Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 87

3.4.2 Isoconversional Treatment

The recovered enthalpy of aging, Δ H a , can be estimated as the difference in the in-
tegrals of the DSC curves for aged and unaged samples [ 64 ]. The measurements are
performed on the same sample, which is first relaxed for a few minutes at a tempera-
ture well above T g , then cooled quickly at a controlled rate to a temperature well below
T g , and then heated back to the initial temperature at a given heating rate. This would
produce a DSC trace for unaged glass. To obtain the trace for aged glass, the sample
is exposed to the same temperature protocol, except that the cooling segment is inter-
rupted by the aging segment, which maintains temperature T a for a period t a . After that
the cooling segment continues, followed by the heating segment. The difference in the
integrals of the respective DSC traces would yield Δ H a related to a given aging time t a .
Another point on the kinetic curve Δ H a versus t a is produced by maintaining the whole
cooling-heating protocol but changing the length of the aging segment. An example
of Δ H a versus t a is shown in Fig. 3.23 for aging of maltitol (Mt) glass [ 65 ].
The aging temperatures are usually taken within 10 ﾰC below the glass transition
temperatures. It may take months to reach equilibrium at 10 ﾰC below T g and about
a day at 5 ﾰC below T g . Equilibrium is easy to detect when converting the time to
the logarithmic scale (Fig. 3.23 ). On this scale, aging progresses almost linearly
with time. On approaching equilibrium, the line breaks and turns horizontal. For
example, it takes Mt glass about 20 h to reach equilibrium at 6 ﾰC below its T g
(Fig. 3.23 ). The time to equilibrium in seconds, t ∞ , can be estimated by using an
equation proposed by Struik: [ 59 ]

t

∞ ≈

100 exp[ . ( )].

g

077 T − T

(3.26)

a

Fig. 3.23 Progress of
maltitol aging at 40 ﾰC. Solid
circles represent recovered
enthalpy of aging, open
circles conversion. (Partially
adapted from Chen and
Vyazovkin [ 65 ] with permis-
sion of ACS)

t / min

1 10 100 1000

5

1.0

4

0.8

3

0.6

2

0.4

∆ H a

1

α

0.2

0

0.0

0 500 1000 1500

t / min