Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 163

4.2 Polymerization and Cross-Linking

See plastic Nature working to this end,
The single atoms each to other tend,
Attract, attracted to, the next in place,
Form'd and impell'd its neighbour to embrace.
Alexander Pope, An Essay on Man

4.2.1 Background to Polymerization

Polymerization is a process of linking of small molecules (monomers) into a long
molecular chain (polymer). In many monomers, polymerization can be initiated
by increasing temperature giving rise to the so-called thermal polymerization. The
process is initiated by bond breaking in a monomer molecule (M) that gives rise to
highly reactive free radical species (M⇅). The latter can then react with the monomer
yielding a macroradical that starts the growth of a polymer chain:

MM MM ⋅+ →⋅

MM ⋅+ →⋅ M MMM

The mechanism can be summarized as follows:

k

p

(4.1)

MMM ⋅+ →⋅

+1 , n n

where k p is the rate constant of propagation.
Polymer chain propagation can be reversible:

k

p

(4.2)

MMM ⋅+ ⇔⋅

+1 , n n

k

dp

with the reverse process being depropagation. To occur spontaneously, the process
of polymerization has to be exothermic, which is unavoidable because of a dra-
matic decrease in the entropy that accompanies polymerization. As for any exo-
thermic process, an increase in temperature shifts equilibrium toward reactants, i.e.,
the monomer (4.2). At a certain temperature, the rate constants of propagation and
depropagation ( k dp ) become equal. At this point, a change in the Gibbs free energy,

k
k

p

∆ G TK RT =− ln =− ln ,

(4.3)

dp

becomes zero so that polymerization would reach equilibrium. This brings about the
concept of ceiling temperature, i.e., the temperature above which a monomer cannot