Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 77

Fig. 3.12 Schematic representation of the temperature dependencies of the relaxation time ( a )
and the respective activation energies ( b ). a Curve 1 represents a typical VTF dependence of
the ʱ -relaxation. Straight lines 2-4 represent various processes occurring in the glassy state: 2
nonequilibrium mode of the ʱ -relaxation; 3 ʱ ′ process; 4 ʲ -process. b Sub- T g processes 2-4 have
significantly lower activation energy than the ʱ -process (1). VTF Vogel-Tammann-Fulcher.
(Reproduced from Vyazovkin and Dranca [ 35 ] with permission of Elsevier)

expect the activation energy values to be markedly smaller and decreasing with
decreasing temperature down to the values characteristic of the ʲ -process.
It should be noted that beyond the ʲ -relaxation, there are some processes that
occur below T g and similarly demonstrate the temperature dependencies of the Ar-
rhenius type and the activation energies that are smaller than those for cooperative
ʱ -process occurring above T g [ 34 ]. One of them is the nonequilibrium mode of the
ʱ -relaxation that manifests itself as a break point in the respective VTF dependence
that occurs at T g and gives rise to a smaller slope and, thus, lower activation en-
ergy (Fig. 3.12 ) [ 35 ]. The latter is either somewhat larger [ 36 , 37 ] or comparable
[ 37 ] to that of the ʲ- process. Another is the so-called ʱ ′-relaxation process that is
observed in metallic [ 38 ] as well as polymeric glasses [ 39 ]. It is reported [ 38 ] to be
associated with the “frozen-in relaxation sites” and has small activation energies
(Fig. 3.12 ), which makes it very similar to the regular ʲ -relaxation. However, both
nonequilibrium ʱ -process and ʱ ′-process are detected at higher temperatures than
the regular ʲ -process.

3.3.2 Isoconversional Treatment

In order to apply an isoconversional method to the DSC data on the glass transition,
one needs first to determine the extent of conversion. This can be done in a way
similar to calculating the normalized heat capacity [ 40 ].