Chemistry Reference
In-Depth Information
is possible to calculate the distribution of sequences of each monomer in the mac-
romolecule and the drift of copolymer composition with the extent of conversion
of monomers to polymer.
9.2
Simple Copolymer Equation
To predict the course of a copolymerization we need to be able to express the compo-
sition of a copolymer in terms of the concentrations of the monomers in the reaction
mixture and some ready measure of the relative reactivities of these monomers. The
utility of such a model can be tested by comparing experimental and estimated com-
positions of copolymers formed from given monomer concentrations. As a general
rule in science, the preferred model is the simplest one which fits the facts. For
chain-growth copolymerizations, this turns out to be the simple copolymer model,
which was the earliest useful theory in this connection
[1,2]
. All other relations that
have been proposed include more parameters than the simple copolymer model. We
focus here on the simple copolymer theory because the basic concepts of copolymer-
ization are most easily understood in this framework and because it is consistent with
most copolymer composition and sequence distribution data.
In the copolymerization chain-growth reaction, we shall concentrate only on
the propagation step in which a monomer adds to an active site at the end of a
macromolecular species and the active site is transferred to the new terminal unit
created by this addition.
M
1
MM
M
(9-1)
-
Here M denotes a monomer and the asterisk means an active site which could be
a radical, ion (with an appropriate counterion), or a carbon
metal bond. The reactiv-
ity of the active site is assumed to be determined solely by the nature of the terminal
monomer residue that carries this site. Thus, for copolymerizations of monomers A
and B, the two species AABAABA
and BBABAA
would be indistinguishable.
For simplicity, the simple copolymer equation will be developed for the case
of free radical reactions. The four possible propagation reactions with monomers
M
1
and M
2
are
k
11
M
:
1
M
:
1
1
M
:
1
½
M
1
-
rate
k
11
½
M
1
(9-2)
5
k
12
M
:
2
M
:
1
1
M
:
1
½
M
2
-
rate
5
k
12
½
M
2
(9-3)
k
22
M
:
2
M
:
2
1
M
:
2
½
M
2
-
rate
k
22
½
M
2
(9-4)
5
k
21
M
:
1
M
:
2
1
5
k
21
½M
:
2
½
M
1
-
rate
M
1
(9-5)
In these expressions M
i
stands for a radical of any size ending in a unit
derived from monomer M
i
and [M
i
] denotes the total concentration of all such
radicals, regardless of molecular chain length or structure. Similarly
k
ij
is the
propagation rate constant for addition of monomer M
j
to radical M
i
. (Then
k
ii
is
