Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 169

Fig. 4.4 The solid line sepa-
rates the liquid and glassy
states (see Fig. 4.2 ). Polym-
erization is performed under
rising temperature conditions.
Dashed lines 1, 2, and 3
represent variation of sample
temperature at successively
faster heating rates. Points A,
B, and C represent conver-
sions and temperatures of
transition between the liquid
and glass phases

/LTXLG

&

%

$

*ODVV

α

some intermediate heating rate (curve 2 in Fig. 4.4 ). Just as in the previous situa-
tion, the system vitrifies at some intermediate extent of reaction (point B). However,
at some point (point C), the rise of the sample temperature outruns the rise of the
glass transition temperature of the monomer-polymer system. At this point, the sys-
tem would devitrify promoting further polymerization. Finally, the third situation
(curve 3 in Fig. 4.4 ) occurs at faster heating rates. That would be the heating rates
at which the sample temperature rises faster than the glass transition temperature of
the monomer-polymer system. Then, the whole polymerization process would take
place in the liquid state without vitrification.
Even if vitrification does not happen, the kinetics of the later stages of polym-
erization is likely to be limited by the process of diffusion. However, vitrification
makes the transition from a kinetic to diffusion regime more evident. At any rate,
the transition between the two regimes can usually be detected as a change in the
effective activation energy of the polymerization process. The change is easy to un-
derstand if we consider a typical bimolecular reaction (e.g., a monomer and radical)
as a sequence of two steps:

k k

D R
+→ ⋅⋅⋅ →

(4.17)

ABAB AB

Before the species A and B can react and form the product AB, they have to ap-
proach each other at sufficiently close distance and assume a proper reaction ori-
entation. This is accomplished through molecular motion, i.e., diffusion. The rate
of this process is determined by the diffusion rate constant k D . Once the species ac-
complish an appropriate reaction situation, a chemical reaction takes place. Its rate
is determined by the reaction rate constant, k R .
At the initial stages of the process (4.17), the viscosity of the reaction medium
is low and molecular mobility is fast. Under this circumstance, k D is likely to be
significantly larger than k R so that the rate of the whole process is determined by the
slowest step which is the chemical reaction. It means that the effective activation