Helical structures from neutral biopolymers - Physical Gels from Biological and Synthetic Polymers - page 200

40

(a)

35

10 4

30

10 3

25

20

10 2

15

10

10

5

1

0

0 5000 10000 15000 20000

Time (s)

(b)

10 4

10 3

G ′

10 2

c = 2% g cm − 3
c = 4.5% g cm − 3
c = 8% g cm − 3

G G G G

10

G ″

G ′ G ″

1

0 0.01 0.02 0.03

c helix (g/cm − 3 )

0.04 0.05

Storage and loss moduli versus time for three gelatin concentrations: 2% w/v, 4.5% w/v and 8% w/v:
(a) time dependence of the shear moduli (1 Hz, sample A1) during cooling and annealing; (b) relation
between the shear moduli and helix concentration during experiments shown in (a). Adapted from
Joly-Duhamel et al.( 2002a ) © 2002 American Chemical Society.

Figure 7.13

The kinetics of increase of the dynamic moduli during a cooling and annealing
protocol is shown in Figure 7.13a when temperature is lowered to the same final

temperature at the same cooling rate, but for different gelatin concentrations. The shear
and loss moduli both show a large increase during the cooling step. Over this range the
modulus is indeed not far from a c 2 dependence.
In these experiments, as the concentration is a variable, helix concentrations c helix
should be calculated. The helix concentration c helix can be simply calculated from the
helix fraction

χ through the relation

c helix ¼ χ c gelatin : ð 7 : 5 Þ

In Figure 7.13b , G 0 and G 00 are plotted versus c helix for three gelatin concentrations. It
appears that the shear moduli are simply related to c helix : for the same values of c helix ,very
similar values of G 0 are observed, whereas G 00 depends on the gelatin concentration. In