Chemistry Reference
In-Depth Information
F
2
5
1
F
1
(9-15)
2
Equations (9-13) and (9-14)
are alternative versions of the simple copolymer
equation. Measurements of corresponding feed and copolymer compositions
should yield values of
r
1
and
r
2
which can then be used to predict the relative
concentrations of monomer in copolymers formed from any other mixtures of the
particular monomers. The equations given are differential expressions and define
the composition of the copolymer formed at any instant during the polymeriza-
tion. They may be integrated, as noted in
Section 9.5
, to follow reactions in which
one monomer is consumed more rapidly than the other.
Assumptions are invoked whenever an attempt is made to reduce the complex-
ities of the real world to a mathematically tractable model. Following are some of
the assumptions which are implied in the simple copolymer model:
1.
Radicals M
:
1
are formed by an initiation reaction as well as by propagation
reaction (9-5) and are eliminated by termination reactions and by propagation
step (9-3). [Reaction (9-2) has no effect on
M
:
1
:
] If the kinetic chains are
long, initiation and termination reactions are rare compared to propagation
events and the former may be ignored. If the kinetic chain is long, then so
is the molecular chain length (Section 8.6). The effects of initiation and
termination reactions and of side reactions can probab
ly
be neglected safely
if the copolymer molecular weight is fairly high (say,
M
n
$B
½
000).
2.
The equal reactivity hypothesis in this case assumes that the rates of the
propagation and termination reactions are independent of the size of the
macromolecular radical and depend on its composition only through the
terminal unit bearing the actual site.
3.
Equations (9-13) and (9-14)
are dimensionless; all units cancel on each side of
the equality sign. Thus, the reactivity ratios are indicated to be independent of
dilution and of the concentration units used. The reactivity ratios for a
particular monomer pair should be the same in bulk and in dilute solution
copolymerizations.
4.
The reactivity ratios should likewise be independent of initiator concentration,
reaction rate, and overall extent of monomer conversion, since no rate
constants appear as such in the copolymer composition equation.
5.
Reactivity ratios should be independent of inhibitors, retarders, chain transfer
reagents, or solvents. We see later (
Section 9.12.3
) that solvent independence
is not universal, but the effect is small.
6.
Addition of complexing agents that might change the mechanism of the
reaction or the reactivity of monomers will, of course, alter the reactivity
ratios (
Section 9.12.4
).
7.
When the ratio of unreacted monomer concentrations is [M
1
]/[M
2
], the
increment of copolymer formed has the relative composition
d
[M
1
]/
d
[M
2
].
From
Eq. (9-13)
, the copolymer composition will change continuously as the
reaction proceeds unless
d
[M
1
]/
d
[M
2
]
100
;
[M
1
]/[M
2
]. Thus when emulsion SBR
rubber is made from a mixture of 72 parts butadiene (M
1
) with 28 parts
5
