Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 185

Fig. 4.16 The E ʱ dependen-
cies for epoxy-amine cure
under nonisothermal ( circles )
and isothermal ( squares ) con-
ditions. Nonisothermal runs
performed at 1-4 ﾰC min − 1 ,
isothermal at 80-120 ﾰC. The
viscosity data for this reac-
tion are shown in Fig. 4.14 .
(Adapted from Vyazovkin
and Sbirrazzuoli [ 41 ] with
permission of Wiley)

α

increase is a consequence of the trivial decrease of viscosity with temperature,
which can only occur in the early stages of cross-linking (e.g., ʱ < 0.2 in Fig. 4.14 ).
Then following the same line of thought as above (Eqs. 4.30, 4.33, and 4.34), we
can derive the effective activation energy as follows [ 41 ]:

( E Tk Ek

kk

+ ) + Ek Ek

kk

+
+

η D η D

E = ≈ ,

(4.36)

ef

+

D D

Considering that most of cures are typically conducted at moderate temperatures
( T < 200 ﾰC), the RT term in 4.36 is less than 4 kJ mol − 1 and can be neglected rela-
tive to the E η value which is quite large (50-90 [ 51 - 53 ] kJ mol − 1 ) in epoxy systems.
Equation 4.36 suggests that if at lower temperatures the reaction system has high
viscosity so that k D << k, the process of curing would start in a diffusion regime and
its effective activation energy would be close to the activation energy of viscous
flow. However, as temperature rises and viscosity decreases, the process would
change from a diffusion to kinetic regime. Again, all this should be expected to hap-
pen in the initial stages of the nonisothermal cure process before viscosity starts to
increase quickly due to an increase in the molecular weight of the polymer product
(e.g., ʱ > 0.2 in Fig. 4.14 ).
An example of diffusion control in the initial stages of nonisothermal cure in an
epoxy-amine system [ 41 ] is shown in Fig. 4.16 . The phenomenon manifests itself
in the form of a decreasing E ʱ dependence at ʱ < 0.2. For this system, at ʱ < 0.2, vis-
cosity undergoes a significant decrease (Fig. 4.14 ), and the respective value of E η
estimated from the viscosity data is 80 kJ mol − 1 . This value is practically the same
value as E ʱ at the initial cure stages, which is predicted by the model (Eqs. 4.35 and
4.36). Note that no decrease in E ʱ is observed in the same region for an isothermal
cure. This is because the effect is associated exclusively with a decrease in viscosity
but under isothermal conditions the viscosity of a curing system can only increase.