The sol–gel transition - Physical Gels from Biological and Synthetic Polymers - page 85

0.8

Gel point

0.6

0.4

ω ω ω ω 5

0.2

0

-0.2

ω 1

-0.4

-0.6

0.1 1 10 10 0 1000

t a (h)

Figure 3.10 Winter - Chambon criteria for PVC - Reomol (Ciba Geigy) plasticizer, with ageing time t a as

gelation parameter at a fixed concentration of PVC: loss tangent against ageing time for angular

frequencies ω 1 = 1.26, ω 2 = 3.9, ω 3 = 12.6, ω 4 = 39, ω 5 = 126 rad s − 1 , T = 110°C. Adapted with
permission from te Nijenhuis and Winter ( 1989 ) © 1989 American Chemical Society.

with power-law criteria at n = 0.8, choosing as a parameter the time at a xed concen-

tration of PVC (9.9 wt%) at various temperatures; see Figure 3.10 .
In the case of PVC gelation, therefore, authors working under various experimental
conditions found a region where the Winter Chambon criteria apply. This does not, of

course, mean that these systems are gels, and it would be very interesting to validate these
measurements by proving that the different systems exhibited the same state of connectivity
and degree of crystallinity at the various locations of the measured gelation times.
Another example analogous to gel formation in synthetic polymer solutions is
provided by an isotactic poly(propylene) (iPP) melt. There is no solvent in this case,
and the melt starts to crystallize in supercooled conditions. The time evolution of tan

-

δ

versus the angular frequency is shown in Figure 3.11 . The loss angle shows quite a

different behaviour from the other

ω

gures: tan δ is only frequency-independent in a

narrow frequency range (10 - 2 < <2×10 - 2 rad s − 1 ) marked by a horizontal line. The

degree of crystallinity at the gel point for this sample is very low and the authors could
not measure it. The question of the functionality of the cross-linking junctions is also
raised in this investigation. The gel time for this sample decreases with the degree of
supercooling associated with the higher degree of crystallinity. A low degree of
supercooling allows the largest crystals to form with a low functionality of the crystals
(number of tie chains per crystal) because of a larger extent of chain folding. The
authors observed an apparent gel point with a low degree of crystallinity at low
supercooling, meaning that the crystals would be more ef

ω

cient in making the network
than at high supercooling, but this contradicts current understanding of the crystal
morphology. Here again the connectivity between the crystals was not established at
the point associated with gelation.
A

final example is found with a biopolymer gel, gelatin. Gelation was investigated by
Peyrelasse et al.( 1996 ) by taking temperature as the gelation parameter. The exponent
was found to be n = 0.62 and the gelation temperature 36°C, independent of