Helical structures from neutral biopolymers - Physical Gels from Biological and Synthetic Polymers - page 199

elasticity is extremely sensitive to the helix fraction. As soon as the helix fraction passes
beyond the threshold, the shear modulus becomes almost independent of frequency and
increases progressively with helix growth. The loss modulus also increases with time
before the gelation threshold, as expected. G 00 is frequency-dependent but the low-

frequency (Newtonian) limit G 00 / cult to access because G 00 corresponds to a

small value in this limit, and the kinetics of helix formation continues.
In all the theories discussed in Chapter 3 , the elastic modulus increases with the
fraction of bonds. If we assume that the helix fraction can be compared to the fraction
of cross-links (bonds), a power-law dependence is expected for the elastic modulus
versus distance to the gel point:

ω is dif

t

χ
χ c -

G 0 ≈

1 ; χ > χ c : ð 7 : 4 Þ

cant assumption in itself, since what really matters is not the proportion of
residues in the helical conformation but the number and distribution of helices, but it is
reasonable to assume the two are proportional when

This is a signi

χ ~ χ c . The exponent t for elasticity

de <0.1 (Djabourov et al.,

1988b ) which corresponds to that of a random network of resistors in the percolation
theory, while in the classical Flory

ned in Chapter 3 is found here to be t = 1.8 ± 0.1, in the range ε

Stockmayer approach, it should be close to t =3.This
still suggests that, despite the complexity of the local helical structure ( Section 7.2.6 ),
percolation type theories provide a simple framework for interpreting elasticity if the
proportion of triple-helical residues is identi

-

ed with randomly distributed, permanent
cross-links. The relation between elasticity and structural parameters is insensitive to the
kinetics of helix growth, which varies strongly with temperature.

7.2.7.2 All gelatin networks

In the case illustrated, the sol

gel transition showed a very simple correlation. On the
other hand it is known that many different gelatin samples exist, with various origins and
molecular masses. Various thermal treatments can also be applied and they are likely to
modify the distribution of the helical sequences, as shown before. Is the storage modulus
always simply related to the helix fraction? What is the effect of molecular mass,
concentration or other parameters? These aspects are examined below.

-

Concentration dependence of the shear modulus
For many years it was known that the shear modulus increases with concentration, but it
also depends on the temperature and time. Consequently the variation is not just the
commonly reported c 2 dependence, and temperature also plays a role in the Eldridge -

Ferry (EF) model ( Chapter 3 ). Although gelatin gels are not in an equilibrium state, the
EF approach is still useful, and is widely employed. However, it is important to point out
that the commonly reported c 2 proportionality will hold only away from the critical
concentration (say, c >5c 0 ) where, in practice, the majority of experiments have been
performed; as c approaches c 0 from above, the apparent exponent will increase very
markedly.