(520b) Dynamic Prediction of Microstructure and Molecular Size in Coordination Terpolymerizations Including Cross-Linking and Branching

Dynamic prediction of microstructure and molecular size in coor

The
production of terpolymers using coordination catalysts is a subject
with a great industrial importance, being the
ethylene-propylene-diene (EPDM) the most representative chemical
system within this class of polymers^[1-4]. For technical
reasons, only a very low content (less than 2 mol %) of diene monomer
(such as ethylidene norbornene (ENB)) can usually be incorporated in
the terpopolymer. Chain branching and cross-linking, leading
eventually to gel formation are important limiting factors to
increase the diene content as desired to obtain products with
improved properties.

The
choice of the cyclic structure of the co-monomer is an important
issue for the control of the properties of the obtained materials.
For this reason, nowadays a significant research effort in this area
is devoted to co- and ter- coordination polymerizations involving
different cycloolefins and cyclodiolefins^[5] (such as
2,5-norbornadiene (NBD) and dicyclopentadiene (DCPD)). Due to
branching and cross-linking reactions, gelation was also
experimentally observed in this kind of chemical systems. Besides,
the production of new functionalized polymers is another important
area for the application of this class of polymerizations. The
incorporation of an aromatic monomer like styrene is expected to be
of great interest to produce versatile materials for many industrial
applications. In this context, the terpolymerization of ethylene with
dicyclopentadiene and styrene has been recently reported^[6].

For
non-linear irreversible polymerizations, the solution of the
population balances of polymer species obtained from the involved
kinetic schemes can be obtained in an automated way starting with the
method of the characteristics^[7-8]. This general kinetic
method can deal with complex polymerization schemes even after
gelation and is free from several simplifying assumptions used in the
description of this class of polymerization systems: moment closures,
absence of multiple active centers (such as poly-radicals),
quasi-steady state for the concentrations of active centers, chain
transfer only to "dead" polymer, cross-linking only of "dead"
chains, the long-chain hypothesis, and so on. Comparisons of the
predictions of the present approach with alternative techniques
(pseudo-kinetic method, Monte Carlo, the classical method of the
moments and numerical fractionation) has shown that the use of these
approximation conditions can have important deleterious effects and
therefore an improved accuracy and reliability in the calculations
can now be obtained ^[8-11].

In
the present work this kinetic method is applied to the analysis of
general coordination terpolymerizations including cross-linking and
branching in their kinetic schemes. Generic chemical systems are
considered (no particular one is selected) and the often found
situation where two monomers with a single double bond (such as
ethylene and styrene) and a diene (such as dicyclopentadiene) are
polymerized is considered. Five different active centers in the
polymer are supposed to exist and two kinds of double bonds (pendant
and terminal) are considered. The kinetic scheme comprises the
following generic steps: catalyst activation, initiations of the
monomers and polymer double bonds, propagations (5 active centers ×
5 kinds of double bonds),
b
-hydride
eliminations (with terminal double bonds formation), transfers to
agent and co-catalyst, poisoning and deactivation and transfers to
monomers (also with terminal double bonds formation). In this
situation, a total number of 72 chemical reactions are considered.
The automation of the simulation method allows analyzing some
particular chemical system as a special case of this general case
study.

It is shown that even
in these complex conditions it is possible to carry out the
prediction of chain length distributions (CLD, mono or
multidimensional) before and after gelation (if it occurs). Recent
developments concerning the prediction of sequence length
distributions (SLD) and mean-square radius of gyration (RG) for
non-linear irreversible polymerizations are also applied to this case
study. This allows a dynamic prediction of the micro-structure and
molecular size of this kind of polymers which can be useful in
practice in order to have a deeper insight on the properties of the
networks formed and to improve the estimation of kinetic parameters
of these polymerization systems.

References

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