Biomedical Engineering Reference
In-Depth Information
1
0.9
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
N
= 400
R
= 50
R
= 55
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
χ
0
T
0
= 767 k
0
5
10
15
20
25
30
T
(
°
C)
Figure 7.10
Computed values for helix fraction versus temperature.
χ
0
is the helix fraction at the end of the
rst step,
χ
equil
is the hypothetical value reached after infinite time, if the long maturation process
were to be completed. Various values for R are represented on the graph, highlighting solution
concentration effects. Adapted from Djabourov et al.(
1988a
) with permission from EDP Sciences.
step,
χ
equil
(T) can be computed from the statistical model and behaves as a step-like
function within a narrow temperature range, similar to the denaturation curve of native
collagen. This means that the upper limit will always be lower than 100%.
The broad outline of the gelation of gelatin solutions is now accepted as being uniquely
related to the renaturation of the collagen type triple helix, unlike ionic-induced gelation
in polysaccharides, where the mechanisms are still debated as they touch upon on both
conformation and aggregation effects (
Chapter 5
). A similar problem is encountered in
agarose gels (see below). The conformational change in gelatin is determined by the
nature and composition of the collagen. In practice, the total fraction
χ
of renatured
helices may reach 0.75, but will still increase in time, at a
xed temperature. Indeed,
since it has never been observed to reach a limit, it can be argued that the gel does not
have an equilibrium helix fraction at less than 100%, and that this is a value that will
never be reached for the reasons above. In practice, the helix fraction in a typical gel is
around 20
-
40%.
7.2.7
Rheology of gelatin gels
7.2.7.1
The sol
gel transition
The rheology of gelatin gels has been widely investigated in the past; a
-
first reference is
that of Leick (
1904
), who measured birefringence induced under elongation and who
suggested that the elastic modulus of the gels varies with the square of gelatin concen-
tration. In 1948, Ferry published a review on protein gels (Ferry,
1948
), in which he
reported that the rigidity (shear modulus) of gelatin gels varies as the square of the protein
concentration, and that it decreases with increasing temperature and with decreasing
average molecular mass. In a subsequent paper, Ferry and Eldridge (
1949
) reported
optical rotation measurements on solutions versus temperature, where they concluded
that speci
'
...
cOR
is primarily related to intramolecular cross-links
while a
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