Chemistry Reference
In-Depth Information
established only if deviations between calculated and observed copolymer compo-
sitions are shown to be systematic as the feed composition or monomer dilution is
varied. Random errors do not necessarily show that
the basic model
is
inapplicable.
The simple copolymer model is a first-order Markov chain in which the prob-
ability of reaction of a given monomer and a macroradical depends only on the
terminal unit in the radical. This involves consideration of four propagation rate
constants in binary copolymerizations,
Eqs. (9-2)
(9-4)
. The mechanism can be
extended by including a penultimate unit effect in the macroradical. This involves
eight rate constants. A third-order case includes antepenultimate units and 16 rate
coefficients. A true test of this model is not provided by fitting experimental and
predicted copolymer compositions, since a match must be obtained sooner or later
if the number of data points is not saturated by the adjustable reactivity ratios. A
much better test is provided by comparing sequence distributions of monomer
units in the copolymers. Such data are unfortunately very sparse at this time, and
the reality of the penultimate unit model has not been proved.
An alternative hypothesis to account for deviations from simple copolymer
behavior invokes reactions in which one or more of the propagation steps is sig-
nificantly reversible under the reaction conditions. For example, if reaction (9-4)
is not important,
k
22
and
r
2
will both be zero and
Eq. (9-13)
will reduce to
d½
M
1
=d½
M
2
5
1
1
r
1
½
M
1
=½
M
2
(9-79)
This is the case, for example, in the copolymerization of carbon monoxide and
ethylene where the CO will not add to itself but does copolymerize with the ole-
fin monomer. General theoretical treatments have been developed for such cases,
taking into account temperature and penultimate effects. Again, the superiority of
these more complicated theories over the simpler copolymer model is not proved
for all systems to which they have been applied.
PROBLEMS
9-1
(a) Calculate the copolymer composition (in mole percent) formed at an
early stage of the reaction of methyl methacrylate (monomer 1) at
5 mol/liter and 5-ethyl-2-vinyl pyridine at 1 mol/liter concentration.
Reactivity ratios are
r
1
5
0.69.
(b) What molar ratio of monomers in the feed produces a copolymer com-
position which is the same as the feed composition?
0.40 and
r
2
5
9-2
Calculate the composition (mole fractions) of the initial terpolymer which
would be formed from the radical polymerization of a feed containing
0.414 mol fraction methacrylonitrile (MAN), 0.424 mol fraction styrene
(S), and 0.162 mol fraction alpha-methylstyrene (AMS). Reactivity ratios
are:
