Biomedical Engineering Reference
In-Depth Information
10
6
10
5
10
4
10
3
Gellan K
+
Gellan Na
+
Agarose
Gelatin
10
2
10
1
10
0
0
5
10
c
(wt %) of polymer
15
20
25
Comparison between storage moduli for agarose, gelatin and gellan at various polymer
concentrations. Adapted with permission from Clark et al.(
1983
) © 1983 American Chemical
Society, and from Milas and Rinaudo (
1996
) ©1996 Elsevier.
Figure 7.24
horizontal and vertical scaling factors. The horizontal factor largely re
ects the value of the
critical concentration c
0
, which in this case is around 0.17%w/w for agarose and 1.2%w/w
for gelatin. As discussed in
Chapter 3
and elsewhere, the value of c
0
is by no means
universal
for example, it is lower for a sample of mammalian gelatin formed at 5°C than
for the same sample formed at 20°C, and will also depend upon the cooling regime.
However, even with appropriate horizontal scaling, the data for gelatin and agarose
will never superimpose because it appears that the modulus of an agarose gel is
substantially greater at the same value of c/c
0
. In most approaches this can be attributed
to differences in the
-
fibrillar structure of agarose and gelatin, as we discuss below. For
more rigid network structures such as agarose, elasticity is very unlikely to be entropic.
In other words, the contribution per cross-link comes from bending and twisting
contributions, which raise the enthalpy of the system. Consequently we adopt the
term
and, in one approach, assign its contribution to a generalized front
factor, sometimes denoted a, which for agarose is estimated to be
'
enthalpic
'
10 (Clark and Ross-
≳
Murphy,
1987
).
Because of the careful work on gelatin described above, the generalized behaviour of
shear modulus on helix concentration is now
firmly established. However, without
further hypotheses this does not tell us what we need to know to establish the concen-
tration of junction zones, and without this no a priori estimate of the shear modulus can be
made simply from the available structural information. The contribution of the local
rigidity of junctions in the elasticity of rubber-like networks is not elucidated.
The mesh sizes for agarose and gelatin gels at equal concentration (c ~ 2 wt%) are,
respectively, 100 nm and only a few nanometres; the latter contains an entangled network
with both triple helices and coils. The
fibrils in agarose gels are rigid and non-entangled;
therefore, without modi
cation the models proposed for gelatin should not apply to
agarose. In the latter case, the rigidity of the network comes from both:
*
long and rigid rods with variable thicknesses, constituted from the aggregation of
double helices
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