Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 145

melting than melting of the gel structures formed on annealing at 25 ﾰC. For this
reason, a transition from melting of the lower temperature structures to melting of
the higher temperature structures should occur at conversion less than 0.5. Indeed,
the descending E ʱ dependence breaks down around ʱ = 0.3 and climbs sharply to
E ʱ ≈ 195 kJ mol −1 at ʱ ≈ 0.5. Since that point on the overall melting process be-
comes dominated by melting of the gel structures formed on annealing at 25 ﾰC.
Accordingly, the initial values of E ʱ for the second descending part are similar to
the respective E ʱ values estimated for melting of the gel prepared at 25 ﾰC. It is quite
remarkable that the initial parts of both descending E ʱ dependencies reveal the exis-
tence of two differing energy barriers whose values agree with the values found for
melting of the individual gels produced by annealing at 15 and 25 ﾰC, respectively.
The gel structure becomes increasingly more complex when gels are prepared
under the conditions of nonisothermal cooling. DSC melting data of gels prepared
by continuous cooling at 1 ﾰC min −1 are presented in Fig. 3.72 . By comparison to
isothermally prepared gels, these gels melt over a significantly wider temperature
range. This indicates the existence of a wide distribution of the gel structures hav-
ing differing thermal stabilities. On cooling, gelation initiates at ~ 40 ﾰC, peaks at
~ 23.0 (40 wt. %) or 20.6 ﾰC (20 wt. %), and finishes around 0 ﾰC. Nonisothermal
gelation can be thought of as a large number of short isothermal annealing steps
conducted consecutively in the temperature range from 40 to 0 ﾰC. Such annealing
program should produce a large number of gel structures whose melting tempera-
tures decrease with decreasing the annealing temperature in a manner similar to that
shown in Fig. 3.70 . The mass fractions of the structures should depend on the rate
of cross-linking (Fig. 3.72 ). At the cooling rate 1 ﾰC min −1 , the rate maxima occur
around 20 ﾱ 5 ﾰC so that the structures formed in largest fractions should be expected
to have thermal stability similar to that of the structures formed on isothermal an-
nealing at 15, 20, and 25 ﾰC. However, gelation continues at slower yet significant
rate at temperature below 15 ﾰC. This process should yield the gel structures whose

Fig. 3.72 Formation and
melting of the gels obtained
from 20 and 40 wt. % solu-
tions. Exothermic gelation
is measured on cooling at
1 ﾰC min −1 , endothermic
melting at 5 ﾰC min −1 .
(Reproduced from Dranca
and Vyazovkin [ 178 ] with
permission of Elsevier)

23.0 o C

0.5

20.6 o C

0.0

28.9 o C

-0.5

-1.0

-1.5

-2.0

20%
40%

31.9 o C

-2.5

-10 0 0 0 0 0 0

T / o C