Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 177

A contribution of etherification increases with temperature and may become domi-
nant at ʱ > 0.8 [ 30 ]. Last but not least, at higher temperatures, DGEBA is capable of
homopolymerization:

(4.21)

This reaction can be catalyzed by tertiary amines, and this type of species is formed
as a product of reaction 4.19.
One of the popular models used to describe the kinetic of epoxy-amine curing
is the model of Sourour and Kamal [ 31 ]. The model assumes that the process is
initiated by uncatalyzed epoxy ring opening, which is promoted by hydrogen-bond
donor molecules. This reaction is characterized by the rate constant k 1 . Once this
reaction takes place, it produces hydroxyl groups that catalyze epoxy ring opening,
i.e., the process becomes autocatalytic. The rate constant for this catalyzed step is
k 2 . According to the Sourour-Kamal model, the process rate is describable by the
following equation:

d
d

α

=+ − ( k α k )( 1 α )( B − α ),

(4.22)

1 2

t

where B is the initial ratio of diamine equivalents to epoxide equivalents. The model
does not make any distinction between the primary and secondary amine reaction
and is only applicable when the process is not complicated by diffusion.
The Sourour-Kamal model can be used to predict the isoconversional activation
energy by substituting the rate from Eq. 4.22 into 4.23:

ER t
T

∂ ln( dd

1

α / ) kE kE

k

+
+

α
α

11 22
1

=− = .

(4.23)

α

−

k

∂

2

α

It follows from Eq. 4.23 that at ʱ ₒ 0, E ʱ ₒ E 1 ; i.e., at the lowest extents of con-
version, E ʱ should yield an estimate for the activation energy of the uncatalyzed
reaction. However, when ʱ ₒ 1, the E ʱ value does not generally approach E 2 , but
the weight average of E 1 and E 2 with k 1 and k 2 being the weights. In other words,
at ʱ ₒ 1, E ʱ would approach E 2 only when the rate constant for the uncatalyzed
reaction is much smaller than the one for the catalyzed reaction, i.e., when k 1 << k 2 .
A similar autocatalytic model has been proposed by Kamal [ 32 ]. The model is
based on the following equation:

d
d

α

(4.24)

m n

=+ − ( k α k )( 1 α ) ,

1 2

t