Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 81

3.5

E=170 kJ mol -1

3.0

2.5

2.0

E=290 kJ mol -1

1.5

0.00267 0.00270 0.00273

T -1 /K -1

Fig. 3.16 Plot of ln ʲ versus T g −1 measured for the glass transition in polystyrene at nine heating
rates from 5 to 25 ﾰC min −1 . T g was measured twice at each heating rate and determined as the tem-
perature at midpoint of the glass transition step. The E values of 290 and 170 kJ mol −1 are found
respectively from the three slowest and the three fastest heating rates. (Adapted from Vyazovkin
and Dranca [ 30 ] with permission of ACS)

dielectric and mechanical spectroscopy, for the ʱ -relaxation [ 44 , 46 ]. Of course,
one should not expect precise agreement between the absolute values. This is not
only because different techniques measure different physical properties but also
because the activation energy of the ʱ -relaxation depends on temperature and the
temperature regions employed by different techniques rarely coincide. In particular,
it has been reported [ 50 ] that the E values derived from DSC data obtained on cool-
ing are markedly larger than those derived from the heating data. However, what is
essential is that a variation in E is detected by different techniques, including DSC,
as long as DSC data are analyzed by an isoconversional method.
Although an isoconversional method consistently produces a decreasing E versus
α dependence for the transition from the glass to liquid phase, the absolute values
of E and the degree of its variability with temperature change dramatically between
the glassy substances. Note that an E versus ʱ dependence (e.g., Fig. 3.15 ) can be
converted to an E versus T dependence by replacing the values of ʱ with the mean
value of the temperatures related to this ʱ at different heating rates (see Fig. 3.14 ).
Figure 3.17 presents a set of the E versus T dependencies evaluated by applying an
isoconversional method to the glass transition in a series of substances: poly(vinyl
chloride) (PVC), poly( n -butyl methacrylate) (PBMA), PVP, poly(ethylene 2,6-naph-
thalate) (PEN), PS, poly(ethylene terephthalate) (PET), and boron oxide (B 2 O 3 ) [ 44 ,
46 ]. The differences in the activation energy variability are really staggering. At one
extreme, we have PVC and PET, in which the glass transition occurs in a very nar-
row temperature range and accompanied by a drastic change in the activation energy.
At another extreme we see PBMA and B 2 O 3 whose glass transition stretches over a
wide temperature range with little change in the activation energy.