Chemistry Reference
In-Depth Information
In the absence of side reactions the number average degree of polymerization
will be
d
[M]/
d
[I] if initiation is by nucleophilic attack on the monomer or 2
d
[M]/
d
[I] if initiation is by electron transfer followed by dimerization of the monomeric
radical anions (
d
[M] and
d
[I] are the reacted concentrations of monomer and initi-
ator, respectively). If the rate of initiation is very rapid compared to the propaga-
tion rate and the initiator is mixed very rapidly and efficiently into the reaction
mixture, then all macroions should start growing at almost the same time and
should add monomer at equal rates. The active centers can be terminated deliber-
ately and simultaneously since there are no spontaneous termination reactions
under appropriate experimental conditions. Polymers made in such reactions have
molecular weight distributions which approximate the Poisson distribution. That
is, the number fraction
x
i
of
i
-mers is
e
2
μ
a
i
x
i
5
=
i
(11-13)
!
where
a
equals the number of moles of monomer reacted per mole of initiator.
The ratio of weight to number average chain lengths is
DP
w
=
DP
n
5
1
1
=
DP
n
(11-14)
1
and the molecular weight distribution is narrow if the degree of polymerization
*
100. (Recall also Section 2.5.)
A major interest in narrow distribution polymers is for research and molecular
weight calibrations in gel permeation chromatography. Narrow-molecular-weight
polystyrenes are made by initiation with alkali metal alkyls that are particularly
effective in this application but that only polymerize conjugated monomers like
styrene or butadiene.
The detailed kinetics of homogeneous anionic propagation reactions differ in
hydrocarbon solvents and in media like ethers and amines which can solvate the
metal counterion. These systems are discussed separately below.
Solvating Solvents.
In these media the rate of polymerization is found to be
directly proportional to the monomer concentration as would be expected for a
propagation reaction like
-
-
+
+
(11-15)
Z
MMM
Z
MMM
+
M
The dependence of the propagation rate on initiator concentration is more
complex, however, and can be explained as reflecting the existence of more
than one kind of active center in media that can solvate the counterion. The
simplest situation, which is used here for illustration, corresponds to an equilib-
rium between free ions and ion pairs. [It is likely that various kinds of ion pairs
exist (cf.
Eq. 11-1
) but these ramifications can be neglected in this simple treat-
ment.] The reactions involved in the actual propagation steps in the polymeriza-
tion of a monomer M by an alkyl
lithium compound RLi can then be
represented as
