Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 105

Then, if in Eq. 3.57, the derivate of ʦ is taken at a constant extent of conversion, it
would yield an isoconversional value of the activation energy:

dln
d

Λ
1 .

(3.59)

ER
T

α =−

−

Substituting Λ from Eq. 3.52 into Eq. 3.59 and taking its respective derivative al-
lows us to derive [ 107 ] a practically important equation:

2 2 2

EU T
TT

KR TTTT
TTT

−−
−

(3.60)

* m m

α =

+ .

g

2 2

( − ) ( )

∞ m

In this equation, the left-hand side represents an experimental temperature depen-
dence of the effective activation energy derived by an isoconversional method. The
right-hand side, however, is a theoretical dependence whose parameters U * and K g
can be determined by fitting this dependence to the experimental one. Therefore,
isoconversional analysis of the overall rate of DSC data can be used to extract the
parameters of the Hoffman-Lauritzen theory that otherwise would have to be evalu-
ated from the microscopy data on linear growth of the spherulites.
Analysis of the right-hand side of Eq. 3.60 suggests that the second term is nega-
tive in the temperature range between ~ 0.618 T m and T m . The absolute value of this
term quickly increases as temperature approaches T m . This means that the effective
activation energy of the melt crystallization should have very large negative values
at small supercoolings as well as at low extents of conversions when the measure-
ments are done on continuous cooling. As temperature of the melt crystallization
decreases further away from T m , the effective activation energy should increase
toward zero. The first term, on the other hand, is always positive. Its value increases
as temperature approaches T ∞ . Therefore, as the temperature of the glass crystal-
lization increases, the effective activation energy should decrease toward zero.
The overall temperature dependence of the effective activation energy is shown in
Fig. 3.36 [ 108 ].

3.6.2 Isoconversional Treatment

The first step in isoconversional analysis of the polymer crystallization data is
identifying an appropriate isoconversional method. The major point of concern is
the treatment of the melt crystallization data, i.e., the data obtained on cooling. It
has been emphasized in Sect. 2.1.2 (Figs. 2.6, 2.10) that the rigid integral methods
should not be used for treating the data obtained on cooling. Adequate isoconver-
sional methods include the flexible integral methods or the differential method of
Friedman.