Biomedical Engineering Reference
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temperature at 75°C and 80°C. The results were qualitatively similar to those found
around pH 7, but the critical concentrations were typically lower, with good cure data
being measured around 8% w/w and extrapolated values of the critical concentration c
0
being found around 5
6%.
Gosal et al. analysed the results in terms of both a constant power law fractal approach
(Bremer et al.,
1989
,
1993
) and a classical branching model (Clark and Ross-Murphy,
1987
; Clark et al.,
2001
). The range of concentration data was quite limited
-
-
by practical
considerations
over the range 8% to 14%, so it could be described equally well by either
of the models. It was argued, however, that the fractal description appeared inconsistent
with the uniform
-
fibrillar networks expected for such
fine-stranded protein gels, these
networks being unlikely to be self-similar over a signi
cant length scale.
An analysis was carried out to evaluate critical exponents, using a method due to van der
Linden and Sagis (
2001
). They suggested that the power-law exponent
γ
for gel formation
1)
γ
), for a variety of protein systems, belongs to
ned as the exponent in G
0
~(c/c
0
-
(here de
acertain
~ 1.7. This method requires knowledge of c
0
,but
the technique employed calculates this at the same time as the exponent
'
universality class
'
which gives
γ
.
Analysis of the data in the Gosal paper used a different method and produced a good
γ
fit, with the parameter
γ
lying in the range 2.2
-
2.8. Within this region there did not appear
γ
to be any obvious discontinuity in
values, even though data was used from pH 2 to pH 7
corresponding to the structural transition from essentially
fibrillar systems to increasingly
colloidal or particulate ones. Other analyses in the same paper produced a variety of
estimates, typically 2.7 ± 0.5. Unfortunately this covers almost all the expected range,
including the classical value of 3. As pointed out in
Chapter 3
, such approaches are very
testing
perhaps too testing for the experimental data currently available.
Another technique of considerable value is particle tracking microrheology (PTM)
(Corrigan and Donald,
2009
), introduced in
Chapter 3
. Using PTM, gels were observed
to form at signi
-
cantly lower concentrations than determined by bulk rheometry, where
the authors claim oscillatory shear forces may disrupt either
fibril or network formation.
This result has important consequence, although, as we pointed out in
Chapter 3
, the
strain and frequency regimes employed in PTM are rather different from those used in
small-deformation oscillatory testing.
As far as large-deformation data is concerned, there is very little on
protein
systems, simply because of the requirements for tens of grams of sample. In one study, WPI
(a mixture of
'
pure
'
-Lg and other milk proteins) was used to form translucent heat-induced gels.
Those gels formed at pH 7.0 and 6.5 were classi
β
ed as
'
strong
'
(they had fracture stresses
of ~60 kPa) and
(fracture strain > 1.2), whereas gels formed at low pH generally
had lower fracture stresses (1
'
rubbery
'
0.7) (Errington and
Foegeding,
1998
). Although this behaviour is observed in a number of other studies, it is
fair to say that comparison has not, in our perception, been made under comparable
conditions. For example, if the materials had the same low deformation modulus, then
fracture measurements might be easier to compare. Interestingly, few if any studies have
examined the area under the failure stress/strain curve. Recent work by van den Berg and
co-workers (van den Berg et al.,
2007a
,
2007b
,
2008
) has tried to correlate failure proper-
ties with macroscopic and microscopic appearance for a range of gel structures.
-
15 kPa) and fracture strains (0.3
-
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