Page 190 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Ionic Chain-Reaction and Complex Coordination Polymerization 153

The DP can also be described when internal dissociation is the dominant termination step as
follows:

+
R p k p [M][M ]
DP = = = k [M]
+
R k [M ]
t t (5.15)
But if chain transfer is the dominant termination step then

+
R p k p [M][M ] k p
DP = = = = k (5.16)
+
R k [M][M ] k
tr tr tr
It is important to note that regardless of how termination occurs the molecular weight is inde-
pendent of the concentration of the initiator. However, the rate of ionic-chain polymerization is
dependent on the dielectric constant of the solvent, the resonance stability of the carbonium ion, the
stability of the gegenion, and the electropositivity of the initiator.
The rates of all single step reactions increase as the temperature increases. This may not be true
for the “net effect” for multistep reactions such as those involved with multistep polymerizations,
here the cationic polymerization. For cationic polymerizations the activation energies are generally
of the order E > E > E . Remembering that the description of the specific rate constant is

tr
i
p
k = A e –Ea/RT (5.17)
the overall or “net” activation energy for chain growth from Equation 5.11 is

E (overall) = E + E – E (5.18)
tr
i
p
and for chain length from Equation 5.16 it is
E (overall) = E – E (5.19)
p
tr
For many cationic polymerizations, the net activation is negative, using the relationships given in
Equation 5.11, so that the overall rate of polymerization decreases, for these cases, as the tempera-
ture is increased. Further, using Equation 5.16 and since E > E , the overall degree of polymeriza-
tr
p
tion does decrease as the temperature is increased. This is pictured in Figure 4.4.
Butyl rubber (IIR) is widely used for inner tubes and as a sealant. It is produced using the cationic
polymerization with the copolymerization of isobutylene in the presence of a small amount (10%) of
isoprene. Thus, the random copolymer chain contains a low concentration of widely spaced isolated
double bonds, from the isoprene, that are later cross-linked when the butyl rubber is cured. A rep-
resentative structure is shown in 5.20, where the number of units derived from isobutylene units
greatly outnumbers the number the units derived from the isoprene monomer. The steric require-
ments of the isobutylene-derived units cause the chains to remain apart giving it a low stress/strain
value and a low T .
g
R

CH 3 H 2 C CH 3
H C + (5.20)
2
CH 3 H C CH 2 R CH 3
3
CH 3

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K10478.indb 153 9/14/2010 3:38:55 PM