Hydrophobically associated networks - Physical Gels from Biological and Synthetic Polymers - page 176

10 5

0.2

2 3

1

10 4

0.1

10 3

0.0

10 2

10 1

-0.1

10 0

-0.2

10 -1

Flow (mW)
G ' (Pa)
G ” (Pa) 10 -2

-0.3

10 -3

10 20 30 40 50 60 70

Temperature (˚C)

Data for micellization of EG56® versus temperature, as determined by microcalorimetry (solid
curve) and by rheological measurements (G ʹ ( □ ) and G ʺ ( ● ) at 1 Hz) for c = 10% w/w. Adapted with
permission from Pham Trong et al.( 2008 ) © 2008 Elsevier.

Figure 6.14

Figure 6.14 is that, in the temperature range where the main enthalpic transition occurs,
when micelles form there is an increase in G 0 accompanying the increase of G 00 .
The frequency dependence of the shear moduli follows a frequency - temperature

superposition master curve. The coef cient a(T) for the frequency horizontal shift factor

shows a very large variation, from 1 to 500, within a narrow temperature range, from 30°
C to 42°C, while the vertical shift b(T) factor which controls the amplitude of the shear
moduli varies only by a factor of 2. The crossing point characterizing the lifetime of the
junctions increases from 0.15 s to nearly 80 s and follows an Arrhenius plot as a function
of temperature between 30°C and 42°C (measurements were not performed between
20°C and 30°C). In contrast with the telechelic HM polymers, the spectrum corresponds
to a superposition of a number of Maxwell elements with different characteristic times.
The frequency dependence of the complex viscosity and the master curve are shown in
Figures 6.15a and 6.15b .
In these heat-set solutions the molecules are branched and, strictly speaking, existing
theories cannot apply. However, in the LRC model ( Chapter 4 ;Leibleret al., 1991 )for
entangled solutions of polymers containing a

fixed number of sticky groups, the
terminal relaxation time T d , or the inverse of the crossing frequency, is related to the
average fraction of stickers engaged in an associated state; see Equation (4.26). The
assumption for the mechanisms of stress relaxation in this model is that chain motion is
controlled by topological constraints, which should not be too different from the
polymers without stickers. For times longer than T d , the structure of the network
changes as the stickers detach from one tie point and reassociate at another point. For
these heat-set networks, as temperature increases the terminal time is signi cantly

lengthened relative to that of the non-aggregated polymer, as the average fraction of
stickers in the associated state increases from 0 to a maximum of 1, because micelle