Chemistry Reference
In-Depth Information
9.13
Rates of Free-Radical Copolymerizations
The simple copolymer model, with two reactivity ratios for a binary comonomer
reaction, explains copolymer composition data for many systems. It appears to be
inadequate, however, for prediction of copolymerization rates. (The details of var-
ious models that have been advanced for this purpose are omitted here, in view of
their limited success.) Copolymerization rates have been rationalized as a function
of feed composition by invoking more complicated models in which the reactivity
of a macroradical is assumed to depend not just on the terminal monomer unit but
on the two last monomers in the radical-ended chain. This is the penultimate
model, which is mentioned in the next section.
At present, the kinetic parameters for prediction of copolymerization rates are
scanty, except for a few low conversion copolymerizations of styrene and some
acrylic comonomers. Engineering models of high conversion copolymerizations
are, however, overdetermined, in the sense that the number of input parameters
(kinetic rate constants, activation energies, enthalpies of polymerization, and so
on) outnumber the output parameters (such as copolymer conversion and compo-
sition). Any number of copolymerization rate models may be found to fit the
experimental data adequately, because the model designer is forced to rely on
some adjustable parameters at some point in the exercise. This does not mean that
such models may not be useful, for training reactor operators, for example, but it
does indicate that any such model will be more reliable for interpolation of data
between than for insights into the mechanism of the copolymerization.
9.14
Alternative Copolymerization Models
A series of judgments, revised without ceasing, goes to make up the incontes-
table progress of science.
—Duclaux
The extensive reactivity ratio data in the literature exhibit a wide scatter for many
monomer pairs. This is partly due to errors in copolymer analysis and computa-
tional methods that result in larger uncertainties in
r
1
and
r
2
than was realized
when the results were reported. Another factor reflects the frequent reliance on an
inadequate number of data points because copolymerization experiments tend to
be tedious and time consuming.
Deviations from the behavior of the simple copolymer model have been noted
for various systems and have prompted the development of alternative models, all
of which use more parameters than the two reactivity ratios in
Eq. (9-13)
. Such
models will often fit particular sets of copolymerization data better than the sim-
ple copolymer model. It appears in retrospect, however, that many of the apparent
deviations from this model may be accounted for by large uncertainties in reactiv-
ity ratio values. The inadequacy of
the simple copolymer
theory can be
