Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 92

Chen as well as Bershtein et al. proposed that a shift in the annealing peak tem-
perature, T p , with the heating rate, ʲ, can be used to determine the activation energy
of the underlying process as follows:

dln
d

β
1 .

(3.31)

ER T =−

−

p

The E values estimated from the annealing peaks were found [ 81 - 84 ] being several
times smaller than the respective activation energies for the glass transition (i.e., ʱ -
relaxation) event. The ratio of the respective activation energies was consistent with
that reported [ 85 , 86 ] for the ʲ - and ʱ -relaxations in polymers.
The annealing peaks observed below T g result from the same reason as the regu-
lar aging peaks at the end of the glass transition step (Fig. 3.22 ). It is nothing else
but endothermic recovery of the enthalpy lost on aging. The only difference is that
when a glass is aged well below T g (typically around 0.8 T g ), the recovery takes
place before the glass transition step begins. However, as aging temperature is in-
creased, the position of the annealing peak shifts to higher temperature so that it can
appear at the beginning of the glass transition step, or in its middle, or ultimately at
its end as regular aging peak (Fig. 3.27 ).
As long as the recovery occurs below the beginning of the glass transition step,
the molecular mobility in the respective temperature region is likely to be domi-
nated by the local noncooperative process, including the ʲ -relaxation (Fig. 3.12 ). It
thus seems reasonable to expect that a fair estimate of the E ʲ value can be obtained
by analyzing the annealing peak data. We have tested this method of estimating E ʲ
on a variety of polymeric (PS and its nanocomposite [ 30 ], PVP [ 87 ], poly(methyl
methacrylate) (PMMA) [ 35 ], PET [ 35 ]), and small molecule organic (ursodeoxy-
cholic acid [ 87 ], IM [ 41 ], glucose (Gl) [ 35 ], Mt [ 35 ]) glasses. For most of these
glasses, the E ʲ values are known from traditional studies based on dielectric or me-

Fig. 3.27 DSC curves
obtained on heating of
polystyrene at 10 ﾰC min −1
without annealing and
after annealing for 30 min
at different temperatures.
Arrows point at the location
of annealing peaks. (Adapted
from Vyazovkin and Dranca
[ 30 ] with permission of ACS)

not annealed
30 o C
40 o C

50 o C

60 o C 70 o C

20 40 60 80 100 120 140

T / o C