Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 90

Fig. 3.26 Decrease in the
excess heat capacity of malti-
tol at 39 ﾰC. Solid line repre-
sents the KWW fit (Eq. 3.29).
KWW Kohlrausch-Wil-
liams-Watts. (Adapted from
Chen and Vyazovkin [ 70 ]
with permission of Elsevier)

1.50

1.0

1.48

0.8

1.46

0.6

1.44

0.4

1.42

0.2

1.40

0.0

1.38

0246810 12 14 16 18

t / h

temperature with small amplitude temperature perturbations. The effect has been
attributed [ 71 ] to the heat capacity contributions from faster modes of molecular
motion that include the noncooperative ʲ or Johari-Goldstein process and faster
portions of the cooperative ʱ -process. An advantage of the heat capacity relaxation
measurements is that the measurements are conducted continuously and take less
time than the discrete and laborious enthalpy relaxation measurements.
The loss of the excess heat capacity for Mt glass is presented in Fig. 3.26 . The C P
versus t data are converted to the ʱ versus t curves as follows:

CCt
CC

−
−

() ,

P , i P

(3.30)

α=

P , i P , f

where C P, i , C P, f, and C P ( t ) are respectively the initial (nonaged), final (plateau),
and current values of the heat capacity. The resulting ʱ versus t curves obtained at
several aging temperatures can be treated by an isoconversional method in the same
fashion as the enthalpy relaxation curves. The E ʱ versus ʱ dependence evaluated
from the heat capacity relaxation data is quite similar to that determined from the
enthalpy relaxation measurements (Fig. 3.25 ). In both cases, the E ʱ values for the
early stages of aging are about three times smaller than the activation energy for the
glass transition.
Isoconversional analysis of the aging kinetics indicates that the early stages of
the process are dominated by a faster process having smaller activation energy and
the later stages by a slower process of larger activation energy. Because at conver-
sions close to unity, the E ʱ value approaches the activation energy of the glass tran-
sition, it is logical to conclude that the slower process of larger activation energy
is the cooperative ʱ -relaxation. Then the faster process of lower activation energy
is likely to be associated with relaxations of low cooperativity. As discussed earlier
(Fig. 3.12 ), these may include the nonequilibrium mode of ʱ -, ʱ΄ -, and ʲ -relaxations.
They have progressively smaller activation energies, each of which being smaller
than the typical values found for the ʱ -relaxation. Mt is known [ 73 ] to demonstrate
the nonequilibrium ʱ -mode. Although the activation energy has not been reported