Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 174

Not only does vitrification occur throughout a range of conversions, but it also
occurs at some finite rate. Therefore, it is possible to picture a situation when vitri-
fication can be delayed or avoided when the polymerization temperature is raised
sufficiently fast. It has been claimed [ 21 ] that such an effect is observed during the
polymerization of p -xylylene. When analyzing DSC polymerization data collected
in a wide range of the heating rates, the authors discovered that the Friedman plots
(Fig. 4.9a ) show a break for the heating rates above 10 K min − 1 . It is especially
distinct at larger values of ʱ .
Separate analysis of the slower and faster heating rates by the differential meth-
od of Friedman [ 3 ] and the integral method of Vyazovkin [ 22 ] resulted in the E ʱ
plots presented in Fig. 4.9b . The initial parts ( ʱ < 0.2) of the dependencies do not
show significant difference for the two ranges of the heating rates. E ʱ ₒ0 for the
slow heating rates is somewhat larger than for the faster ones perhaps indicating
a larger contribution of the initiation step. However, both dependencies merge at
ʱ ~ 0.2 where the E ʱ value becomes practically identical with activation energy
36 kJ mol −1 reported [ 23 ] for polymerization of p -xylylene in hexane and toluene
solutions. Nevertheless, a substantial difference is observed at higher conversions
when polymerization switches from a kinetic to diffusion regime. The E ʱ depen-
dence increases for slow heating rates and decreases for the faster ones. Note that at
all heating rates used polymerization proceeded below the glass transition tempera-
ture of poly( p -xylylene), which is 13 ﾰC [ 19 ]. That is, the reaction system should
normally vitrify under such conditions (see Fig. 4.4 ). To explain the difference
of the diffusion regimes, the authors [ 21 ] suggest that vitrification occurs only at
slower heating rates. At faster heating rates, the sample temperature increases faster
than the glass transition temperature of the reacting mixture so that polymerization
proceeds without vitrification. Ultimately, the difference in the E ʱ dependencies is
explained by the difference in the viscous conditions of the reaction medium.
4.2.3 Background to Cross-Linking
Cross-linking links polymer chains together giving rise to a polymer network.
Cross-linking can be either physical or chemical. Physical cross-linking occurs via
weak bonds (e.g., hydrogen or van der Waals bonds). Examples of such cross-link-
ing are discussed in Sect. 3.10 dealing with physical gels. Chemical cross-linking
involves the formation of strong covalent or ionic bonds. Cross-linked polymers
form two important classes of polymeric materials: elastomers and thermosets. An
elastomer is a cross-linked polymer above its glass transition temperature. A good
example of an elastomer is vulcanized rubber, which is polyisoprene or polybuta-
diene covalently cross-linked with sulfur. A thermoset is a cross-linked polymer
below its glass transition temperature.
In this section, we focus on the cross-linking that leads to the formation of ther-
moset materials because this is one of the most common thermal processes whose
kinetics is routinely measured by DSC. A more technical name used most frequently
for this process is curing. Among a variety of thermoset materials [ 24 , 25 ], the