Biomedical Engineering Reference
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comparatively small number of intermolecular links is responsible for the rigidity of
gels
. Following this, they published a paper (Eldridge and Ferry,
1954
) which became a
reference in the
'
field of gel rheology, proposing their model for the elasticity of gelatin
gels, relating the melting temperature of the gels to protein concentration and molecular
mass. They assumed that the cross-links of the gel were formed by binary association
between chains, although their model was devised while the exact structure of the gelatin
junctions was still unknown, since the triple-helical structure of native collagen was not
revealed until the following year (1955); see Section 7.2.2.
Since that time, the sol
gel transition has been reanalysed using a number of
percolation type models (
Chapter 3
). To relate the small-deformation rheological
properties to structural parameters, it is obviously necessary to have some model of
the network structure. Unfortunately the length of the overall helical
-
is
unknown, although their width (at around 1 nm) corresponds to that of the tropocolla-
gen triple helix. The most reliable techniques for determining the helix fraction
'
junction zones
'
-
optical rotation and DSC
are both essentially short distance scale methods, so they
cannot identify the length of the helix, only the number of residues in the helical
conformation.
However, because gelatin gelation is a kinetic process, it is important to follow
identical paths for the structural and rheological investigations. As the physical junctions
are fragile, gelation can only be investigated by limiting the strain, rather than the stress,
to very small values (less than a few percent). Extensive investigations on the time and
temperature dependence of dynamic moduli of gelatin gels have been performed by te
Nijenhuis (
1981a
,
1981b
), who established that an
-
was necessary before
the storage modulus starts to increase. He found that this time is short (1min) at low
temperatures (1
'
induction time
'
2°C), whereas it increases to about 8 h at 25°C, and found a maximum
gelation temperature of ~27°C.
Such important changes of the viscoelastic moduli within a narrow range of temper-
atures cannot be understood without parallel investigations of the conformational
changes.
Figure 7.11
shows that both measurements (rheology and optical rotation)
can be performed with great accuracy during ageing, after a rapid quench from hot
solution to a lower temperature, between 24°C and 28°C, using two independent
temperature-controlled baths.
Figure 7.11a
shows that the helix fraction increases at
different rates, as was already mentioned in the
previous section
;in
Figure 7.11b
the
increase of shear modulus with time at a
-
fixed frequency is displayed. Obviously, there is
no direct proportionality between these two measurements, so it is interesting to elimi-
nate the time parameter and plot shear modulus versus helix fraction, for the various
temperatures. This is shown in
Figure 7.12
.
The parameter de
corresponds to a thresh-
old in the helix fraction, after which the elastic modulus starts increasing. The threshold is
close to
ned by te Nijenhuis as an
'
induction time
'
χ
c
= 0.07 in the example shown in
Figure 7.12
, and is reached in 7 min at
T = 24°C and in 214 min at T = 28°C. The existence of a critical threshold is predicted by
all percolation type theories, but the surprising result is that all data collapses to a single
curve, even though these correspond to very different rates of nucleation and growth of
helices. The threshold is very low for a low-concentration system, meaning that the
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