Chemistry Reference
In-Depth Information
We can consider the formation of the polymer from a rheological point of
view. Suppose we arrange conditions such that the final product is essentially a
solid. Prior to initiation the solution monomers show a low viscosity that is
only a little different from the solvent itself. As the reaction is initiated,
oligomers form and crosslink sites develop. The excluded volume begins to
increase and the viscosity starts to rise. We can think of this as a progressive
increase in the loss modulus with time and the extent of the reaction. As the
chains become longer there is an increased ability to store energy and the
storage modulus also rises. Initially, we would anticipate the loss modulus
would be greater than the storage modulus. However, as the reaction pro-
gresses toward the formation of a solid and completion, the storage modulus
must become greater than the loss modulus. At some intermediate time between
these two states the storage and loss moduli equate and we can define this time
as a gel point. When the reaction is complete, which is some time after the gel
point has been reached, we have complete connectivity and the molecular
weight is effectively infinite. In this case we have a chemical gel. A similar
argument could be applied to a physical gel where connectivity results from
reversible bonding between elements in the network. However, in both cases
because we know that the storage and loss moduli are frequency dependent, the
gelation time would appear to depend upon the frequency selected.
Chambon and Winter
36
investigated this phenomenon experimentally and
theoretically. They studied poly(dimethyl siloxane) (PDMS) networks. They
began with a prepolymer of divinyl terminated PDMS that they reacted with
tetrakis(dimethylsiloxy) silane. This was performed in the presence of a platinum-
based catalyst. This system was based on earlier work of Valles and Macosko.
37
The system had a major advantage in that the catalyst could be ''instantly''
poisoned by minute amounts of sulfur. Thus, the reaction could be terminated
and the rheology measured. However, current rheometric techniques allow the
application of multiple wave forms that can now be used to circumvent this step.
The storage and loss moduli were followed with time and at points either side of
the crossover between the storage and loss moduli, frequency sweeps performed.
Prior to and post gelation the samples showed a progressively increasing storage
and loss modulus. At the gel point a power-law dependence can be used to
describe the behaviour over a wide frequency range (Section 4.8.2).
p
2G
ðÞ
sin mp
=
2
G
0
ðÞ¼
Þ
So
m
ð
5
:
140
Þ
ð
p
2G
ðÞ
cos mp
=
2
G
00
ðÞ¼
Þ
So
m
ð
5
:
141
Þ
ð
The term S represents the strength of the network. The power-law exponent m
was found to depend on the stoichiometric ratio r of crosslinker to sites. When
they were in balance, i.e. r
¼
1, then m
¼
1/2. From eqns (5.140) and (5.141) this is
the only condition where G
0
ð
o
Þ¼
G
00
ð
o
Þ
over all frequencies where the power-
law equation applies. If the stoichiometry was varied, the gel point was frequency
dependent. This was also found to be the case for poly(urethane) networks.
