for rods in solution (a), compared with experimental phase diagram
for poly(benzyl l-glutamate)
'
Figure 3.14
dimethylformamide (PBLG-DMF) system (b). From Miller et al.
(
1978
) with permission from John Wiley & Sons.
-
Here
ϕ
nem
are the respective critical volume fractions of the limit concentrations
of isotropic and nematic phases. For volume fractions lying between
ϕ
iso
and
ϕ
iso
and
ϕ
nem
there is
a transitional region which can display some nematic character.
Flory solved the same problem with a lattice model (Flory,
1956
), and his solution
predicts higher values of the two critical volume fractions:
8
12
:
5
iso
≈
D
;
nem
≈
D
:
ð
3
:
36
Þ
L
=
L
=
Extensions such as those by Warner and Flory (
1980
) and Khokhlov and Semenov (
1982
)
have included a degree of
flexibility via, for example, the worm-like chain model. Such
effects tend to increase the critical values of
in the
numerators. Qualitatively all these predictions are useful, although they have proved to
be quantitatively imprecise. This is partly because few macromolecules are even close to
rod-like, and partly because the theories neglect the polydispersity of M
w
(or length). Both
factors act to increase the critical
ϕ
,byincreasingthe
'
constant
'
ϕ
s. However, the Flory theory makes the useful assertion
that no isotropic
-
nematic transition can occur unless L/D
≳
6. He was able to calculate a
'
'
new phase diagram, distinguished by the so-called
shown in
Figure 3.14
.
Miller made a series of measurements at various concentrations and temperatures, and
his results showed qualitative agreement with Flory
chimney region
'
s predictions, including an apparent
'
s work by investigating the rheology of a range of
values for PBLG concentration and M
w
, particularly in benzyl alcohol (Sasaki et al.,
1983
). These gels were extremely fragile and tended to
chimney
'
. Sasaki extended Miller
'
flow at strains above a few
percent. This and subsequent work strongly suggests that the gel structure is not linked
directly to the tendency to form liquid crystals. Miller suggested that the gelation is a
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