Chemistry Reference
In-Depth Information
When terminations are diffusion controlled, most termination events involve two highly entangled
chains whose ends move by the “reaction-diffusion” process [
119
]. In this process, terminations occur
because of the propagation-induced diffusion of the chain ends of growing macroradicals. This means
that the rates of terminations depend upon the chain lengths [
113
].
Diffusion theories have been proposed that relate the rate constant of termination to the initial
viscosity of the polymerization medium. The rate-determining step of termination, the segmental
diffusion of the chain ends, is inversely proportional to the microviscosity of the solution [
123
].
Yokota and Itoh [
124
] modified the rate equation to include the viscosity of the medium. According to
that equation, the overall polymerization rate constant should be proportional to the square root of the
initial viscosity of the system.
The number average termination rate constants in a methyl methacrylate polymerization were
measured with an in-line ESR spectrometer. This was done by observing the radical decay rates [
120
].
The results are in disagreement with the concept of termination by propagation-diffusion that is
expected to be dominant at high conversion rates. Instead, the termination rate constants decrease
dramatically in the posteffect period at high conversions. Actually, a fraction of the radicals were
found trapped during the polymerization. Thus, there are two types of radicals in the reaction mixture,
trapped and free radicals. In the propagations and termination reactions, the two types of radical
populations have very different reactivities [
120
].
Shipp and coworkers [
120
] described a method for analyzing the chain length dependence of
termination rate coefficients of the reacting radicals in low conversion free radical polymerizations.
Their method involves comparing experimental molecular weight distributions of polymers formed in
pulsed laser photolysis experiments with those predicted by kinetic simulation. The method is
enabled by direct measurements of the concentration of radicals generated per laser pulse. Knowledge
of the radical concentrations should mean that the only unknowns in the simulations are the
termination rate coefficients. They concluded that the analysis demonstrates the need for chain length
dependent termination rate constants in describing polymerization kinetics.
Free-radical photopolymerizations (see Chap.
10
) of multifunctional acrylic monomers result in
cross-linked polymeric networks. The kinetic picture of such polymerizations varies from ordinary
linear polymerization because the diffusion of free radicals and functional groups becomes severely
restricted. This causes growing polymer chains to rapidly cyclize and cross-link into clusters
(microgels). The clusters become linked up into networks. Many free radicals become trapped, but
terminations take place by combinations and by chain transferring. The cumulative chain length in
such polymerizations can be calculated from the following equation [
125
]:
n ¼
xn
m0
n
rg
where,
w
is the conversion of functional groups and
n
m0
is the initial number of functional groups and
n
rg
is the total number of radicals generated.
3.6 Copolymerization
If more than one monomer species is present in the reaction medium, a copolymer or an interpolymer
can result from the polymerization reaction. Whether the reaction products will consist of copolymers
or just a mixture of homopolymers of both, however, depends largely upon the reactivity of the
monomers. A useful and a simplifying assumption in kinetic analyses of free-radical copolymer-
izations is that the reactivity of polymer radicals is governed entirely by the terminal monomer units
[
52
]. For instance, a growing polymer radical that contains a methyl methacrylate terminal unit, is
