Biomedical Engineering Reference
In-Depth Information
(
Chapter 8
),
κ
-carrageenan (
Chapter 5
) and even mixed gels, such as konjac gluco-
mannan and
-carrageenan, where differential scanning calorimetry (DSC) melt traces
are particularly broadened. The model predicts the gel
κ
sol transition temperatures by
means of the zipper mechanism and includes concentration effects. It also predicts a
hysteresis between setting and melting temperatures.
-
3.9
Liquid crystal gels
One
final aspect of the sol
-
gel transition which needs to be mentioned here involves
those
, which occur quite widely, formed from liquid crystalline materials. Liquid
crystals show behaviour intermediate between that of a liquid and that of a crystalline
solid: they will
'
gels
'
flow and even statically, they tend to show birefringence,
indicating an underlying crystalline type order.
Many of these materials are formed from low molecular mass surfactant systems, and
are largely outside the scope of this monograph. However, lyotropic liquid crystal gels
can also be formed from polymeric systems, particularly from high molecular mass
'
ow but, under
by which we mean polymers of high persistence length. Such materials can form
from many different molecular species, and some are discussed in other chapters, for
example xanthan (
Chapter 5
) and protein
rods
'-
fibrillar systems (
Chapter 9
). However, the best
exemplar and among the most carefully studied, are the so-called Miller gels, formed
from poly(
, l-glutamate) (PBLG) in various solvents including benzyl alcohol
and dimethylformamide (DMF), studied by Miller and co-workers (Miller et al.,
1978
;
Tohyama and Miller,
1981
). PBLG is helicogenic in these and some other solvents; that is
to say it readily forms a single-chain
γ
-benzyl-
α
-helical conformer.
At this point, and particularly since this section is positioned in the sol
α
-
gel transition
chapter, it is important to point out that these
-
viscoelastic liquids, i.e. they have no equilibrium modulus, and can also sustain a steady
shear
'
gels
'
are usually
-
rheologically at least
flow, either at long times or at higher stresses and strains, without rupturing.
The formation of complex, optically anisotropic structures from rods was well known
to Onsager in his 1949 paper (Onsager,
1949
). He examined the behaviour of rod-like
systems which mutually exclude one another
disorder transition is
driven by a competition between orientational entropy (minimized by an isotropic
distribution of rods) and translational entropy (minimized by a parallel array of aligned
rods). He established that there can be a net reduction in overall entropy if a set of rods
undergoes a transition to a state where they are aligned more or less parallel to one
another. Then, above some critical volume fraction, an isotropic solution of rods will
show a spontaneous phase transition to a nematic phase. This critical volume fraction
depends on the ratio of length L to diameter D of the rod, and also on the precise form of
the rod, but if L >> D the approximate solutions give
'
is volume. The order
-
3
:
3
4
:
5
iso
≈
D
;
nem
≈
D
:
ð
3
:
35
Þ
L
=
L
=
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