Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 173

steady state E ʱ should drop (see Eq. 4.11) to about 60-70 kJ mol − 1 , which is ap-
proximately E ʱ at ʱ = 0.2 in Fig. 4.7 .
As polymerization progresses further, the rate control changes from a kinetic
to diffusion regime as reflected in the E ʱ dependence that begins to climb up to
the larger values of the activation energy past ʱ = 0.2 (Fig. 4.7 ). The increasing
character of the dependence indicates (see Fig. 4.5 ) that the rate is limited by the
mobility of large molecules or long segments of the polymer chains. Note that dif-
fusion control becomes operative long before the reaction system vitrifies. As seen
from Fig. 4.3 , complete vitrification of the reaction system depends on temperature
and occurs roughly at ʱ = 0.7. It is important to realize that the primary cause of a
change from kinetic to diffusion control is an increase in viscosity that may or may
not lead to vitrification.
It should also be kept in mind that, if it occurs, vitrification is smeared over a
wide range of conversions because of the molecular weight distribution of the form-
ing polymer product. This is illustrated in Fig. 4.8 that presents a dependence of the
glass transition temperature on the number average molecular weight of polysty-
rene (PS) [ 11 ]. If styrene is polymerized at 80 ﾰC, the forming PS can be expected
to vitrify when M n exceeds the value, for which T g is 80 ﾰC. The respective M n is
~9000 g mol − 1 . However, when the number average molecular weight of PS is
9000 g mol −1 , there are significant fractions of the polymer that have smaller and
larger M n values. The distribution of the molecular weights is equivalent to the dis-
tribution of the glass transition temperatures (Fig. 4.8 ). It means that vitrification
would start with the fractions of higher molecular weight as soon as their T g rises
above the temperature of polymerization. At the same time, the polymer chains of
lower molecular weight would still possess the liquid-state mobility and continue to
grow until T g of most of polymer fractions reaches the temperature of polymeriza-
tion that would lead to vitrification of the whole reaction mixture.
Fig. 4.8 Curve A is depen-
dence of the glass transition
temperature of the molecu-
lar weight of polystyrene
( T g ≈ 100 °C-1.8 10 5 / M n )
[ 11 ]. T g = 80 ﾰC corresponds
to M n ~ 9000 g mol −1 . Curves
B and C represent respective
distributions in M n and T g