Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 134

Gelation and Gel Melting
librium at T gel . At the low temperature side, it ceases on gel freezing at T fr . The
temperature rate dependence is obviously akin to that presented in Figs. 3.32 and
3.36 to illustrate respectively the nucleation rate in accord with the Turnbull-Fisher
model and crystallization rate in accord with the Hoffman-Lauritzen model. The
temperature dependence of the rate is negative above T max and positive below it.
Consecutively, the effective Arrhenius activation energy should be negative when
estimated in the temperature range T max - T gel and positive when evaluated in the
range T fr - T max . An actual example [ 165 ] of the Arrhenius plot for gelation of a gela-
tin solution at several temperatures is presented in Fig. 3.61 . The maximum of the
gelation rate is found in the range 14-19 ﾰC. The activation energy is estimated to
be − 130 kJ mol −1 above T max and 55 kJ mol −1 below it.
All in all, empirical evidence suggests that the kinetics of physical gelation
can be parameterized in terms of some nucleation model. However, there are no
nucleation models designed specifically for the process of physical gelation. In
this situation, one can use the Turnbull-Fisher (Eq. 3.44) and Hoffman-Lauritzen
(Eq. 3.52) models as empirical tools for exploring the kinetics of physical gelation
as demonstrated in a number of publications [ 158 , 164 , 166 - 169 ].

3.10.2 Isoconversional Treatment of Gelation

Aqueous solutions of gelatin provide a well-known example of physical gelation that
takes place on cooling. Gelatin is denatured (i.e., randomly coiled) form of collagen,
whose native state is a triple helix made of three polypeptide chains cross-linked

-1 19

14

9

24

E=+55 kJ/mol

4

27

1

-2

E=-130 kJ/mol

30

-3

0.0033 0.0034 0.0035 .0036 .0037

T -1 / K -1

Fig. 3.61 Arrhenius plot of the initial rate of the heat release for gelation of a gelatin solution mea-
sured at eight different temperatures. The numbers by the points are the temperatures in ﾰC. The
activation energy is negative in the temperature range 24-30 ﾰC and positive in the temperature
range 1-9 ﾰC. (Reproduced from Chen and Vyazovkin [ 165 ] with permission of Wiley)