Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 140

(Fig. 3.65 ). The resulting Δ G * (Table 3.3 ) do not demonstrate any significant de-
pendence on the concentration and are around 10 kJ mol −1 , which is comparable to
the energy of a hydrogen bond [ 139 ]. Note that breaking a hydrogen bond between
water and methoxyl group is likely to be a limiting step in nucleation of methylcel-
lulose microcrystallites that serve as cross-link points in the gel. Overall, empirical
application of the Turnbull-Fisher model suggests that the effect of the concentra-
tion on the kinetics of gelation of aqueous methylcellulose is due to a change in the
conditions of diffusion but not the conditions of nucleation.
To conclude this section, we need to mention an interesting fact that the so-
lutions that normally gel on cooling can be made to gel on heating [ 164 , 176 ].
Anomalous gelation of this kind can be accomplished when the solution is cooled
fast enough to outrun gelation. Then the solution can reach a supercooled state that
can be turned into gel on heating. This situation is similar to cooling the melt fast
enough to bypass crystallization so that it turns into a glass which can then crystal-
lize on heating, i.e. undergo cold crystallization. It has been demonstrated [ 176 ] that
in very diluted (~ 1 wt. %) solutions of gelatin, gelation can be suppressed when the
solutions are cooled at 20 ﾰC min −1 . However, the solutions of regular concentration
that gel much faster require very fast cooling rates to bypass gelation. For example,
suppressing gelation in a 40 wt. % solution of gelatin requires the solution to be
cooled not slower than 500 ﾰC s −1 [ 164 ]. Such fast cooling rates are accomplishable
when using ultrafast DSC [ 177 ] on samples of very small (typically submicrogram)
masses.
Figure 3.67 shows ultrafast DSC data obtained on heating of supercooled gelatin
solution. The application of an isoconversional method to these data results in a

T increases

0.04

120 3000

0.03

2000

100

0.02

0.01

1000

80

0.00

-10-50 5 0 5

60

T / o C

40

20

0.0 0.2 0.4 0.6 0.8 1.0

α

Fig. 3.67 Variation of the activation energy with conversion for gelation of 40 wt. % aqueous solu-
tion of gelatin on heating. The inset shows DSC curves obtained at the heating rates 1000, 2000,
and 3000 ﾰC s −1 . Prior to heating, the solution was cooled at 1000 ﾰC s −1 . (Adapted from Guigo
et al. [ 164 ] with permission of RSC)