Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 190

Fig. 4.21 Evolution of the
storage ( G ′) and loss ( G ″)
moduli during curing of
the DGEBA-PDA system
at 2 ﾰC min − 1 . The curve
denoted “DSC” represents
the conversion of curing as
estimated by integration of
the DSC curve measured
at 2 ﾰC min − 1 . (Reproduced
from Sbirrazzuoli et al. [ 60 ]
with permission of Wiley)

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~ 0.53. The value is quite close to the theoretical ʱ gel = 0.577 (Eq. 4.26). At about
145 ﾰC, the storage modulus reaches the so-called glassy plateau. This is the point
when the reacting system is completely vitrified. The respective conversion is ~ 0.9.
Of course, vitrification does not occur instantaneously at this point. It starts at some
conversion past gelation (i.e., ʱ ~ 0.53) and finishes at ʱ ~ 0.9. Note that this is the
region where the E ʱ values drop most quickly (Fig. 4.20 ). Clearly, the decrease in
the effective activation energy of cure correlates with dramatic changes in viscosity
of the reaction system.
It should be stressed that isoconversional calculations of the activation energy is
not the only way to obtain insights into the kinetics and mechanisms of the cross-
linking process. Estimating the preexponential factors by using the techniques dis-
cussed in Sect. 2.2 can also be of value. For example, Alzina et al. [ 61 ] have discov-
ered that the reaction of curing between DGEBA and PDA can be accelerated by
adding organically modified montmorillonite clay. The acceleration manifests itself
as a shift of the reaction to lower temperature when clay is present (Fig. 4.22 ). The
E ʱ dependencies for curing in these two systems are shown in Fig. 4.23 . Surpris-
ingly, the system containing montmorillonite demonstrates larger activation energy
than the system without it. Generally, when the reaction rate accelerates, one should
expect the activation energy to decrease.
Another reason of the reaction rate acceleration can be an increase in the value of
the preexponential factor. The ln A values estimated by using the compensation ef-
fect (Sect. 2.2.2) are displayed in Fig. 4.23 . Indeed, the preexponential factors for the
system containing montmorillonite are greater than for system without it. Therefore,
the acceleration arises from entropic (steric) rather than enthalpic reasons. Conver-
sion of the E ʱ dependencies to the dependencies of E ʱ versus T allowed Alzina et al.
to fit data to Eq. 4.25 and determine the Arrhenius parameters of the uncatalyzed ( A 1
and E 1 ) and catalyzed ( A 2 and E 2 ) reactions. The parameters are shown in Table 4.1 .
The noteworthy result is that the ratio A 1 / A 2 has more than doubled in the presence
of montmorillonite. The likely explanation of the effect is improving the efficiency
of reaction collisions for the curing reaction on the clay surface [ 61 ].