Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 99

Assuming that the temperature dependence of Δ G * is determined only by Δ T (see
Eq. 3.39), Eq. 3.42 can be rewritten as:

− E

RT

−
(

A

(3.44)

D

wT w () exp = exp ,

0

2

)

RT ∆ T

where A is constant that includes all the parameters from the right-hand side of
Eq. 3.39 but Δ T . With regard to Eq. 3.43, the effective activation energy is:

2 T

T

1

EE A =−

(

− .

(3.45)

D

3 2

) ( )

∆ ∆ T

The temperature dependence of E that results from Eq. 3.45 is shown in Fig. 3.33 . The
equation suggests that when crystallization occurs on cooling from the melt at small
supercoolings, E should demonstrate large negative values ( E ₒ − ∞, when Δ T ₒ 0).
On the other hand, when crystallization occurs on heating from the glass phase, E
should demonstrate positive value whose magnitude for early stages of crystalliza-
tion should be comparable to the E D value. When one decreases the temperature of
the melt crystallization or increases the temperature of the glass crystallization, the
effective activation energy respectively increases or decreases toward zero.
The above analysis can be extended to predict the dependencies of the isocon-
versional activation energies on conversion. Expressing the rate of the nucleation-
driven crystallization by the basic rate equation

d
d

α

= ()( wT f α ), (3.46)

t

the isoconversional activation energy can be estimated as usual (see Eq. 1.13):

Fig. 3.33 Theoretical depen-
dencies of the activation
energy for the melt and glass
crystallization predicted by
Eq. 3.45

Glass:
E > 0

E D ← E

E=0

Melt:
E < 0

8

T