Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 182

Fig. 4.14 Experimentally
measured temperature depen-
dencies of the extent of cure
and dynamic viscosity for an
epoxy-amine system cured at
the heating rate of 2 ﾰC min − 1 .
Solid line represents the
extent of cure estimated from
DSC data at the same heat-
ing rate. (Reproduced from
Vyazovkin and Sbirrazzuoli
[ 41 ] with permission of
Wiley)

7 R &

molecular weight of individual polymer branches. There also is some local short-
range flow that can be measured in terms of dynamic viscosity [ 11 ], η * . The latter
can be used to follow the molecular mobility of the reaction medium throughout the
whole process of cross-linking.
Figure 4.14 demonstrates a variation of the dynamic viscosity throughout the
process of epoxy-amine curing under nonisothermal conditions [ 41 ]. The initial
stages of the process ( ʱ < 0.2) demonstrate a trivial decrease of the reactant viscos-
ity with increasing temperature. Under isothermal conditions, this stage would be
characterized by a very minor increase in viscosity. At later stages, an increase in
viscosity due to cross-linking outweighs its decrease due to increasing temperature
so that the overall effect is an increase in viscosity. The rising viscosity is reflective
of retardation of the molecular mobility, which is the process that ultimately causes
a change in the rate control from a kinetic to diffusion regime.
Despite the fact that a curing system undergoes a dramatic decrease in mobility
at gelation, it is generally believed [ 24 , 37 ] that this process does not cause a tran-
sition from a kinetic to diffusion regime. It is certainly possible that the dramatic
decrease in translational mobility of the network formed may not affect the local
mobility of the dangling branches and monomer molecules so that they continue to
react without any significant retardation. The commonly accepted view [ 24 , 25 , 37 ]
is that a transition to a diffusion regime is associated with vitrification. Neverthe-
less, one cannot ignore the cases when such a transition has been detected [ 42 - 44 ]
well before vitrification.
To model a transition from a kinetic to diffusion regime, one needs to introduce
a diffusion term into the basic rate equation (1.1). The term can be introduced either
as a multiplicand or as an addend. The following rate equation [ 37 ]:

d α

= kT f () ( ) () αϕη (4.28)

d t