Biomedical Engineering Reference
In-Depth Information
10
5
10
4
pH
=
2
10
3
pH
=
3
pH
=
7
10
2
10
1
0
2468
10
c
(wt%)
12
14
16
18
Observed log modulus versus log concentration for three
β
-Lg gels: at pH= 7 (particulate,
■
) and at
pH= 3 (ne-stranded,
●
), adapted from Kavanagh et al. (2000c); and at pH= 2 (amyloid strands,
▲
), adapted from Veerman et al. (2002a). © American Chemical Society.
Figure 9.8
As pointed out in
Chapter 3
and elsewhere in this volume, two of the most fundamental
parameters which need to be acquired for all the above systems
-
not least to establish
whether or not we have a gel or a sol
are c
0
and the modulus concentration dependence
exponent. Values of c
0
for these materials are typically 1
-
15%, and tend to decrease with
increasing ionic strength or more extreme preparation conditions (i.e. heating to 80°C
rather than 60°C) (Clark,
1998
). What is clear is that, in general, c
0
values are higher by as
much as two orders of magnitude than those found, for example, for
-
fibrous polysaccharide
gels, and higher even than typical values for gelatin gels. That said, as we mentioned above,
the fundamental
fibrillar structure is much larger
-
say, 3
-
5nminwidth
-
than for most of
-
the polysaccharide systems
typically an order of magnitude lower.
Figure 9.8
shows a comparison between three types of
β
-Lg heat-set acid gels at three
different pHs: pH 2 from Veerman et al.(
2002b
) and pH 3 and pH 7 from Kavanagh
et al.(
2000c
). In the
first case, solutions were heated at 80°C for 10 h and subsequently
cooled to 20°C for 2 h. After this procedure a strain sweep was performed. In the latter
two solutions, gelation was studied at 80°C for times of up to 6 h. Differences in the
heating protocol and ionic strength are likely to in
uence any observed differences in c
0
and concentration exponent, and any correlation with the morphology and
flexibility of
the aggregated structures. This
figure illustrates the challenge in interpreting the rheo-
logical properties of these protein gels, clearly showing that polymer concentration alone
is not suf
cient to determine the value of the shear modulus.
Reported values of the concentration exponent tend to vary widely, many clustering around
2
2.5 but both lower and higher values being reported (Clark and Ross-Murphy,
1987
). We
would not expect a single exponent to describe the concentration dependence over a wide
range. It is true that at high concentrations
-
particularly when expressed as c/c
0
,say>10c/c
0
-
an apparent limit exponent is reached. Equally, as we approach c
0
, higher and higher apparent
exponents are seen, since here the log G
0
versus c plot tends to a pronounced curvature.
-
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