Chemistry Reference
In-Depth Information
radical. This is the probability
P
11
that an M
1
unit follows an M
1
unit in the copoly-
mer, and since the only other reaction assumed important for this radical is (9-3),
M
:
1
½
k
11
½
M
1
r
1
½
M
1
P
11
5
(9-16)
M
2
5
M
:
1
½
M
:
1
½
k
11
½
M
1
1
k
12
½
r
1
½
M
1
1
½
M
2
Similarly, the probability
P
21
that an M
1
unit follows an M
2
unit in the poly-
mer is
M
:
2
½
k
21
½
M
1
½
M
1
P
21
5
(9-17)
M
2
5
M
:
2
½
M
:
2
½
k
21
½
M
1
1
k
22
½
r
2
½
M
2
1
½
M
1
1, then
P
11
and
P
21
defined above are equal. That is to say,
the likelihood that an M
1
unit follows an M
1
unit equals the likelihood that it fol-
lows an M
2
unit in the product. The absolute value of this probability depends on
the relative concentrations of monomers in the feed, but the equivalence of proba-
bilities is independent of the feed and copolymer compositions. A similar equality
for
P
22
and
P
12
can be shown by analogous reasoning, and this equivalence of
probabilities is a necessary condition for a random distribution of monomer resi-
dues in the copolymer.
Random copolymers will be formed, or course, if each radical attacks either
monomer with equal facility (
k
11
5
If, however,
r
1
r
2
5
1). Free-radical copol-
ymerization of ethylene and vinyl acetate is an example of such a system, but this
is not a common case. Random monomer distributions are obtained more gener-
ally if
k
11
/k
12
is approximately equal to
k
21
/k
22
. That is to say,
r
1
.1
/r
2
. This means
that
k
11
/k
22
and
k
21
/k
22
will be simultaneously either greater or less than unity or,
in other words, that both radicals prefer to react with the same monomer.
If
r
1
r
2
5
k
12
,
k
22
5
k
21
,
r
1
5
r
2
5
1, copolymer
Eq. (9-13)
reduces to
d
½
M
1
r
1
½
M
2
5
½
M
1
M
1
r
2
½
(9-18)
M
2
5
d
½
½
M
2
The copolymer and feed compositions in random copolymerizations are identi-
cal only in the rare case when both reactivity ratios equal unity. The copolymer
composition curves in
Fig. 9.1
are typical of copolymerizations that are effec-
tively random (
r
1
r
2
B
1). The curves show no inflection points; they do not cross
the 45
line corresponding to equal feed and copolymer compositions. There is no
appreciable range of monomer feeds over which both monomers enter random
copolymers in significant quantities if
both
reactivity ratios are not near unity,
and the difficulty of making such copolymers becomes more severe as the differ-
ence in absolute values of
r
1
and
r
2
increases.
Some commercially important examples of random free radical copolymeriza-
tions include the styrene
butadiene pair mentioned above, in which
r
1
r
2
5
1.1
and vinyl chloride (
r
1
5
0.9. In
these products a given monomer is randomly linked to monomers of the same or
different type. The relative amount of each monomer in the copolymer depends
1.4)
vinyl acetate (
r
2
5
0.65), for which
r
1
r
2
5
